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

Percentage Accurate: 66.6% → 99.8%

Time: 9.6s

Alternatives: 11

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: 66.6% 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

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -12000000:\\ \;\;\;\;x + \frac{1 + \left(\frac{x + -1}{y} - x\right)}{y}\\ \mathbf{elif}\;y \leq 8400000000:\\ \;\;\;\;1 + \frac{y}{y + 1} \cdot \left(x + -1\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{1}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -12000000.0)
   (+ x (/ (+ 1.0 (- (/ (+ x -1.0) y) x)) y))
   (if (<= y 8400000000.0)
     (+ 1.0 (* (/ y (+ y 1.0)) (+ x -1.0)))
     (+ x (/ 1.0 y)))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -12000000.0) {
		tmp = x + ((1.0 + (((x + -1.0) / y) - x)) / y);
	} else if (y <= 8400000000.0) {
		tmp = 1.0 + ((y / (y + 1.0)) * (x + -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 <= (-12000000.0d0)) then
        tmp = x + ((1.0d0 + (((x + (-1.0d0)) / y) - x)) / y)
    else if (y <= 8400000000.0d0) then
        tmp = 1.0d0 + ((y / (y + 1.0d0)) * (x + (-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 <= -12000000.0) {
		tmp = x + ((1.0 + (((x + -1.0) / y) - x)) / y);
	} else if (y <= 8400000000.0) {
		tmp = 1.0 + ((y / (y + 1.0)) * (x + -1.0));
	} else {
		tmp = x + (1.0 / y);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -12000000.0:
		tmp = x + ((1.0 + (((x + -1.0) / y) - x)) / y)
	elif y <= 8400000000.0:
		tmp = 1.0 + ((y / (y + 1.0)) * (x + -1.0))
	else:
		tmp = x + (1.0 / y)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -12000000.0)
		tmp = Float64(x + Float64(Float64(1.0 + Float64(Float64(Float64(x + -1.0) / y) - x)) / y));
	elseif (y <= 8400000000.0)
		tmp = Float64(1.0 + Float64(Float64(y / Float64(y + 1.0)) * Float64(x + -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 <= -12000000.0)
		tmp = x + ((1.0 + (((x + -1.0) / y) - x)) / y);
	elseif (y <= 8400000000.0)
		tmp = 1.0 + ((y / (y + 1.0)) * (x + -1.0));
	else
		tmp = x + (1.0 / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -12000000.0], N[(x + N[(N[(1.0 + N[(N[(N[(x + -1.0), $MachinePrecision] / y), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 8400000000.0], N[(1.0 + N[(N[(y / N[(y + 1.0), $MachinePrecision]), $MachinePrecision] * N[(x + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(1.0 / y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.2e7

   1. Initial program 27.7%

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

      1. associate-/l* 54.2%

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

      2. +-commutative 54.2%

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

   3. Simplified 54.2%

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

   5. Taylor expanded in y around -inf 99.9%

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

   7. Simplified 99.9%

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

   if -1.2e7 < y < 8.4e9

   1. Initial program 99.9%

      \[1 - \frac{\left(1 - x\right) \cdot y}{y + 1} \]
   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 8.4e9 < y

   1. Initial program 32.4%

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

      1. associate-/l* 50.9%

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

      2. +-commutative 50.9%

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

   3. Simplified 50.9%

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

   5. Taylor expanded in y around inf 100.0%

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

      1. associate--l+ 100.0%

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

      2. div-sub 100.0%

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

      3. sub-neg 100.0%

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

      4. +-commutative 100.0%

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

      5. neg-sub0 100.0%

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

      6. associate-+l- 100.0%

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

      7. neg-sub0 100.0%

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

      8. mul-1-neg 100.0%

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

      9. associate-*r/ 100.0%

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

      10. mul-1-neg 100.0%

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

      11. unsub-neg 100.0%

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

      12. sub-neg 100.0%

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

      13. metadata-eval 100.0%

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

   7. Simplified 100.0%

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

   8. Taylor expanded in x around 0 100.0%

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

4. Final simplification 99.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -12000000:\\ \;\;\;\;x + \frac{1 + \left(\frac{x + -1}{y} - x\right)}{y}\\ \mathbf{elif}\;y \leq 8400000000:\\ \;\;\;\;1 + \frac{y}{y + 1} \cdot \left(x + -1\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{1}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 99.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -160000000:\\ \;\;\;\;x + \frac{1 - x}{y}\\ \mathbf{elif}\;y \leq 52000000000:\\ \;\;\;\;1 + \frac{y}{y + 1} \cdot \left(x + -1\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{1}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -160000000.0)
   (+ x (/ (- 1.0 x) y))
   (if (<= y 52000000000.0)
     (+ 1.0 (* (/ y (+ y 1.0)) (+ x -1.0)))
     (+ x (/ 1.0 y)))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -160000000.0) {
		tmp = x + ((1.0 - x) / y);
	} else if (y <= 52000000000.0) {
		tmp = 1.0 + ((y / (y + 1.0)) * (x + -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 <= (-160000000.0d0)) then
        tmp = x + ((1.0d0 - x) / y)
    else if (y <= 52000000000.0d0) then
        tmp = 1.0d0 + ((y / (y + 1.0d0)) * (x + (-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 <= -160000000.0) {
		tmp = x + ((1.0 - x) / y);
	} else if (y <= 52000000000.0) {
		tmp = 1.0 + ((y / (y + 1.0)) * (x + -1.0));
	} else {
		tmp = x + (1.0 / y);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -160000000.0:
		tmp = x + ((1.0 - x) / y)
	elif y <= 52000000000.0:
		tmp = 1.0 + ((y / (y + 1.0)) * (x + -1.0))
	else:
		tmp = x + (1.0 / y)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -160000000.0)
		tmp = Float64(x + Float64(Float64(1.0 - x) / y));
	elseif (y <= 52000000000.0)
		tmp = Float64(1.0 + Float64(Float64(y / Float64(y + 1.0)) * Float64(x + -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 <= -160000000.0)
		tmp = x + ((1.0 - x) / y);
	elseif (y <= 52000000000.0)
		tmp = 1.0 + ((y / (y + 1.0)) * (x + -1.0));
	else
		tmp = x + (1.0 / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -160000000.0], N[(x + N[(N[(1.0 - x), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 52000000000.0], N[(1.0 + N[(N[(y / N[(y + 1.0), $MachinePrecision]), $MachinePrecision] * N[(x + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(1.0 / y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.6e8

   1. Initial program 27.1%

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

      1. associate-/l* 54.0%

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

      2. +-commutative 54.0%

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

   3. Simplified 54.0%

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

   5. Taylor expanded in y around inf 99.7%

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

      1. associate--l+ 99.7%

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

      2. div-sub 99.7%

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

      3. sub-neg 99.7%

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

      4. +-commutative 99.7%

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

      5. neg-sub0 99.7%

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

      6. associate-+l- 99.7%

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

      7. neg-sub0 99.7%

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

      8. mul-1-neg 99.7%

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

      9. associate-*r/ 99.7%

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

      10. mul-1-neg 99.7%

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

      11. unsub-neg 99.7%

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

      12. sub-neg 99.7%

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

      13. metadata-eval 99.7%

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

   7. Simplified 99.7%

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

   if -1.6e8 < y < 5.2e10

   1. Initial program 99.7%

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

   if 5.2e10 < y

   1. Initial program 32.4%

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

      1. associate-/l* 50.9%

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

      2. +-commutative 50.9%

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

   3. Simplified 50.9%

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

   5. Taylor expanded in y around inf 100.0%

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

      1. associate--l+ 100.0%

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

      2. div-sub 100.0%

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

      3. sub-neg 100.0%

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

      4. +-commutative 100.0%

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

      5. neg-sub0 100.0%

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

      6. associate-+l- 100.0%

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

      7. neg-sub0 100.0%

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

      8. mul-1-neg 100.0%

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

      9. associate-*r/ 100.0%

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

      10. mul-1-neg 100.0%

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

      11. unsub-neg 100.0%

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

      12. sub-neg 100.0%

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

      13. metadata-eval 100.0%

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

   7. Simplified 100.0%

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

   8. Taylor expanded in x around 0 100.0%

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

4. Final simplification 99.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -160000000:\\ \;\;\;\;x + \frac{1 - x}{y}\\ \mathbf{elif}\;y \leq 52000000000:\\ \;\;\;\;1 + \frac{y}{y + 1} \cdot \left(x + -1\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{1}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 86.5% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 2.1:\\ \;\;\;\;1 + x \cdot y\\ \mathbf{elif}\;y \leq 1.1 \cdot 10^{+44}:\\ \;\;\;\;\frac{1}{y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -1.0)
   x
   (if (<= y 2.1) (+ 1.0 (* x y)) (if (<= y 1.1e+44) (/ 1.0 y) x))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -1.0) {
		tmp = x;
	} else if (y <= 2.1) {
		tmp = 1.0 + (x * y);
	} else if (y <= 1.1e+44) {
		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 <= 2.1d0) then
        tmp = 1.0d0 + (x * y)
    else if (y <= 1.1d+44) 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 <= 2.1) {
		tmp = 1.0 + (x * y);
	} else if (y <= 1.1e+44) {
		tmp = 1.0 / y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -1.0:
		tmp = x
	elif y <= 2.1:
		tmp = 1.0 + (x * y)
	elif y <= 1.1e+44:
		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 <= 2.1)
		tmp = Float64(1.0 + Float64(x * y));
	elseif (y <= 1.1e+44)
		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 <= 2.1)
		tmp = 1.0 + (x * y);
	elseif (y <= 1.1e+44)
		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, 2.1], N[(1.0 + N[(x * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.1e+44], N[(1.0 / y), $MachinePrecision], x]]]

Derivation

1. Split input into 3 regimes

2. if y < -1 or 1.09999999999999998e44 < y

   1. Initial program 31.7%

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

      1. associate-/l* 56.2%

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

      2. +-commutative 56.2%

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

   3. Simplified 56.2%

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

   5. Taylor expanded in y around inf 76.0%

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

   if -1 < y < 2.10000000000000009

   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 98.4%

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

   6. Taylor expanded in x around inf 98.0%

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

      1. neg-mul-1 98.0%

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

   8. Simplified 98.0%

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

      1. cancel-sign-sub 98.0%

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

      2. +-commutative 98.0%

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

   10. Applied egg-rr 98.0%

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

   if 2.10000000000000009 < y < 1.09999999999999998e44

   1. Initial program 39.8%

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

      1. associate-/l* 39.8%

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

      2. +-commutative 39.8%

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

   3. Simplified 39.8%

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

   5. Taylor expanded in y around inf 88.6%

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

      1. associate--l+ 88.6%

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

      2. div-sub 88.6%

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

      3. sub-neg 88.6%

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

      4. +-commutative 88.6%

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

      5. neg-sub0 88.6%

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

      6. associate-+l- 88.6%

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

      7. neg-sub0 88.6%

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

      8. mul-1-neg 88.6%

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

      9. associate-*r/ 88.6%

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

      10. mul-1-neg 88.6%

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

      11. unsub-neg 88.6%

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

      12. sub-neg 88.6%

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

      13. metadata-eval 88.6%

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

   7. Simplified 88.6%

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

   8. Taylor expanded in x around 0 61.4%

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

4. Final simplification 86.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 2.1:\\ \;\;\;\;1 + x \cdot y\\ \mathbf{elif}\;y \leq 1.1 \cdot 10^{+44}:\\ \;\;\;\;\frac{1}{y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 74.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 0.75:\\ \;\;\;\;1 - y\\ \mathbf{elif}\;y \leq 2.4 \cdot 10^{+44}:\\ \;\;\;\;\frac{1}{y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -1.0) x (if (<= y 0.75) (- 1.0 y) (if (<= y 2.4e+44) (/ 1.0 y) x))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -1.0) {
		tmp = x;
	} else if (y <= 0.75) {
		tmp = 1.0 - y;
	} else if (y <= 2.4e+44) {
		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 <= 0.75d0) then
        tmp = 1.0d0 - y
    else if (y <= 2.4d+44) 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 <= 0.75) {
		tmp = 1.0 - y;
	} else if (y <= 2.4e+44) {
		tmp = 1.0 / y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -1.0:
		tmp = x
	elif y <= 0.75:
		tmp = 1.0 - y
	elif y <= 2.4e+44:
		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 <= 0.75)
		tmp = Float64(1.0 - y);
	elseif (y <= 2.4e+44)
		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 <= 0.75)
		tmp = 1.0 - y;
	elseif (y <= 2.4e+44)
		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, 0.75], N[(1.0 - y), $MachinePrecision], If[LessEqual[y, 2.4e+44], N[(1.0 / y), $MachinePrecision], x]]]

Derivation

1. Split input into 3 regimes

2. if y < -1 or 2.40000000000000013e44 < y

   1. Initial program 31.7%

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

      1. associate-/l* 56.2%

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

      2. +-commutative 56.2%

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

   3. Simplified 56.2%

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

   5. Taylor expanded in y around inf 76.0%

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

   if -1 < y < 0.75

   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 98.4%

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

   6. Taylor expanded in x around 0 81.4%

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

   if 0.75 < y < 2.40000000000000013e44

   1. Initial program 39.8%

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

      1. associate-/l* 39.8%

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

      2. +-commutative 39.8%

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

   3. Simplified 39.8%

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

   5. Taylor expanded in y around inf 88.6%

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

      1. associate--l+ 88.6%

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

      2. div-sub 88.6%

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

      3. sub-neg 88.6%

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

      4. +-commutative 88.6%

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

      5. neg-sub0 88.6%

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

      6. associate-+l- 88.6%

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

      7. neg-sub0 88.6%

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

      8. mul-1-neg 88.6%

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

      9. associate-*r/ 88.6%

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

      10. mul-1-neg 88.6%

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

      11. unsub-neg 88.6%

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

      12. sub-neg 88.6%

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

      13. metadata-eval 88.6%

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

   7. Simplified 88.6%

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

   8. Taylor expanded in x around 0 61.4%

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

Alternative 5: 98.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1 \lor \neg \left(y \leq 0.82\right):\\ \;\;\;\;x + \frac{1}{y}\\ \mathbf{else}:\\ \;\;\;\;1 + y \cdot \left(x + -1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= y -1.0) (not (<= y 0.82)))
   (+ x (/ 1.0 y))
   (+ 1.0 (* y (+ x -1.0)))))

C

double code(double x, double y) {
	double tmp;
	if ((y <= -1.0) || !(y <= 0.82)) {
		tmp = x + (1.0 / 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 <= 0.82d0))) then
        tmp = x + (1.0d0 / 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 <= 0.82)) {
		tmp = x + (1.0 / 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 <= 0.82):
		tmp = x + (1.0 / y)
	else:
		tmp = 1.0 + (y * (x + -1.0))
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((y <= -1.0) || !(y <= 0.82))
		tmp = Float64(x + Float64(1.0 / 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 <= 0.82)))
		tmp = x + (1.0 / 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, 0.82]], $MachinePrecision]], N[(x + N[(1.0 / 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 0.819999999999999951 < y

   1. Initial program 32.5%

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

      1. associate-/l* 54.5%

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

      2. +-commutative 54.5%

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

   3. Simplified 54.5%

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

   5. Taylor expanded in y around inf 97.6%

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

      1. associate--l+ 97.6%

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

      2. div-sub 97.6%

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

      3. sub-neg 97.6%

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

      4. +-commutative 97.6%

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

      5. neg-sub0 97.6%

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

      6. associate-+l- 97.6%

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

      7. neg-sub0 97.6%

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

      8. mul-1-neg 97.6%

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

      9. associate-*r/ 97.6%

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

      10. mul-1-neg 97.6%

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

      11. unsub-neg 97.6%

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

      12. sub-neg 97.6%

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

      13. metadata-eval 97.6%

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

   7. Simplified 97.6%

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

   8. Taylor expanded in x around 0 96.8%

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

   if -1 < y < 0.819999999999999951

   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 98.4%

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

4. Final simplification 97.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1 \lor \neg \left(y \leq 0.82\right):\\ \;\;\;\;x + \frac{1}{y}\\ \mathbf{else}:\\ \;\;\;\;1 + y \cdot \left(x + -1\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 98.4% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1:\\ \;\;\;\;x + \frac{1 - x}{y}\\ \mathbf{elif}\;y \leq 0.78:\\ \;\;\;\;1 + y \cdot \left(x + -1\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{1}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -1.0)
   (+ x (/ (- 1.0 x) y))
   (if (<= y 0.78) (+ 1.0 (* y (+ x -1.0))) (+ x (/ 1.0 y)))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -1.0) {
		tmp = x + ((1.0 - x) / y);
	} else if (y <= 0.78) {
		tmp = 1.0 + (y * (x + -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 <= (-1.0d0)) then
        tmp = x + ((1.0d0 - x) / y)
    else if (y <= 0.78d0) then
        tmp = 1.0d0 + (y * (x + (-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 <= -1.0) {
		tmp = x + ((1.0 - x) / y);
	} else if (y <= 0.78) {
		tmp = 1.0 + (y * (x + -1.0));
	} else {
		tmp = x + (1.0 / y);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -1.0:
		tmp = x + ((1.0 - x) / y)
	elif y <= 0.78:
		tmp = 1.0 + (y * (x + -1.0))
	else:
		tmp = x + (1.0 / y)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -1.0)
		tmp = Float64(x + Float64(Float64(1.0 - x) / y));
	elseif (y <= 0.78)
		tmp = Float64(1.0 + Float64(y * Float64(x + -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 <= -1.0)
		tmp = x + ((1.0 - x) / y);
	elseif (y <= 0.78)
		tmp = 1.0 + (y * (x + -1.0));
	else
		tmp = x + (1.0 / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -1.0], N[(x + N[(N[(1.0 - x), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 0.78], N[(1.0 + N[(y * N[(x + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(1.0 / y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -1

   1. Initial program 30.8%

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

      1. associate-/l* 56.2%

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

      2. +-commutative 56.2%

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

   3. Simplified 56.2%

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

   5. Taylor expanded in y around inf 97.8%

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

      1. associate--l+ 97.8%

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

      2. div-sub 97.8%

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

      3. sub-neg 97.8%

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

      4. +-commutative 97.8%

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

      5. neg-sub0 97.8%

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

      6. associate-+l- 97.8%

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

      7. neg-sub0 97.8%

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

      8. mul-1-neg 97.8%

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

      9. associate-*r/ 97.8%

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

      10. mul-1-neg 97.8%

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

      11. unsub-neg 97.8%

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

      12. sub-neg 97.8%

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

      13. metadata-eval 97.8%

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

   7. Simplified 97.8%

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

   if -1 < y < 0.78000000000000003

   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 98.4%

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

   if 0.78000000000000003 < y

   1. Initial program 34.6%

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

      1. associate-/l* 52.5%

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

      2. +-commutative 52.5%

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

   3. Simplified 52.5%

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

   5. Taylor expanded in y around inf 97.4%

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

      1. associate--l+ 97.4%

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

      2. div-sub 97.4%

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

      3. sub-neg 97.4%

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

      4. +-commutative 97.4%

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

      5. neg-sub0 97.4%

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

      6. associate-+l- 97.4%

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

      7. neg-sub0 97.4%

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

      8. mul-1-neg 97.4%

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

      9. associate-*r/ 97.4%

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

      10. mul-1-neg 97.4%

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

      11. unsub-neg 97.4%

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

      12. sub-neg 97.4%

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

      13. metadata-eval 97.4%

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

   7. Simplified 97.4%

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

   8. Taylor expanded in x around 0 97.4%

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

4. Final simplification 98.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1:\\ \;\;\;\;x + \frac{1 - x}{y}\\ \mathbf{elif}\;y \leq 0.78:\\ \;\;\;\;1 + y \cdot \left(x + -1\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{1}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 98.0% accurate, 0.7× speedup

Math

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

FPCore

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

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 + (x * 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 <= (-1.0d0)) .or. (.not. (y <= 1.0d0))) then
        tmp = x + (1.0d0 / y)
    else
        tmp = 1.0d0 + (x * y)
    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 + (x * y);
	}
	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 + (x * y)
	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(x * y));
	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 + (x * y);
	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[(x * y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1 or 1 < y

   1. Initial program 32.5%

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

      1. associate-/l* 54.5%

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

      2. +-commutative 54.5%

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

   3. Simplified 54.5%

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

   5. Taylor expanded in y around inf 97.6%

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

      1. associate--l+ 97.6%

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

      2. div-sub 97.6%

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

      3. sub-neg 97.6%

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

      4. +-commutative 97.6%

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

      5. neg-sub0 97.6%

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

      6. associate-+l- 97.6%

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

      7. neg-sub0 97.6%

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

      8. mul-1-neg 97.6%

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

      9. associate-*r/ 97.6%

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

      10. mul-1-neg 97.6%

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

      11. unsub-neg 97.6%

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

      12. sub-neg 97.6%

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

      13. metadata-eval 97.6%

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

   7. Simplified 97.6%

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

   8. Taylor expanded in x around 0 96.8%

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

   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* 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 98.4%

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

   6. Taylor expanded in x around inf 98.0%

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

      1. neg-mul-1 98.0%

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

   8. Simplified 98.0%

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

      1. cancel-sign-sub 98.0%

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

      2. +-commutative 98.0%

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

   10. Applied egg-rr 98.0%

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

4. Final simplification 97.4%

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

Alternative 8: 99.8% accurate, 0.7× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 66.2%

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

   1. associate-/l* 77.2%

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

   2. +-commutative 77.2%

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

3. Simplified 77.2%

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

5. Taylor expanded in x around inf 77.5%

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

   1. associate--r+ 77.5%

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

   2. sub-neg 77.5%

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

   3. cancel-sign-sub-inv 77.5%

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

   4. metadata-eval 77.5%

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

   5. *-lft-identity 77.5%

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

   6. mul-1-neg 77.5%

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

   7. +-commutative 77.5%

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

   8. associate-+l+ 85.0%

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

   9. mul-1-neg 85.0%

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

   10. distribute-neg-frac2 85.0%

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

   11. distribute-rgt-neg-out 85.0%

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

   12. distribute-neg-in 85.0%

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

   13. metadata-eval 85.0%

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

   14. sub-neg 85.0%

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

7. Simplified 85.0%

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

   1. frac-add 57.6%

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

   2. div-inv 56.7%

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

   3. *-un-lft-identity 56.7%

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

   4. distribute-lft-out 68.6%

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

   5. associate-*r* 66.8%

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

   6. pow2 66.8%

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

9. Applied egg-rr 66.8%

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

11. Simplified 99.8%

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

12. Final simplification 99.8%

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

Alternative 9: 74.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 0.62:\\ \;\;\;\;1 - y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -1.0) x (if (<= y 0.62) (- 1.0 y) x)))

C

double code(double x, double y) {
	double tmp;
	if (y <= -1.0) {
		tmp = x;
	} else if (y <= 0.62) {
		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 <= 0.62d0) 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 <= 0.62) {
		tmp = 1.0 - y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -1.0:
		tmp = x
	elif y <= 0.62:
		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 <= 0.62)
		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 <= 0.62)
		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, 0.62], N[(1.0 - y), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if y < -1 or 0.619999999999999996 < y

   1. Initial program 32.5%

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

      1. associate-/l* 54.5%

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

      2. +-commutative 54.5%

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

   3. Simplified 54.5%

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

   5. Taylor expanded in y around inf 70.9%

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

   if -1 < y < 0.619999999999999996

   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 98.4%

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

   6. Taylor expanded in x around 0 81.4%

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

Alternative 10: 73.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 1.1 \cdot 10^{+25}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (if (<= y -1.0) x (if (<= y 1.1e+25) 1.0 x)))

C

double code(double x, double y) {
	double tmp;
	if (y <= -1.0) {
		tmp = x;
	} else if (y <= 1.1e+25) {
		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 <= 1.1d+25) 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 <= 1.1e+25) {
		tmp = 1.0;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -1.0:
		tmp = x
	elif y <= 1.1e+25:
		tmp = 1.0
	else:
		tmp = x
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -1.0)
		tmp = x;
	elseif (y <= 1.1e+25)
		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 <= 1.1e+25)
		tmp = 1.0;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -1.0], x, If[LessEqual[y, 1.1e+25], 1.0, x]]

Derivation

1. Split input into 2 regimes

2. if y < -1 or 1.1e25 < y

   1. Initial program 32.2%

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

      1. associate-/l* 55.1%

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

      2. +-commutative 55.1%

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

   3. Simplified 55.1%

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

   5. Taylor expanded in y around inf 73.6%

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

   if -1 < y < 1.1e25

   1. Initial program 97.7%

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

      1. associate-/l* 97.7%

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

      2. +-commutative 97.7%

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

   3. Simplified 97.7%

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

   5. Taylor expanded in y around 0 78.3%

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

Alternative 11: 38.9% 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 66.2%

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

   1. associate-/l* 77.2%

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

   2. +-commutative 77.2%

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

3. Simplified 77.2%

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

5. Taylor expanded in y around 0 42.5%

   \[\leadsto \color{blue}{1} \]
6. 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 2024112 
(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))))