Diagrams.Trail:splitAtParam from diagrams-lib-1.3.0.3, D

Percentage Accurate: 66.1% → 99.8%

Time: 8.4s

Alternatives: 16

Speedup: 1.0×

Specification

Math

\[\begin{array}{l} \\ 1 - \frac{\left(1 - x\right) \cdot y}{y + 1} \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (- 1.0 (/ (* (- 1.0 x) y) (+ y 1.0))))

C

double code(double x, double y) {
	return 1.0 - (((1.0 - x) * y) / (y + 1.0));
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = 1.0d0 - (((1.0d0 - x) * y) / (y + 1.0d0))
end function

Java

public static double code(double x, double y) {
	return 1.0 - (((1.0 - x) * y) / (y + 1.0));
}

Python

def code(x, y):
	return 1.0 - (((1.0 - x) * y) / (y + 1.0))

Julia

function code(x, y)
	return Float64(1.0 - Float64(Float64(Float64(1.0 - x) * y) / Float64(y + 1.0)))
end

MATLAB

function tmp = code(x, y)
	tmp = 1.0 - (((1.0 - x) * y) / (y + 1.0));
end

Wolfram

code[x_, y_] := N[(1.0 - N[(N[(N[(1.0 - x), $MachinePrecision] * y), $MachinePrecision] / N[(y + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Initial Program: 66.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ 1 - \frac{\left(1 - x\right) \cdot y}{y + 1} \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (- 1.0 (/ (* (- 1.0 x) y) (+ y 1.0))))

C

double code(double x, double y) {
	return 1.0 - (((1.0 - x) * y) / (y + 1.0));
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = 1.0d0 - (((1.0d0 - x) * y) / (y + 1.0d0))
end function

Java

public static double code(double x, double y) {
	return 1.0 - (((1.0 - x) * y) / (y + 1.0));
}

Python

def code(x, y):
	return 1.0 - (((1.0 - x) * y) / (y + 1.0))

Julia

function code(x, y)
	return Float64(1.0 - Float64(Float64(Float64(1.0 - x) * y) / Float64(y + 1.0)))
end

MATLAB

function tmp = code(x, y)
	tmp = 1.0 - (((1.0 - x) * y) / (y + 1.0));
end

Wolfram

code[x_, y_] := N[(1.0 - N[(N[(N[(1.0 - x), $MachinePrecision] * y), $MachinePrecision] / N[(y + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Alternative 1: 99.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -270000:\\ \;\;\;\;x + \frac{\left(1 - x\right) + \frac{x + -1}{y}}{y}\\ \mathbf{elif}\;y \leq 1100000000:\\ \;\;\;\;1 + \frac{y \cdot \left(1 - x\right)}{-1 - y}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{1}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -270000.0)
   (+ x (/ (+ (- 1.0 x) (/ (+ x -1.0) y)) y))
   (if (<= y 1100000000.0)
     (+ 1.0 (/ (* y (- 1.0 x)) (- -1.0 y)))
     (+ x (/ 1.0 y)))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -270000.0) {
		tmp = x + (((1.0 - x) + ((x + -1.0) / y)) / y);
	} else if (y <= 1100000000.0) {
		tmp = 1.0 + ((y * (1.0 - x)) / (-1.0 - y));
	} else {
		tmp = x + (1.0 / y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (y <= (-270000.0d0)) then
        tmp = x + (((1.0d0 - x) + ((x + (-1.0d0)) / y)) / y)
    else if (y <= 1100000000.0d0) then
        tmp = 1.0d0 + ((y * (1.0d0 - x)) / ((-1.0d0) - y))
    else
        tmp = x + (1.0d0 / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (y <= -270000.0) {
		tmp = x + (((1.0 - x) + ((x + -1.0) / y)) / y);
	} else if (y <= 1100000000.0) {
		tmp = 1.0 + ((y * (1.0 - x)) / (-1.0 - y));
	} else {
		tmp = x + (1.0 / y);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -270000.0:
		tmp = x + (((1.0 - x) + ((x + -1.0) / y)) / y)
	elif y <= 1100000000.0:
		tmp = 1.0 + ((y * (1.0 - x)) / (-1.0 - y))
	else:
		tmp = x + (1.0 / y)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -270000.0)
		tmp = Float64(x + Float64(Float64(Float64(1.0 - x) + Float64(Float64(x + -1.0) / y)) / y));
	elseif (y <= 1100000000.0)
		tmp = Float64(1.0 + Float64(Float64(y * Float64(1.0 - x)) / Float64(-1.0 - y)));
	else
		tmp = Float64(x + Float64(1.0 / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -270000.0)
		tmp = x + (((1.0 - x) + ((x + -1.0) / y)) / y);
	elseif (y <= 1100000000.0)
		tmp = 1.0 + ((y * (1.0 - x)) / (-1.0 - y));
	else
		tmp = x + (1.0 / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -270000.0], N[(x + N[(N[(N[(1.0 - x), $MachinePrecision] + N[(N[(x + -1.0), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1100000000.0], N[(1.0 + N[(N[(y * N[(1.0 - x), $MachinePrecision]), $MachinePrecision] / N[(-1.0 - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(1.0 / y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.7e5

   1. Initial program 21.9%

      \[1 - \frac{\left(1 - x\right) \cdot y}{y + 1} \]
   2. Step-by-step derivation

      1. associate-/l* 47.1%

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

      2. +-commutative 47.1%

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

   3. Simplified 47.1%

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

   5. Taylor expanded in y around -inf 100.0%

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

      1. mul-1-neg 100.0%

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

      2. unsub-neg 100.0%

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

      3. mul-1-neg 100.0%

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

      4. neg-sub0 100.0%

         \[\leadsto x - \frac{-1 \cdot \frac{x - 1}{y} - \color{blue}{\left(0 - \left(x - 1\right)\right)}}{y} \]

      5. associate-+l- 100.0%

         \[\leadsto x - \frac{-1 \cdot \frac{x - 1}{y} - \color{blue}{\left(\left(0 - x\right) + 1\right)}}{y} \]

      6. neg-sub0 100.0%

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

      7. +-commutative 100.0%

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

      8. sub-neg 100.0%

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

      9. unsub-neg 100.0%

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

      10. neg-mul-1 100.0%

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

      11. +-commutative 100.0%

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

   7. Simplified 100.0%

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

   if -2.7e5 < y < 1.1e9

   1. Initial program 100.0%

      \[1 - \frac{\left(1 - x\right) \cdot y}{y + 1} \]
   2. Add Preprocessing

   if 1.1e9 < y

   1. Initial program 32.0%

      \[1 - \frac{\left(1 - x\right) \cdot y}{y + 1} \]
   2. Step-by-step derivation

      1. associate-/l* 48.9%

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

      2. +-commutative 48.9%

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

   3. Simplified 48.9%

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

   5. Taylor expanded in y around -inf 100.0%

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

      1. mul-1-neg 100.0%

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

      2. unsub-neg 100.0%

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

      3. mul-1-neg 100.0%

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

      4. neg-sub0 100.0%

         \[\leadsto x - \frac{-1 \cdot \frac{x - 1}{y} - \color{blue}{\left(0 - \left(x - 1\right)\right)}}{y} \]

      5. associate-+l- 100.0%

         \[\leadsto x - \frac{-1 \cdot \frac{x - 1}{y} - \color{blue}{\left(\left(0 - x\right) + 1\right)}}{y} \]

      6. neg-sub0 100.0%

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

      7. +-commutative 100.0%

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

      8. sub-neg 100.0%

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

      9. unsub-neg 100.0%

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

      10. neg-mul-1 100.0%

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

      11. +-commutative 100.0%

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

   7. Simplified 100.0%

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

   8. Taylor expanded in y around inf 100.0%

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

   9. Taylor expanded in x around 0 100.0%

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

4. Final simplification 100.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -270000:\\ \;\;\;\;x + \frac{\left(1 - x\right) + \frac{x + -1}{y}}{y}\\ \mathbf{elif}\;y \leq 1100000000:\\ \;\;\;\;1 + \frac{y \cdot \left(1 - x\right)}{-1 - y}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{1}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 73.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1.34 \cdot 10^{-92}:\\ \;\;\;\;1 - y\\ \mathbf{elif}\;y \leq 2750000:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;y \leq 1.15 \cdot 10^{+45}:\\ \;\;\;\;\frac{1}{y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -1.0)
   x
   (if (<= y 1.34e-92)
     (- 1.0 y)
     (if (<= y 2750000.0) (* y x) (if (<= y 1.15e+45) (/ 1.0 y) x)))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -1.0) {
		tmp = x;
	} else if (y <= 1.34e-92) {
		tmp = 1.0 - y;
	} else if (y <= 2750000.0) {
		tmp = y * x;
	} else if (y <= 1.15e+45) {
		tmp = 1.0 / y;
	} else {
		tmp = 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 <= (-1.0d0)) then
        tmp = x
    else if (y <= 1.34d-92) then
        tmp = 1.0d0 - y
    else if (y <= 2750000.0d0) then
        tmp = y * x
    else if (y <= 1.15d+45) then
        tmp = 1.0d0 / y
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (y <= -1.0) {
		tmp = x;
	} else if (y <= 1.34e-92) {
		tmp = 1.0 - y;
	} else if (y <= 2750000.0) {
		tmp = y * x;
	} else if (y <= 1.15e+45) {
		tmp = 1.0 / y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -1.0:
		tmp = x
	elif y <= 1.34e-92:
		tmp = 1.0 - y
	elif y <= 2750000.0:
		tmp = y * x
	elif y <= 1.15e+45:
		tmp = 1.0 / y
	else:
		tmp = x
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -1.0)
		tmp = x;
	elseif (y <= 1.34e-92)
		tmp = Float64(1.0 - y);
	elseif (y <= 2750000.0)
		tmp = Float64(y * x);
	elseif (y <= 1.15e+45)
		tmp = Float64(1.0 / y);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -1.0)
		tmp = x;
	elseif (y <= 1.34e-92)
		tmp = 1.0 - y;
	elseif (y <= 2750000.0)
		tmp = y * x;
	elseif (y <= 1.15e+45)
		tmp = 1.0 / y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -1.0], x, If[LessEqual[y, 1.34e-92], N[(1.0 - y), $MachinePrecision], If[LessEqual[y, 2750000.0], N[(y * x), $MachinePrecision], If[LessEqual[y, 1.15e+45], N[(1.0 / y), $MachinePrecision], x]]]]

Derivation

1. Split input into 4 regimes

2. if y < -1 or 1.15000000000000006e45 < y

   1. Initial program 28.4%

      \[1 - \frac{\left(1 - x\right) \cdot y}{y + 1} \]
   2. Step-by-step derivation

      1. associate-/l* 50.3%

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

      2. +-commutative 50.3%

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

   3. Simplified 50.3%

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

   5. Taylor expanded in y around inf 78.6%

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

   if -1 < y < 1.33999999999999995e-92

   1. Initial program 100.0%

      \[1 - \frac{\left(1 - x\right) \cdot y}{y + 1} \]
   2. Step-by-step derivation

      1. associate-/l* 100.0%

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

      2. +-commutative 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in y around 0 99.5%

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

   6. Taylor expanded in x around 0 80.3%

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

   if 1.33999999999999995e-92 < y < 2.75e6

   1. Initial program 99.8%

      \[1 - \frac{\left(1 - x\right) \cdot y}{y + 1} \]
   2. Step-by-step derivation

      1. associate-/l* 99.7%

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

      2. +-commutative 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in y around 0 83.5%

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

   6. Taylor expanded in y around inf 55.6%

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

   7. Taylor expanded in x around inf 56.5%

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

      1. *-commutative 56.5%

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

   9. Simplified 56.5%

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

   if 2.75e6 < y < 1.15000000000000006e45

   1. Initial program 20.3%

      \[1 - \frac{\left(1 - x\right) \cdot y}{y + 1} \]
   2. Step-by-step derivation

      1. associate-/l* 27.5%

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

      2. +-commutative 27.5%

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

   3. Simplified 27.5%

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

   5. Taylor expanded in y around -inf 99.9%

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

      1. mul-1-neg 99.9%

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

      2. unsub-neg 99.9%

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

      3. mul-1-neg 99.9%

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

      4. neg-sub0 99.9%

         \[\leadsto x - \frac{-1 \cdot \frac{x - 1}{y} - \color{blue}{\left(0 - \left(x - 1\right)\right)}}{y} \]

      5. associate-+l- 99.9%

         \[\leadsto x - \frac{-1 \cdot \frac{x - 1}{y} - \color{blue}{\left(\left(0 - x\right) + 1\right)}}{y} \]

      6. neg-sub0 99.9%

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

      7. +-commutative 99.9%

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

      8. sub-neg 99.9%

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

      9. unsub-neg 99.9%

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

      10. neg-mul-1 99.9%

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

      11. +-commutative 99.9%

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

   7. Simplified 99.9%

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

   8. Taylor expanded in y around inf 99.9%

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

   9. Taylor expanded in x around 0 71.7%

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

Alternative 3: 98.8% accurate, 0.5× speedup

Math

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

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= y -1.0) (not (<= y 1.0)))
   (+ x (/ (- 1.0 x) y))
   (+ 1.0 (* (* y (- 1.0 x)) (+ y -1.0)))))

C

double code(double x, double y) {
	double tmp;
	if ((y <= -1.0) || !(y <= 1.0)) {
		tmp = x + ((1.0 - x) / y);
	} else {
		tmp = 1.0 + ((y * (1.0 - x)) * (y + -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 <= (-1.0d0)) .or. (.not. (y <= 1.0d0))) then
        tmp = x + ((1.0d0 - x) / y)
    else
        tmp = 1.0d0 + ((y * (1.0d0 - x)) * (y + (-1.0d0)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((y <= -1.0) || !(y <= 1.0)) {
		tmp = x + ((1.0 - x) / y);
	} else {
		tmp = 1.0 + ((y * (1.0 - x)) * (y + -1.0));
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (y <= -1.0) or not (y <= 1.0):
		tmp = x + ((1.0 - x) / y)
	else:
		tmp = 1.0 + ((y * (1.0 - x)) * (y + -1.0))
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((y <= -1.0) || !(y <= 1.0))
		tmp = Float64(x + Float64(Float64(1.0 - x) / y));
	else
		tmp = Float64(1.0 + Float64(Float64(y * Float64(1.0 - x)) * Float64(y + -1.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((y <= -1.0) || ~((y <= 1.0)))
		tmp = x + ((1.0 - x) / y);
	else
		tmp = 1.0 + ((y * (1.0 - x)) * (y + -1.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[y, -1.0], N[Not[LessEqual[y, 1.0]], $MachinePrecision]], N[(x + N[(N[(1.0 - x), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], N[(1.0 + N[(N[(y * N[(1.0 - x), $MachinePrecision]), $MachinePrecision] * N[(y + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1 or 1 < y

   1. Initial program 28.2%

      \[1 - \frac{\left(1 - x\right) \cdot y}{y + 1} \]
   2. Step-by-step derivation

      1. associate-/l* 48.5%

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

      2. +-commutative 48.5%

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

   3. Simplified 48.5%

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

   5. Taylor expanded in y around inf 99.4%

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

      1. associate--l+ 99.4%

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

      2. div-sub 99.4%

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

   7. Simplified 99.4%

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

   if -1 < y < 1

   1. Initial program 100.0%

      \[1 - \frac{\left(1 - x\right) \cdot y}{y + 1} \]
   2. Step-by-step derivation

      1. associate-/l* 99.9%

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

      2. +-commutative 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in y around 0 98.9%

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

      1. sub-neg 98.9%

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

      2. +-commutative 98.9%

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

      3. associate-+r+ 98.9%

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

      4. sub-neg 98.9%

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

      5. remove-double-neg 98.9%

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

      6. distribute-neg-in 98.9%

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

      7. +-commutative 98.9%

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

      8. sub-neg 98.9%

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

      9. distribute-rgt-neg-in 98.9%

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

      10. *-commutative 98.9%

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

      11. distribute-rgt-neg-out 98.9%

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

      12. +-commutative 98.9%

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

      13. neg-sub0 98.9%

          \[\leadsto 1 - y \cdot \left(\left(1 - x\right) \cdot \left(-y\right) + \left(\color{blue}{\left(0 - x\right)} + 1\right)\right) \]

      14. associate-+l- 98.9%

          \[\leadsto 1 - y \cdot \left(\left(1 - x\right) \cdot \left(-y\right) + \color{blue}{\left(0 - \left(x - 1\right)\right)}\right) \]

      15. neg-sub0 98.9%

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

      16. mul-1-neg 98.9%

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

      17. *-commutative 98.9%

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

      18. neg-mul-1 98.9%

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

      19. associate-*r* 98.9%

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

      20. +-commutative 98.9%

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

      21. associate-*r* 98.9%

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

      22. neg-mul-1 98.9%

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

   7. Simplified 98.9%

      \[\leadsto 1 - \color{blue}{\left(y \cdot \left(1 - x\right)\right) \cdot \left(1 - y\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 99.2%

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

Alternative 4: 99.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -54000000:\\ \;\;\;\;x + \frac{\frac{-1}{y} - -1}{y}\\ \mathbf{elif}\;y \leq 38000000000:\\ \;\;\;\;1 + \frac{y \cdot \left(1 - x\right)}{-1 - y}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{1}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -54000000.0)
   (+ x (/ (- (/ -1.0 y) -1.0) y))
   (if (<= y 38000000000.0)
     (+ 1.0 (/ (* y (- 1.0 x)) (- -1.0 y)))
     (+ x (/ 1.0 y)))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -54000000.0) {
		tmp = x + (((-1.0 / y) - -1.0) / y);
	} else if (y <= 38000000000.0) {
		tmp = 1.0 + ((y * (1.0 - x)) / (-1.0 - y));
	} else {
		tmp = x + (1.0 / y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (y <= (-54000000.0d0)) then
        tmp = x + ((((-1.0d0) / y) - (-1.0d0)) / y)
    else if (y <= 38000000000.0d0) then
        tmp = 1.0d0 + ((y * (1.0d0 - x)) / ((-1.0d0) - y))
    else
        tmp = x + (1.0d0 / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (y <= -54000000.0) {
		tmp = x + (((-1.0 / y) - -1.0) / y);
	} else if (y <= 38000000000.0) {
		tmp = 1.0 + ((y * (1.0 - x)) / (-1.0 - y));
	} else {
		tmp = x + (1.0 / y);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -54000000.0:
		tmp = x + (((-1.0 / y) - -1.0) / y)
	elif y <= 38000000000.0:
		tmp = 1.0 + ((y * (1.0 - x)) / (-1.0 - y))
	else:
		tmp = x + (1.0 / y)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -54000000.0)
		tmp = Float64(x + Float64(Float64(Float64(-1.0 / y) - -1.0) / y));
	elseif (y <= 38000000000.0)
		tmp = Float64(1.0 + Float64(Float64(y * Float64(1.0 - x)) / Float64(-1.0 - y)));
	else
		tmp = Float64(x + Float64(1.0 / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -54000000.0)
		tmp = x + (((-1.0 / y) - -1.0) / y);
	elseif (y <= 38000000000.0)
		tmp = 1.0 + ((y * (1.0 - x)) / (-1.0 - y));
	else
		tmp = x + (1.0 / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -54000000.0], N[(x + N[(N[(N[(-1.0 / y), $MachinePrecision] - -1.0), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 38000000000.0], N[(1.0 + N[(N[(y * N[(1.0 - x), $MachinePrecision]), $MachinePrecision] / N[(-1.0 - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(1.0 / y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -5.4e7

   1. Initial program 18.9%

      \[1 - \frac{\left(1 - x\right) \cdot y}{y + 1} \]
   2. Step-by-step derivation

      1. associate-/l* 45.2%

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

      2. +-commutative 45.2%

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

   3. Simplified 45.2%

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

   5. Taylor expanded in y around -inf 100.0%

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

      1. mul-1-neg 100.0%

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

      2. unsub-neg 100.0%

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

      3. mul-1-neg 100.0%

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

      4. neg-sub0 100.0%

         \[\leadsto x - \frac{-1 \cdot \frac{x - 1}{y} - \color{blue}{\left(0 - \left(x - 1\right)\right)}}{y} \]

      5. associate-+l- 100.0%

         \[\leadsto x - \frac{-1 \cdot \frac{x - 1}{y} - \color{blue}{\left(\left(0 - x\right) + 1\right)}}{y} \]

      6. neg-sub0 100.0%

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

      7. +-commutative 100.0%

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

      8. sub-neg 100.0%

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

      9. unsub-neg 100.0%

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

      10. neg-mul-1 100.0%

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

      11. +-commutative 100.0%

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

   7. Simplified 100.0%

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

   8. Taylor expanded in x around 0 100.0%

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

   if -5.4e7 < y < 3.8e10

   1. Initial program 100.0%

      \[1 - \frac{\left(1 - x\right) \cdot y}{y + 1} \]
   2. Add Preprocessing

   if 3.8e10 < y

   1. Initial program 32.0%

      \[1 - \frac{\left(1 - x\right) \cdot y}{y + 1} \]
   2. Step-by-step derivation

      1. associate-/l* 48.9%

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

      2. +-commutative 48.9%

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

   3. Simplified 48.9%

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

   5. Taylor expanded in y around -inf 100.0%

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

      1. mul-1-neg 100.0%

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

      2. unsub-neg 100.0%

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

      3. mul-1-neg 100.0%

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

      4. neg-sub0 100.0%

         \[\leadsto x - \frac{-1 \cdot \frac{x - 1}{y} - \color{blue}{\left(0 - \left(x - 1\right)\right)}}{y} \]

      5. associate-+l- 100.0%

         \[\leadsto x - \frac{-1 \cdot \frac{x - 1}{y} - \color{blue}{\left(\left(0 - x\right) + 1\right)}}{y} \]

      6. neg-sub0 100.0%

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

      7. +-commutative 100.0%

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

      8. sub-neg 100.0%

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

      9. unsub-neg 100.0%

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

      10. neg-mul-1 100.0%

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

      11. +-commutative 100.0%

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

   7. Simplified 100.0%

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

   8. Taylor expanded in y around inf 100.0%

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

   9. Taylor expanded in x around 0 100.0%

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

4. Final simplification 100.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -54000000:\\ \;\;\;\;x + \frac{\frac{-1}{y} - -1}{y}\\ \mathbf{elif}\;y \leq 38000000000:\\ \;\;\;\;1 + \frac{y \cdot \left(1 - x\right)}{-1 - y}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{1}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 99.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -80000000:\\ \;\;\;\;x + \frac{\frac{-1}{y} - -1}{y}\\ \mathbf{elif}\;y \leq 52000000000:\\ \;\;\;\;1 + \left(1 - x\right) \cdot \frac{y}{-1 - y}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{1}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -80000000.0)
   (+ x (/ (- (/ -1.0 y) -1.0) y))
   (if (<= y 52000000000.0)
     (+ 1.0 (* (- 1.0 x) (/ y (- -1.0 y))))
     (+ x (/ 1.0 y)))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -80000000.0) {
		tmp = x + (((-1.0 / y) - -1.0) / y);
	} else if (y <= 52000000000.0) {
		tmp = 1.0 + ((1.0 - x) * (y / (-1.0 - y)));
	} else {
		tmp = x + (1.0 / y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (y <= (-80000000.0d0)) then
        tmp = x + ((((-1.0d0) / y) - (-1.0d0)) / y)
    else if (y <= 52000000000.0d0) then
        tmp = 1.0d0 + ((1.0d0 - x) * (y / ((-1.0d0) - y)))
    else
        tmp = x + (1.0d0 / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (y <= -80000000.0) {
		tmp = x + (((-1.0 / y) - -1.0) / y);
	} else if (y <= 52000000000.0) {
		tmp = 1.0 + ((1.0 - x) * (y / (-1.0 - y)));
	} else {
		tmp = x + (1.0 / y);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -80000000.0:
		tmp = x + (((-1.0 / y) - -1.0) / y)
	elif y <= 52000000000.0:
		tmp = 1.0 + ((1.0 - x) * (y / (-1.0 - y)))
	else:
		tmp = x + (1.0 / y)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -80000000.0)
		tmp = Float64(x + Float64(Float64(Float64(-1.0 / y) - -1.0) / y));
	elseif (y <= 52000000000.0)
		tmp = Float64(1.0 + Float64(Float64(1.0 - x) * Float64(y / Float64(-1.0 - y))));
	else
		tmp = Float64(x + Float64(1.0 / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -80000000.0)
		tmp = x + (((-1.0 / y) - -1.0) / y);
	elseif (y <= 52000000000.0)
		tmp = 1.0 + ((1.0 - x) * (y / (-1.0 - y)));
	else
		tmp = x + (1.0 / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -80000000.0], N[(x + N[(N[(N[(-1.0 / y), $MachinePrecision] - -1.0), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 52000000000.0], N[(1.0 + N[(N[(1.0 - x), $MachinePrecision] * N[(y / N[(-1.0 - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(1.0 / y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -8e7

   1. Initial program 18.9%

      \[1 - \frac{\left(1 - x\right) \cdot y}{y + 1} \]
   2. Step-by-step derivation

      1. associate-/l* 45.2%

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

      2. +-commutative 45.2%

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

   3. Simplified 45.2%

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

   5. Taylor expanded in y around -inf 100.0%

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

      1. mul-1-neg 100.0%

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

      2. unsub-neg 100.0%

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

      3. mul-1-neg 100.0%

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

      4. neg-sub0 100.0%

         \[\leadsto x - \frac{-1 \cdot \frac{x - 1}{y} - \color{blue}{\left(0 - \left(x - 1\right)\right)}}{y} \]

      5. associate-+l- 100.0%

         \[\leadsto x - \frac{-1 \cdot \frac{x - 1}{y} - \color{blue}{\left(\left(0 - x\right) + 1\right)}}{y} \]

      6. neg-sub0 100.0%

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

      7. +-commutative 100.0%

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

      8. sub-neg 100.0%

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

      9. unsub-neg 100.0%

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

      10. neg-mul-1 100.0%

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

      11. +-commutative 100.0%

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

   7. Simplified 100.0%

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

   8. Taylor expanded in x around 0 100.0%

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

   if -8e7 < y < 5.2e10

   1. Initial program 100.0%

      \[1 - \frac{\left(1 - x\right) \cdot y}{y + 1} \]
   2. Step-by-step derivation

      1. associate-/l* 99.9%

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

      2. +-commutative 99.9%

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

   3. Simplified 99.9%

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

   if 5.2e10 < y

   1. Initial program 32.0%

      \[1 - \frac{\left(1 - x\right) \cdot y}{y + 1} \]
   2. Step-by-step derivation

      1. associate-/l* 48.9%

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

      2. +-commutative 48.9%

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

   3. Simplified 48.9%

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

   5. Taylor expanded in y around -inf 100.0%

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

      1. mul-1-neg 100.0%

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

      2. unsub-neg 100.0%

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

      3. mul-1-neg 100.0%

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

      4. neg-sub0 100.0%

         \[\leadsto x - \frac{-1 \cdot \frac{x - 1}{y} - \color{blue}{\left(0 - \left(x - 1\right)\right)}}{y} \]

      5. associate-+l- 100.0%

         \[\leadsto x - \frac{-1 \cdot \frac{x - 1}{y} - \color{blue}{\left(\left(0 - x\right) + 1\right)}}{y} \]

      6. neg-sub0 100.0%

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

      7. +-commutative 100.0%

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

      8. sub-neg 100.0%

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

      9. unsub-neg 100.0%

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

      10. neg-mul-1 100.0%

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

      11. +-commutative 100.0%

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

   7. Simplified 100.0%

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

   8. Taylor expanded in y around inf 100.0%

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

   9. Taylor expanded in x around 0 100.0%

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

4. Final simplification 100.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -80000000:\\ \;\;\;\;x + \frac{\frac{-1}{y} - -1}{y}\\ \mathbf{elif}\;y \leq 52000000000:\\ \;\;\;\;1 + \left(1 - x\right) \cdot \frac{y}{-1 - y}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{1}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 98.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -11000000:\\ \;\;\;\;x + \frac{\frac{-1}{y} - -1}{y}\\ \mathbf{elif}\;y \leq 11800000:\\ \;\;\;\;1 + \frac{y \cdot x}{y + 1}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{1}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -11000000.0)
   (+ x (/ (- (/ -1.0 y) -1.0) y))
   (if (<= y 11800000.0) (+ 1.0 (/ (* y x) (+ y 1.0))) (+ x (/ 1.0 y)))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -11000000.0) {
		tmp = x + (((-1.0 / y) - -1.0) / y);
	} else if (y <= 11800000.0) {
		tmp = 1.0 + ((y * x) / (y + 1.0));
	} else {
		tmp = x + (1.0 / y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (y <= (-11000000.0d0)) then
        tmp = x + ((((-1.0d0) / y) - (-1.0d0)) / y)
    else if (y <= 11800000.0d0) then
        tmp = 1.0d0 + ((y * x) / (y + 1.0d0))
    else
        tmp = x + (1.0d0 / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (y <= -11000000.0) {
		tmp = x + (((-1.0 / y) - -1.0) / y);
	} else if (y <= 11800000.0) {
		tmp = 1.0 + ((y * x) / (y + 1.0));
	} else {
		tmp = x + (1.0 / y);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -11000000.0:
		tmp = x + (((-1.0 / y) - -1.0) / y)
	elif y <= 11800000.0:
		tmp = 1.0 + ((y * x) / (y + 1.0))
	else:
		tmp = x + (1.0 / y)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -11000000.0)
		tmp = Float64(x + Float64(Float64(Float64(-1.0 / y) - -1.0) / y));
	elseif (y <= 11800000.0)
		tmp = Float64(1.0 + Float64(Float64(y * x) / Float64(y + 1.0)));
	else
		tmp = Float64(x + Float64(1.0 / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -11000000.0)
		tmp = x + (((-1.0 / y) - -1.0) / y);
	elseif (y <= 11800000.0)
		tmp = 1.0 + ((y * x) / (y + 1.0));
	else
		tmp = x + (1.0 / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -11000000.0], N[(x + N[(N[(N[(-1.0 / y), $MachinePrecision] - -1.0), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 11800000.0], N[(1.0 + N[(N[(y * x), $MachinePrecision] / N[(y + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(1.0 / y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.1e7

   1. Initial program 20.4%

      \[1 - \frac{\left(1 - x\right) \cdot y}{y + 1} \]
   2. Step-by-step derivation

      1. associate-/l* 46.2%

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

      2. +-commutative 46.2%

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

   3. Simplified 46.2%

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

   5. Taylor expanded in y around -inf 100.0%

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

      1. mul-1-neg 100.0%

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

      2. unsub-neg 100.0%

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

      3. mul-1-neg 100.0%

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

      4. neg-sub0 100.0%

         \[\leadsto x - \frac{-1 \cdot \frac{x - 1}{y} - \color{blue}{\left(0 - \left(x - 1\right)\right)}}{y} \]

      5. associate-+l- 100.0%

         \[\leadsto x - \frac{-1 \cdot \frac{x - 1}{y} - \color{blue}{\left(\left(0 - x\right) + 1\right)}}{y} \]

      6. neg-sub0 100.0%

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

      7. +-commutative 100.0%

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

      8. sub-neg 100.0%

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

      9. unsub-neg 100.0%

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

      10. neg-mul-1 100.0%

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

      11. +-commutative 100.0%

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

   7. Simplified 100.0%

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

   8. Taylor expanded in x around 0 99.2%

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

   if -1.1e7 < y < 1.18e7

   1. Initial program 100.0%

      \[1 - \frac{\left(1 - x\right) \cdot y}{y + 1} \]
   2. Step-by-step derivation

      1. associate-/l* 99.9%

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

      2. +-commutative 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in x around inf 97.9%

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

      1. mul-1-neg 97.9%

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

      2. distribute-neg-frac2 97.9%

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

      3. *-commutative 97.9%

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

      4. distribute-neg-in 97.9%

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

      5. metadata-eval 97.9%

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

      6. sub-neg 97.9%

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

   7. Simplified 97.9%

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

   if 1.18e7 < y

   1. Initial program 32.0%

      \[1 - \frac{\left(1 - x\right) \cdot y}{y + 1} \]
   2. Step-by-step derivation

      1. associate-/l* 48.9%

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

      2. +-commutative 48.9%

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

   3. Simplified 48.9%

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

   5. Taylor expanded in y around -inf 100.0%

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

      1. mul-1-neg 100.0%

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

      2. unsub-neg 100.0%

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

      3. mul-1-neg 100.0%

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

      4. neg-sub0 100.0%

         \[\leadsto x - \frac{-1 \cdot \frac{x - 1}{y} - \color{blue}{\left(0 - \left(x - 1\right)\right)}}{y} \]

      5. associate-+l- 100.0%

         \[\leadsto x - \frac{-1 \cdot \frac{x - 1}{y} - \color{blue}{\left(\left(0 - x\right) + 1\right)}}{y} \]

      6. neg-sub0 100.0%

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

      7. +-commutative 100.0%

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

      8. sub-neg 100.0%

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

      9. unsub-neg 100.0%

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

      10. neg-mul-1 100.0%

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

      11. +-commutative 100.0%

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

   7. Simplified 100.0%

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

   8. Taylor expanded in y around inf 100.0%

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

   9. Taylor expanded in x around 0 100.0%

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

4. Final simplification 98.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -11000000:\\ \;\;\;\;x + \frac{\frac{-1}{y} - -1}{y}\\ \mathbf{elif}\;y \leq 11800000:\\ \;\;\;\;1 + \frac{y \cdot x}{y + 1}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{1}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 98.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -11000000:\\ \;\;\;\;x + \frac{1 - x}{y}\\ \mathbf{elif}\;y \leq 11800000:\\ \;\;\;\;1 + \frac{y \cdot x}{y + 1}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{1}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -11000000.0)
   (+ x (/ (- 1.0 x) y))
   (if (<= y 11800000.0) (+ 1.0 (/ (* y x) (+ y 1.0))) (+ x (/ 1.0 y)))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -11000000.0) {
		tmp = x + ((1.0 - x) / y);
	} else if (y <= 11800000.0) {
		tmp = 1.0 + ((y * x) / (y + 1.0));
	} else {
		tmp = x + (1.0 / y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (y <= (-11000000.0d0)) then
        tmp = x + ((1.0d0 - x) / y)
    else if (y <= 11800000.0d0) then
        tmp = 1.0d0 + ((y * x) / (y + 1.0d0))
    else
        tmp = x + (1.0d0 / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (y <= -11000000.0) {
		tmp = x + ((1.0 - x) / y);
	} else if (y <= 11800000.0) {
		tmp = 1.0 + ((y * x) / (y + 1.0));
	} else {
		tmp = x + (1.0 / y);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -11000000.0:
		tmp = x + ((1.0 - x) / y)
	elif y <= 11800000.0:
		tmp = 1.0 + ((y * x) / (y + 1.0))
	else:
		tmp = x + (1.0 / y)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -11000000.0)
		tmp = Float64(x + Float64(Float64(1.0 - x) / y));
	elseif (y <= 11800000.0)
		tmp = Float64(1.0 + Float64(Float64(y * x) / Float64(y + 1.0)));
	else
		tmp = Float64(x + Float64(1.0 / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -11000000.0)
		tmp = x + ((1.0 - x) / y);
	elseif (y <= 11800000.0)
		tmp = 1.0 + ((y * x) / (y + 1.0));
	else
		tmp = x + (1.0 / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -11000000.0], N[(x + N[(N[(1.0 - x), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 11800000.0], N[(1.0 + N[(N[(y * x), $MachinePrecision] / N[(y + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(1.0 / y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.1e7

   1. Initial program 20.4%

      \[1 - \frac{\left(1 - x\right) \cdot y}{y + 1} \]
   2. Step-by-step derivation

      1. associate-/l* 46.2%

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

      2. +-commutative 46.2%

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

   3. Simplified 46.2%

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

   5. Taylor expanded in y around inf 99.2%

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

      1. associate--l+ 99.2%

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

      2. div-sub 99.2%

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

   7. Simplified 99.2%

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

   if -1.1e7 < y < 1.18e7

   1. Initial program 100.0%

      \[1 - \frac{\left(1 - x\right) \cdot y}{y + 1} \]
   2. Step-by-step derivation

      1. associate-/l* 99.9%

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

      2. +-commutative 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in x around inf 97.9%

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

      1. mul-1-neg 97.9%

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

      2. distribute-neg-frac2 97.9%

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

      3. *-commutative 97.9%

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

      4. distribute-neg-in 97.9%

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

      5. metadata-eval 97.9%

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

      6. sub-neg 97.9%

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

   7. Simplified 97.9%

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

   if 1.18e7 < y

   1. Initial program 32.0%

      \[1 - \frac{\left(1 - x\right) \cdot y}{y + 1} \]
   2. Step-by-step derivation

      1. associate-/l* 48.9%

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

      2. +-commutative 48.9%

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

   3. Simplified 48.9%

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

   5. Taylor expanded in y around -inf 100.0%

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

      1. mul-1-neg 100.0%

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

      2. unsub-neg 100.0%

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

      3. mul-1-neg 100.0%

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

      4. neg-sub0 100.0%

         \[\leadsto x - \frac{-1 \cdot \frac{x - 1}{y} - \color{blue}{\left(0 - \left(x - 1\right)\right)}}{y} \]

      5. associate-+l- 100.0%

         \[\leadsto x - \frac{-1 \cdot \frac{x - 1}{y} - \color{blue}{\left(\left(0 - x\right) + 1\right)}}{y} \]

      6. neg-sub0 100.0%

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

      7. +-commutative 100.0%

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

      8. sub-neg 100.0%

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

      9. unsub-neg 100.0%

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

      10. neg-mul-1 100.0%

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

      11. +-commutative 100.0%

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

   7. Simplified 100.0%

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

   8. Taylor expanded in y around inf 100.0%

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

   9. Taylor expanded in x around 0 100.0%

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

4. Final simplification 98.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -11000000:\\ \;\;\;\;x + \frac{1 - x}{y}\\ \mathbf{elif}\;y \leq 11800000:\\ \;\;\;\;1 + \frac{y \cdot x}{y + 1}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{1}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 85.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 2750000:\\ \;\;\;\;1 + y \cdot x\\ \mathbf{elif}\;y \leq 1.5 \cdot 10^{+43}:\\ \;\;\;\;\frac{1}{y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -1.0)
   x
   (if (<= y 2750000.0) (+ 1.0 (* y x)) (if (<= y 1.5e+43) (/ 1.0 y) x))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -1.0) {
		tmp = x;
	} else if (y <= 2750000.0) {
		tmp = 1.0 + (y * x);
	} else if (y <= 1.5e+43) {
		tmp = 1.0 / y;
	} else {
		tmp = 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 <= (-1.0d0)) then
        tmp = x
    else if (y <= 2750000.0d0) then
        tmp = 1.0d0 + (y * x)
    else if (y <= 1.5d+43) then
        tmp = 1.0d0 / y
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (y <= -1.0) {
		tmp = x;
	} else if (y <= 2750000.0) {
		tmp = 1.0 + (y * x);
	} else if (y <= 1.5e+43) {
		tmp = 1.0 / y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -1.0:
		tmp = x
	elif y <= 2750000.0:
		tmp = 1.0 + (y * x)
	elif y <= 1.5e+43:
		tmp = 1.0 / y
	else:
		tmp = x
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -1.0)
		tmp = x;
	elseif (y <= 2750000.0)
		tmp = Float64(1.0 + Float64(y * x));
	elseif (y <= 1.5e+43)
		tmp = Float64(1.0 / y);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -1.0)
		tmp = x;
	elseif (y <= 2750000.0)
		tmp = 1.0 + (y * x);
	elseif (y <= 1.5e+43)
		tmp = 1.0 / y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -1.0], x, If[LessEqual[y, 2750000.0], N[(1.0 + N[(y * x), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.5e+43], N[(1.0 / y), $MachinePrecision], x]]]

Derivation

1. Split input into 3 regimes

2. if y < -1 or 1.50000000000000008e43 < y

   1. Initial program 28.4%

      \[1 - \frac{\left(1 - x\right) \cdot y}{y + 1} \]
   2. Step-by-step derivation

      1. associate-/l* 50.3%

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

      2. +-commutative 50.3%

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

   3. Simplified 50.3%

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

   5. Taylor expanded in y around inf 78.6%

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

   if -1 < y < 2.75e6

   1. Initial program 100.0%

      \[1 - \frac{\left(1 - x\right) \cdot y}{y + 1} \]
   2. Step-by-step derivation

      1. associate-/l* 99.9%

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

      2. +-commutative 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in x around inf 97.9%

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

      1. mul-1-neg 97.9%

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

      2. distribute-neg-frac2 97.9%

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

      3. *-commutative 97.9%

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

      4. distribute-neg-in 97.9%

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

      5. metadata-eval 97.9%

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

      6. sub-neg 97.9%

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

   7. Simplified 97.9%

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

   8. Taylor expanded in y around 0 95.7%

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

   if 2.75e6 < y < 1.50000000000000008e43

   1. Initial program 20.3%

      \[1 - \frac{\left(1 - x\right) \cdot y}{y + 1} \]
   2. Step-by-step derivation

      1. associate-/l* 27.5%

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

      2. +-commutative 27.5%

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

   3. Simplified 27.5%

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

   5. Taylor expanded in y around -inf 99.9%

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

      1. mul-1-neg 99.9%

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

      2. unsub-neg 99.9%

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

      3. mul-1-neg 99.9%

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

      4. neg-sub0 99.9%

         \[\leadsto x - \frac{-1 \cdot \frac{x - 1}{y} - \color{blue}{\left(0 - \left(x - 1\right)\right)}}{y} \]

      5. associate-+l- 99.9%

         \[\leadsto x - \frac{-1 \cdot \frac{x - 1}{y} - \color{blue}{\left(\left(0 - x\right) + 1\right)}}{y} \]

      6. neg-sub0 99.9%

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

      7. +-commutative 99.9%

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

      8. sub-neg 99.9%

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

      9. unsub-neg 99.9%

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

      10. neg-mul-1 99.9%

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

      11. +-commutative 99.9%

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

   7. Simplified 99.9%

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

   8. Taylor expanded in y around inf 99.9%

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

   9. Taylor expanded in x around 0 71.7%

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

4. Final simplification 86.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 2750000:\\ \;\;\;\;1 + y \cdot x\\ \mathbf{elif}\;y \leq 1.5 \cdot 10^{+43}:\\ \;\;\;\;\frac{1}{y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 73.8% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 2.15 \cdot 10^{-84}:\\ \;\;\;\;1 - y\\ \mathbf{elif}\;y \leq 1:\\ \;\;\;\;y \cdot x\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -1.0) x (if (<= y 2.15e-84) (- 1.0 y) (if (<= y 1.0) (* y x) x))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -1.0) {
		tmp = x;
	} else if (y <= 2.15e-84) {
		tmp = 1.0 - y;
	} else if (y <= 1.0) {
		tmp = y * x;
	} else {
		tmp = 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 <= (-1.0d0)) then
        tmp = x
    else if (y <= 2.15d-84) then
        tmp = 1.0d0 - y
    else if (y <= 1.0d0) then
        tmp = y * x
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (y <= -1.0) {
		tmp = x;
	} else if (y <= 2.15e-84) {
		tmp = 1.0 - y;
	} else if (y <= 1.0) {
		tmp = y * x;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -1.0:
		tmp = x
	elif y <= 2.15e-84:
		tmp = 1.0 - y
	elif y <= 1.0:
		tmp = y * x
	else:
		tmp = x
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -1.0)
		tmp = x;
	elseif (y <= 2.15e-84)
		tmp = Float64(1.0 - y);
	elseif (y <= 1.0)
		tmp = Float64(y * x);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -1.0)
		tmp = x;
	elseif (y <= 2.15e-84)
		tmp = 1.0 - y;
	elseif (y <= 1.0)
		tmp = y * x;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -1.0], x, If[LessEqual[y, 2.15e-84], N[(1.0 - y), $MachinePrecision], If[LessEqual[y, 1.0], N[(y * x), $MachinePrecision], x]]]

Derivation

1. Split input into 3 regimes

2. if y < -1 or 1 < y

   1. Initial program 28.2%

      \[1 - \frac{\left(1 - x\right) \cdot y}{y + 1} \]
   2. Step-by-step derivation

      1. associate-/l* 48.5%

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

      2. +-commutative 48.5%

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

   3. Simplified 48.5%

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

   5. Taylor expanded in y around inf 73.7%

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

   if -1 < y < 2.1500000000000002e-84

   1. Initial program 100.0%

      \[1 - \frac{\left(1 - x\right) \cdot y}{y + 1} \]
   2. Step-by-step derivation

      1. associate-/l* 100.0%

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

      2. +-commutative 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in y around 0 99.5%

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

   6. Taylor expanded in x around 0 80.3%

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

   if 2.1500000000000002e-84 < y < 1

   1. Initial program 99.8%

      \[1 - \frac{\left(1 - x\right) \cdot y}{y + 1} \]
   2. Step-by-step derivation

      1. associate-/l* 99.7%

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

      2. +-commutative 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in y around 0 87.1%

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

   6. Taylor expanded in y around inf 57.8%

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

   7. Taylor expanded in x around inf 58.7%

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

      1. *-commutative 58.7%

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

   9. Simplified 58.7%

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

Alternative 10: 73.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 9.2 \cdot 10^{-84}:\\ \;\;\;\;1\\ \mathbf{elif}\;y \leq 1:\\ \;\;\;\;y \cdot x\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -1.0) x (if (<= y 9.2e-84) 1.0 (if (<= y 1.0) (* y x) x))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -1.0) {
		tmp = x;
	} else if (y <= 9.2e-84) {
		tmp = 1.0;
	} else if (y <= 1.0) {
		tmp = y * x;
	} else {
		tmp = 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 <= (-1.0d0)) then
        tmp = x
    else if (y <= 9.2d-84) then
        tmp = 1.0d0
    else if (y <= 1.0d0) then
        tmp = y * x
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (y <= -1.0) {
		tmp = x;
	} else if (y <= 9.2e-84) {
		tmp = 1.0;
	} else if (y <= 1.0) {
		tmp = y * x;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -1.0:
		tmp = x
	elif y <= 9.2e-84:
		tmp = 1.0
	elif y <= 1.0:
		tmp = y * x
	else:
		tmp = x
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -1.0)
		tmp = x;
	elseif (y <= 9.2e-84)
		tmp = 1.0;
	elseif (y <= 1.0)
		tmp = Float64(y * x);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -1.0)
		tmp = x;
	elseif (y <= 9.2e-84)
		tmp = 1.0;
	elseif (y <= 1.0)
		tmp = y * x;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -1.0], x, If[LessEqual[y, 9.2e-84], 1.0, If[LessEqual[y, 1.0], N[(y * x), $MachinePrecision], x]]]

Derivation

1. Split input into 3 regimes

2. if y < -1 or 1 < y

   1. Initial program 28.2%

      \[1 - \frac{\left(1 - x\right) \cdot y}{y + 1} \]
   2. Step-by-step derivation

      1. associate-/l* 48.5%

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

      2. +-commutative 48.5%

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

   3. Simplified 48.5%

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

   5. Taylor expanded in y around inf 73.7%

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

   if -1 < y < 9.19999999999999922e-84

   1. Initial program 100.0%

      \[1 - \frac{\left(1 - x\right) \cdot y}{y + 1} \]
   2. Step-by-step derivation

      1. associate-/l* 100.0%

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

      2. +-commutative 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in x around inf 98.7%

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

      1. mul-1-neg 98.7%

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

      2. distribute-neg-frac2 98.7%

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

      3. *-commutative 98.7%

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

      4. distribute-neg-in 98.7%

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

      5. metadata-eval 98.7%

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

      6. sub-neg 98.7%

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

   7. Simplified 98.7%

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

   8. Taylor expanded in y around 0 79.1%

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

   if 9.19999999999999922e-84 < y < 1

   1. Initial program 99.8%

      \[1 - \frac{\left(1 - x\right) \cdot y}{y + 1} \]
   2. Step-by-step derivation

      1. associate-/l* 99.7%

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

      2. +-commutative 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in y around 0 87.1%

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

   6. Taylor expanded in y around inf 57.8%

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

   7. Taylor expanded in x around inf 58.7%

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

      1. *-commutative 58.7%

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

   9. Simplified 58.7%

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

Alternative 11: 98.5% accurate, 0.6× speedup

Math

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

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= y -1.0) (not (<= y 1.0)))
   (+ x (/ (- 1.0 x) y))
   (+ 1.0 (* y (+ x -1.0)))))

C

double code(double x, double y) {
	double tmp;
	if ((y <= -1.0) || !(y <= 1.0)) {
		tmp = x + ((1.0 - x) / y);
	} else {
		tmp = 1.0 + (y * (x + -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 <= (-1.0d0)) .or. (.not. (y <= 1.0d0))) then
        tmp = x + ((1.0d0 - x) / y)
    else
        tmp = 1.0d0 + (y * (x + (-1.0d0)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((y <= -1.0) || !(y <= 1.0)) {
		tmp = x + ((1.0 - x) / y);
	} else {
		tmp = 1.0 + (y * (x + -1.0));
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (y <= -1.0) or not (y <= 1.0):
		tmp = x + ((1.0 - x) / y)
	else:
		tmp = 1.0 + (y * (x + -1.0))
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((y <= -1.0) || !(y <= 1.0))
		tmp = Float64(x + Float64(Float64(1.0 - x) / y));
	else
		tmp = Float64(1.0 + Float64(y * Float64(x + -1.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((y <= -1.0) || ~((y <= 1.0)))
		tmp = x + ((1.0 - x) / y);
	else
		tmp = 1.0 + (y * (x + -1.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[y, -1.0], N[Not[LessEqual[y, 1.0]], $MachinePrecision]], N[(x + N[(N[(1.0 - x), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], N[(1.0 + N[(y * N[(x + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1 or 1 < y

   1. Initial program 28.2%

      \[1 - \frac{\left(1 - x\right) \cdot y}{y + 1} \]
   2. Step-by-step derivation

      1. associate-/l* 48.5%

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

      2. +-commutative 48.5%

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

   3. Simplified 48.5%

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

   5. Taylor expanded in y around inf 99.4%

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

      1. associate--l+ 99.4%

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

      2. div-sub 99.4%

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

   7. Simplified 99.4%

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

   if -1 < y < 1

   1. Initial program 100.0%

      \[1 - \frac{\left(1 - x\right) \cdot y}{y + 1} \]
   2. Step-by-step derivation

      1. associate-/l* 99.9%

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

      2. +-commutative 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in y around 0 97.6%

      \[\leadsto 1 - \left(1 - x\right) \cdot \color{blue}{y} \]
3. Recombined 2 regimes into one program.

4. Final simplification 98.5%

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

Alternative 12: 98.1% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1 \lor \neg \left(y \leq 1.25\right):\\ \;\;\;\;x + \frac{1 - x}{y}\\ \mathbf{else}:\\ \;\;\;\;1 + y \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= y -1.0) (not (<= y 1.25))) (+ x (/ (- 1.0 x) y)) (+ 1.0 (* y x))))

C

double code(double x, double y) {
	double tmp;
	if ((y <= -1.0) || !(y <= 1.25)) {
		tmp = x + ((1.0 - x) / y);
	} else {
		tmp = 1.0 + (y * 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 <= (-1.0d0)) .or. (.not. (y <= 1.25d0))) then
        tmp = x + ((1.0d0 - x) / y)
    else
        tmp = 1.0d0 + (y * x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((y <= -1.0) || !(y <= 1.25)) {
		tmp = x + ((1.0 - x) / y);
	} else {
		tmp = 1.0 + (y * x);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (y <= -1.0) or not (y <= 1.25):
		tmp = x + ((1.0 - x) / y)
	else:
		tmp = 1.0 + (y * x)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((y <= -1.0) || !(y <= 1.25))
		tmp = Float64(x + Float64(Float64(1.0 - x) / y));
	else
		tmp = Float64(1.0 + Float64(y * x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((y <= -1.0) || ~((y <= 1.25)))
		tmp = x + ((1.0 - x) / y);
	else
		tmp = 1.0 + (y * x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[y, -1.0], N[Not[LessEqual[y, 1.25]], $MachinePrecision]], N[(x + N[(N[(1.0 - x), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], N[(1.0 + N[(y * x), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1 or 1.25 < y

   1. Initial program 28.2%

      \[1 - \frac{\left(1 - x\right) \cdot y}{y + 1} \]
   2. Step-by-step derivation

      1. associate-/l* 48.5%

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

      2. +-commutative 48.5%

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

   3. Simplified 48.5%

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

   5. Taylor expanded in y around inf 99.4%

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

      1. associate--l+ 99.4%

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

      2. div-sub 99.4%

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

   7. Simplified 99.4%

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

   if -1 < y < 1.25

   1. Initial program 100.0%

      \[1 - \frac{\left(1 - x\right) \cdot y}{y + 1} \]
   2. Step-by-step derivation

      1. associate-/l* 99.9%

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

      2. +-commutative 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in x around inf 97.8%

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

      1. mul-1-neg 97.8%

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

      2. distribute-neg-frac2 97.8%

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

      3. *-commutative 97.8%

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

      4. distribute-neg-in 97.8%

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

      5. metadata-eval 97.8%

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

      6. sub-neg 97.8%

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

   7. Simplified 97.8%

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

   8. Taylor expanded in y around 0 96.4%

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

4. Final simplification 97.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1 \lor \neg \left(y \leq 1.25\right):\\ \;\;\;\;x + \frac{1 - x}{y}\\ \mathbf{else}:\\ \;\;\;\;1 + y \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 97.9% accurate, 0.7× speedup

Math

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

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= y -1.0) (not (<= y 1.0))) (+ x (/ 1.0 y)) (+ 1.0 (* y x))))

C

double code(double x, double y) {
	double tmp;
	if ((y <= -1.0) || !(y <= 1.0)) {
		tmp = x + (1.0 / y);
	} else {
		tmp = 1.0 + (y * 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 <= (-1.0d0)) .or. (.not. (y <= 1.0d0))) then
        tmp = x + (1.0d0 / y)
    else
        tmp = 1.0d0 + (y * x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((y <= -1.0) || !(y <= 1.0)) {
		tmp = x + (1.0 / y);
	} else {
		tmp = 1.0 + (y * x);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (y <= -1.0) or not (y <= 1.0):
		tmp = x + (1.0 / y)
	else:
		tmp = 1.0 + (y * x)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((y <= -1.0) || !(y <= 1.0))
		tmp = Float64(x + Float64(1.0 / y));
	else
		tmp = Float64(1.0 + Float64(y * x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((y <= -1.0) || ~((y <= 1.0)))
		tmp = x + (1.0 / y);
	else
		tmp = 1.0 + (y * x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[y, -1.0], N[Not[LessEqual[y, 1.0]], $MachinePrecision]], N[(x + N[(1.0 / y), $MachinePrecision]), $MachinePrecision], N[(1.0 + N[(y * x), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1 or 1 < y

   1. Initial program 28.2%

      \[1 - \frac{\left(1 - x\right) \cdot y}{y + 1} \]
   2. Step-by-step derivation

      1. associate-/l* 48.5%

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

      2. +-commutative 48.5%

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

   3. Simplified 48.5%

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

   5. Taylor expanded in y around -inf 100.0%

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

      1. mul-1-neg 100.0%

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

      2. unsub-neg 100.0%

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

      3. mul-1-neg 100.0%

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

      4. neg-sub0 100.0%

         \[\leadsto x - \frac{-1 \cdot \frac{x - 1}{y} - \color{blue}{\left(0 - \left(x - 1\right)\right)}}{y} \]

      5. associate-+l- 100.0%

         \[\leadsto x - \frac{-1 \cdot \frac{x - 1}{y} - \color{blue}{\left(\left(0 - x\right) + 1\right)}}{y} \]

      6. neg-sub0 100.0%

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

      7. +-commutative 100.0%

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

      8. sub-neg 100.0%

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

      9. unsub-neg 100.0%

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

      10. neg-mul-1 100.0%

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

      11. +-commutative 100.0%

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

   7. Simplified 100.0%

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

   8. Taylor expanded in y around inf 99.4%

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

   9. Taylor expanded in x around 0 98.6%

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

   if -1 < y < 1

   1. Initial program 100.0%

      \[1 - \frac{\left(1 - x\right) \cdot y}{y + 1} \]
   2. Step-by-step derivation

      1. associate-/l* 99.9%

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

      2. +-commutative 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in x around inf 97.8%

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

      1. mul-1-neg 97.8%

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

      2. distribute-neg-frac2 97.8%

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

      3. *-commutative 97.8%

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

      4. distribute-neg-in 97.8%

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

      5. metadata-eval 97.8%

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

      6. sub-neg 97.8%

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

   7. Simplified 97.8%

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

   8. Taylor expanded in y around 0 96.4%

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

4. Final simplification 97.5%

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

Alternative 14: 74.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 0.0056:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (if (<= y -1.0) x (if (<= y 0.0056) 1.0 x)))

C

double code(double x, double y) {
	double tmp;
	if (y <= -1.0) {
		tmp = x;
	} else if (y <= 0.0056) {
		tmp = 1.0;
	} else {
		tmp = 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 <= (-1.0d0)) then
        tmp = x
    else if (y <= 0.0056d0) then
        tmp = 1.0d0
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (y <= -1.0) {
		tmp = x;
	} else if (y <= 0.0056) {
		tmp = 1.0;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -1.0:
		tmp = x
	elif y <= 0.0056:
		tmp = 1.0
	else:
		tmp = x
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -1.0)
		tmp = x;
	elseif (y <= 0.0056)
		tmp = 1.0;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -1.0)
		tmp = x;
	elseif (y <= 0.0056)
		tmp = 1.0;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -1.0], x, If[LessEqual[y, 0.0056], 1.0, x]]

Derivation

1. Split input into 2 regimes

2. if y < -1 or 0.00559999999999999994 < y

   1. Initial program 28.7%

      \[1 - \frac{\left(1 - x\right) \cdot y}{y + 1} \]
   2. Step-by-step derivation

      1. associate-/l* 48.9%

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

      2. +-commutative 48.9%

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

   3. Simplified 48.9%

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

   5. Taylor expanded in y around inf 73.2%

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

   if -1 < y < 0.00559999999999999994

   1. Initial program 100.0%

      \[1 - \frac{\left(1 - x\right) \cdot y}{y + 1} \]
   2. Step-by-step derivation

      1. associate-/l* 99.9%

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

      2. +-commutative 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in x around inf 97.8%

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

      1. mul-1-neg 97.8%

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

      2. distribute-neg-frac2 97.8%

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

      3. *-commutative 97.8%

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

      4. distribute-neg-in 97.8%

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

      5. metadata-eval 97.8%

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

      6. sub-neg 97.8%

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

   7. Simplified 97.8%

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

   8. Taylor expanded in y around 0 72.0%

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

Alternative 15: 38.6% accurate, 11.0× 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 64.1%

   \[1 - \frac{\left(1 - x\right) \cdot y}{y + 1} \]
2. Step-by-step derivation

   1. associate-/l* 74.2%

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

   2. +-commutative 74.2%

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

3. Simplified 74.2%

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

5. Taylor expanded in x around inf 61.0%

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

   1. mul-1-neg 61.0%

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

   2. distribute-neg-frac2 61.0%

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

   3. *-commutative 61.0%

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

   4. distribute-neg-in 61.0%

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

   5. metadata-eval 61.0%

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

   6. sub-neg 61.0%

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

7. Simplified 61.0%

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

8. Taylor expanded in y around 0 37.7%

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

Alternative 16: 3.1% accurate, 11.0× speedup

Math

\[\begin{array}{l} \\ 0 \end{array} \]

FPCore

(FPCore (x y) :precision binary64 0.0)

C

double code(double x, double y) {
	return 0.0;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = 0.0d0
end function

Java

public static double code(double x, double y) {
	return 0.0;
}

Python

def code(x, y):
	return 0.0

Julia

function code(x, y)
	return 0.0
end

MATLAB

function tmp = code(x, y)
	tmp = 0.0;
end

Wolfram

code[x_, y_] := 0.0

Derivation

1. Initial program 64.1%

   \[1 - \frac{\left(1 - x\right) \cdot y}{y + 1} \]
2. Step-by-step derivation

   1. associate-/l* 74.2%

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

   2. +-commutative 74.2%

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

3. Simplified 74.2%

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

5. Taylor expanded in y around inf 25.4%

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

6. Taylor expanded in x around 0 3.1%

   \[\leadsto 1 - \color{blue}{1} \]
7. Step-by-step derivation

   1. metadata-eval 3.1%

      \[\leadsto \color{blue}{0} \]

8. Applied egg-rr 3.1%

   \[\leadsto \color{blue}{0} \]
9. Add Preprocessing

Developer Target 1: 99.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{1}{y} - \left(\frac{x}{y} - x\right)\\ \mathbf{if}\;y < -3693.8482788297247:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y < 6799310503.41891:\\ \;\;\;\;1 - \frac{\left(1 - x\right) \cdot y}{y + 1}\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (- (/ 1.0 y) (- (/ x y) x))))
   (if (< y -3693.8482788297247)
     t_0
     (if (< y 6799310503.41891) (- 1.0 (/ (* (- 1.0 x) y) (+ y 1.0))) t_0))))

C

double code(double x, double y) {
	double t_0 = (1.0 / y) - ((x / y) - x);
	double tmp;
	if (y < -3693.8482788297247) {
		tmp = t_0;
	} else if (y < 6799310503.41891) {
		tmp = 1.0 - (((1.0 - x) * y) / (y + 1.0));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: t_0
    real(8) :: tmp
    t_0 = (1.0d0 / y) - ((x / y) - x)
    if (y < (-3693.8482788297247d0)) then
        tmp = t_0
    else if (y < 6799310503.41891d0) then
        tmp = 1.0d0 - (((1.0d0 - x) * y) / (y + 1.0d0))
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double t_0 = (1.0 / y) - ((x / y) - x);
	double tmp;
	if (y < -3693.8482788297247) {
		tmp = t_0;
	} else if (y < 6799310503.41891) {
		tmp = 1.0 - (((1.0 - x) * y) / (y + 1.0));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = (1.0 / y) - ((x / y) - x)
	tmp = 0
	if y < -3693.8482788297247:
		tmp = t_0
	elif y < 6799310503.41891:
		tmp = 1.0 - (((1.0 - x) * y) / (y + 1.0))
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y)
	t_0 = Float64(Float64(1.0 / y) - Float64(Float64(x / y) - x))
	tmp = 0.0
	if (y < -3693.8482788297247)
		tmp = t_0;
	elseif (y < 6799310503.41891)
		tmp = Float64(1.0 - Float64(Float64(Float64(1.0 - x) * y) / Float64(y + 1.0)));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = (1.0 / y) - ((x / y) - x);
	tmp = 0.0;
	if (y < -3693.8482788297247)
		tmp = t_0;
	elseif (y < 6799310503.41891)
		tmp = 1.0 - (((1.0 - x) * y) / (y + 1.0));
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(N[(1.0 / y), $MachinePrecision] - N[(N[(x / y), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision]}, If[Less[y, -3693.8482788297247], t$95$0, If[Less[y, 6799310503.41891], N[(1.0 - N[(N[(N[(1.0 - x), $MachinePrecision] * y), $MachinePrecision] / N[(y + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$0]]]

Reproduce

herbie shell --seed 2024132 
(FPCore (x y)
  :name "Diagrams.Trail:splitAtParam  from diagrams-lib-1.3.0.3, D"
  :precision binary64

  :alt
  (! :herbie-platform default (if (< y -36938482788297247/10000000000000) (- (/ 1 y) (- (/ x y) x)) (if (< y 679931050341891/100000) (- 1 (/ (* (- 1 x) y) (+ y 1))) (- (/ 1 y) (- (/ x y) x)))))

  (- 1.0 (/ (* (- 1.0 x) y) (+ y 1.0))))