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

Percentage Accurate: 66.2% → 99.9%

Time: 10.3s

Alternatives: 14

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: 66.2% 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: 99.9% accurate, 0.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -11800:\\ \;\;\;\;x + \left(\frac{1}{y} + \frac{\frac{\frac{1 - x}{y} + \left(x + -1\right)}{y} - x}{y}\right)\\ \mathbf{elif}\;y \leq 12500:\\ \;\;\;\;1 - \left(1 - x\right) \cdot \frac{y}{y + 1}\\ \mathbf{else}:\\ \;\;\;\;x + \left(\left(\left(\frac{1}{y} + \frac{1}{{y}^{3}}\right) - \frac{1 - x}{{y}^{2}}\right) - \left(\frac{x}{y} + \frac{x}{{y}^{3}}\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -11800.0)
   (+ x (+ (/ 1.0 y) (/ (- (/ (+ (/ (- 1.0 x) y) (+ x -1.0)) y) x) y)))
   (if (<= y 12500.0)
     (- 1.0 (* (- 1.0 x) (/ y (+ y 1.0))))
     (+
      x
      (-
       (- (+ (/ 1.0 y) (/ 1.0 (pow y 3.0))) (/ (- 1.0 x) (pow y 2.0)))
       (+ (/ x y) (/ x (pow y 3.0))))))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -11800.0) {
		tmp = x + ((1.0 / y) + ((((((1.0 - x) / y) + (x + -1.0)) / y) - x) / y));
	} else if (y <= 12500.0) {
		tmp = 1.0 - ((1.0 - x) * (y / (y + 1.0)));
	} else {
		tmp = x + ((((1.0 / y) + (1.0 / pow(y, 3.0))) - ((1.0 - x) / pow(y, 2.0))) - ((x / y) + (x / pow(y, 3.0))));
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (y <= (-11800.0d0)) then
        tmp = x + ((1.0d0 / y) + ((((((1.0d0 - x) / y) + (x + (-1.0d0))) / y) - x) / y))
    else if (y <= 12500.0d0) then
        tmp = 1.0d0 - ((1.0d0 - x) * (y / (y + 1.0d0)))
    else
        tmp = x + ((((1.0d0 / y) + (1.0d0 / (y ** 3.0d0))) - ((1.0d0 - x) / (y ** 2.0d0))) - ((x / y) + (x / (y ** 3.0d0))))
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (y <= -11800.0) {
		tmp = x + ((1.0 / y) + ((((((1.0 - x) / y) + (x + -1.0)) / y) - x) / y));
	} else if (y <= 12500.0) {
		tmp = 1.0 - ((1.0 - x) * (y / (y + 1.0)));
	} else {
		tmp = x + ((((1.0 / y) + (1.0 / Math.pow(y, 3.0))) - ((1.0 - x) / Math.pow(y, 2.0))) - ((x / y) + (x / Math.pow(y, 3.0))));
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -11800.0:
		tmp = x + ((1.0 / y) + ((((((1.0 - x) / y) + (x + -1.0)) / y) - x) / y))
	elif y <= 12500.0:
		tmp = 1.0 - ((1.0 - x) * (y / (y + 1.0)))
	else:
		tmp = x + ((((1.0 / y) + (1.0 / math.pow(y, 3.0))) - ((1.0 - x) / math.pow(y, 2.0))) - ((x / y) + (x / math.pow(y, 3.0))))
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -11800.0)
		tmp = Float64(x + Float64(Float64(1.0 / y) + Float64(Float64(Float64(Float64(Float64(Float64(1.0 - x) / y) + Float64(x + -1.0)) / y) - x) / y)));
	elseif (y <= 12500.0)
		tmp = Float64(1.0 - Float64(Float64(1.0 - x) * Float64(y / Float64(y + 1.0))));
	else
		tmp = Float64(x + Float64(Float64(Float64(Float64(1.0 / y) + Float64(1.0 / (y ^ 3.0))) - Float64(Float64(1.0 - x) / (y ^ 2.0))) - Float64(Float64(x / y) + Float64(x / (y ^ 3.0)))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -11800.0)
		tmp = x + ((1.0 / y) + ((((((1.0 - x) / y) + (x + -1.0)) / y) - x) / y));
	elseif (y <= 12500.0)
		tmp = 1.0 - ((1.0 - x) * (y / (y + 1.0)));
	else
		tmp = x + ((((1.0 / y) + (1.0 / (y ^ 3.0))) - ((1.0 - x) / (y ^ 2.0))) - ((x / y) + (x / (y ^ 3.0))));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -11800.0], N[(x + N[(N[(1.0 / y), $MachinePrecision] + N[(N[(N[(N[(N[(N[(1.0 - x), $MachinePrecision] / y), $MachinePrecision] + N[(x + -1.0), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision] - x), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 12500.0], N[(1.0 - N[(N[(1.0 - x), $MachinePrecision] * N[(y / N[(y + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(N[(N[(1.0 / y), $MachinePrecision] + N[(1.0 / N[Power[y, 3.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(1.0 - x), $MachinePrecision] / N[Power[y, 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(x / y), $MachinePrecision] + N[(x / N[Power[y, 3.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -11800

   1. Initial program 37.4%

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

      1. associate-/l* 58.0%

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

      2. +-commutative 58.0%

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

   3. Simplified 58.0%

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

   5. Taylor expanded in y around -inf 99.9%

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

   7. Simplified 99.9%

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

      1. associate-+l- 99.9%

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

      2. div-sub 100.0%

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

      3. +-commutative 100.0%

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

   9. Applied egg-rr 100.0%

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

   if -11800 < y < 12500

   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

   if 12500 < y

   1. Initial program 31.7%

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

      1. associate-/l* 53.4%

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

      2. +-commutative 53.4%

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

   3. Simplified 53.4%

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

   5. Taylor expanded in y around inf 100.0%

      \[\leadsto \color{blue}{\left(x + \left(\frac{1}{y} + \frac{1}{{y}^{3}}\right)\right) - \left(-1 \cdot \frac{x}{{y}^{2}} + \left(\frac{1}{{y}^{2}} + \left(\frac{x}{y} + \frac{x}{{y}^{3}}\right)\right)\right)} \]
   6. Step-by-step derivation

      1. associate--l+ 100.0%

         \[\leadsto \color{blue}{x + \left(\left(\frac{1}{y} + \frac{1}{{y}^{3}}\right) - \left(-1 \cdot \frac{x}{{y}^{2}} + \left(\frac{1}{{y}^{2}} + \left(\frac{x}{y} + \frac{x}{{y}^{3}}\right)\right)\right)\right)} \]

      2. associate-+r+ 100.0%

         \[\leadsto x + \left(\left(\frac{1}{y} + \frac{1}{{y}^{3}}\right) - \color{blue}{\left(\left(-1 \cdot \frac{x}{{y}^{2}} + \frac{1}{{y}^{2}}\right) + \left(\frac{x}{y} + \frac{x}{{y}^{3}}\right)\right)}\right) \]

      3. associate--r+ 100.0%

         \[\leadsto x + \color{blue}{\left(\left(\left(\frac{1}{y} + \frac{1}{{y}^{3}}\right) - \left(-1 \cdot \frac{x}{{y}^{2}} + \frac{1}{{y}^{2}}\right)\right) - \left(\frac{x}{y} + \frac{x}{{y}^{3}}\right)\right)} \]

      4. +-commutative 100.0%

         \[\leadsto x + \left(\left(\left(\frac{1}{y} + \frac{1}{{y}^{3}}\right) - \color{blue}{\left(\frac{1}{{y}^{2}} + -1 \cdot \frac{x}{{y}^{2}}\right)}\right) - \left(\frac{x}{y} + \frac{x}{{y}^{3}}\right)\right) \]

      5. mul-1-neg 100.0%

         \[\leadsto x + \left(\left(\left(\frac{1}{y} + \frac{1}{{y}^{3}}\right) - \left(\frac{1}{{y}^{2}} + \color{blue}{\left(-\frac{x}{{y}^{2}}\right)}\right)\right) - \left(\frac{x}{y} + \frac{x}{{y}^{3}}\right)\right) \]

      6. sub-neg 100.0%

         \[\leadsto x + \left(\left(\left(\frac{1}{y} + \frac{1}{{y}^{3}}\right) - \color{blue}{\left(\frac{1}{{y}^{2}} - \frac{x}{{y}^{2}}\right)}\right) - \left(\frac{x}{y} + \frac{x}{{y}^{3}}\right)\right) \]

      7. div-sub 100.0%

         \[\leadsto x + \left(\left(\left(\frac{1}{y} + \frac{1}{{y}^{3}}\right) - \color{blue}{\frac{1 - x}{{y}^{2}}}\right) - \left(\frac{x}{y} + \frac{x}{{y}^{3}}\right)\right) \]

   7. Simplified 100.0%

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

4. Final simplification 100.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -11800:\\ \;\;\;\;x + \left(\frac{1}{y} + \frac{\frac{\frac{1 - x}{y} + \left(x + -1\right)}{y} - x}{y}\right)\\ \mathbf{elif}\;y \leq 12500:\\ \;\;\;\;1 - \left(1 - x\right) \cdot \frac{y}{y + 1}\\ \mathbf{else}:\\ \;\;\;\;x + \left(\left(\left(\frac{1}{y} + \frac{1}{{y}^{3}}\right) - \frac{1 - x}{{y}^{2}}\right) - \left(\frac{x}{y} + \frac{x}{{y}^{3}}\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 99.5% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{y \cdot \left(1 - x\right)}{y + 1}\\ \mathbf{if}\;t\_0 \leq 5 \cdot 10^{-5} \lor \neg \left(t\_0 \leq 1.5\right):\\ \;\;\;\;1 + \left(1 - x\right) \cdot \frac{y}{-1 - y}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{1 + \frac{\frac{1}{y} + -1}{y}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (/ (* y (- 1.0 x)) (+ y 1.0))))
   (if (or (<= t_0 5e-5) (not (<= t_0 1.5)))
     (+ 1.0 (* (- 1.0 x) (/ y (- -1.0 y))))
     (+ x (/ (+ 1.0 (/ (+ (/ 1.0 y) -1.0) y)) y)))))

C

double code(double x, double y) {
	double t_0 = (y * (1.0 - x)) / (y + 1.0);
	double tmp;
	if ((t_0 <= 5e-5) || !(t_0 <= 1.5)) {
		tmp = 1.0 + ((1.0 - x) * (y / (-1.0 - y)));
	} else {
		tmp = x + ((1.0 + (((1.0 / y) + -1.0) / y)) / y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: t_0
    real(8) :: tmp
    t_0 = (y * (1.0d0 - x)) / (y + 1.0d0)
    if ((t_0 <= 5d-5) .or. (.not. (t_0 <= 1.5d0))) then
        tmp = 1.0d0 + ((1.0d0 - x) * (y / ((-1.0d0) - y)))
    else
        tmp = x + ((1.0d0 + (((1.0d0 / y) + (-1.0d0)) / y)) / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double t_0 = (y * (1.0 - x)) / (y + 1.0);
	double tmp;
	if ((t_0 <= 5e-5) || !(t_0 <= 1.5)) {
		tmp = 1.0 + ((1.0 - x) * (y / (-1.0 - y)));
	} else {
		tmp = x + ((1.0 + (((1.0 / y) + -1.0) / y)) / y);
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = (y * (1.0 - x)) / (y + 1.0)
	tmp = 0
	if (t_0 <= 5e-5) or not (t_0 <= 1.5):
		tmp = 1.0 + ((1.0 - x) * (y / (-1.0 - y)))
	else:
		tmp = x + ((1.0 + (((1.0 / y) + -1.0) / y)) / y)
	return tmp

Julia

function code(x, y)
	t_0 = Float64(Float64(y * Float64(1.0 - x)) / Float64(y + 1.0))
	tmp = 0.0
	if ((t_0 <= 5e-5) || !(t_0 <= 1.5))
		tmp = Float64(1.0 + Float64(Float64(1.0 - x) * Float64(y / Float64(-1.0 - y))));
	else
		tmp = Float64(x + Float64(Float64(1.0 + Float64(Float64(Float64(1.0 / y) + -1.0) / y)) / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = (y * (1.0 - x)) / (y + 1.0);
	tmp = 0.0;
	if ((t_0 <= 5e-5) || ~((t_0 <= 1.5)))
		tmp = 1.0 + ((1.0 - x) * (y / (-1.0 - y)));
	else
		tmp = x + ((1.0 + (((1.0 / y) + -1.0) / y)) / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(N[(y * N[(1.0 - x), $MachinePrecision]), $MachinePrecision] / N[(y + 1.0), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$0, 5e-5], N[Not[LessEqual[t$95$0, 1.5]], $MachinePrecision]], N[(1.0 + N[(N[(1.0 - x), $MachinePrecision] * N[(y / N[(-1.0 - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(1.0 + N[(N[(N[(1.0 / y), $MachinePrecision] + -1.0), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 (-.f64 #s(literal 1 binary64) x) y) (+.f64 y #s(literal 1 binary64))) < 5.00000000000000024e-5 or 1.5 < (/.f64 (*.f64 (-.f64 #s(literal 1 binary64) x) y) (+.f64 y #s(literal 1 binary64)))

   1. Initial program 87.0%

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

   if 5.00000000000000024e-5 < (/.f64 (*.f64 (-.f64 #s(literal 1 binary64) x) y) (+.f64 y #s(literal 1 binary64))) < 1.5

   1. Initial program 11.0%

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

      1. associate-/l* 11.1%

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

      2. +-commutative 11.1%

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

   3. Simplified 11.1%

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

   5. Taylor expanded in y around -inf 99.9%

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

   7. Simplified 99.9%

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

   8. Taylor expanded in x around 0 99.9%

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

   9. Taylor expanded in x around 0 99.9%

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

       1. associate--l+ 99.9%

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

       2. unpow2 99.9%

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

       3. associate-/r* 99.9%

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

       4. div-sub 99.9%

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

       5. sub-neg 99.9%

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

       6. metadata-eval 99.9%

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

       7. +-commutative 99.9%

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

   11. Simplified 99.9%

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

4. Final simplification 100.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y \cdot \left(1 - x\right)}{y + 1} \leq 5 \cdot 10^{-5} \lor \neg \left(\frac{y \cdot \left(1 - x\right)}{y + 1} \leq 1.5\right):\\ \;\;\;\;1 + \left(1 - x\right) \cdot \frac{y}{-1 - y}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{1 + \frac{\frac{1}{y} + -1}{y}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 99.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -11800:\\ \;\;\;\;x + \left(\frac{1}{y} + \frac{\frac{\frac{1 - x}{y} + \left(x + -1\right)}{y} - x}{y}\right)\\ \mathbf{elif}\;y \leq 250000:\\ \;\;\;\;1 - \left(1 - x\right) \cdot \frac{y}{y + 1}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{\left(1 - x\right) + \frac{\frac{1}{y} + -1}{y}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -11800.0)
   (+ x (+ (/ 1.0 y) (/ (- (/ (+ (/ (- 1.0 x) y) (+ x -1.0)) y) x) y)))
   (if (<= y 250000.0)
     (- 1.0 (* (- 1.0 x) (/ y (+ y 1.0))))
     (+ x (/ (+ (- 1.0 x) (/ (+ (/ 1.0 y) -1.0) y)) y)))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -11800.0) {
		tmp = x + ((1.0 / y) + ((((((1.0 - x) / y) + (x + -1.0)) / y) - x) / y));
	} else if (y <= 250000.0) {
		tmp = 1.0 - ((1.0 - x) * (y / (y + 1.0)));
	} else {
		tmp = x + (((1.0 - x) + (((1.0 / y) + -1.0) / y)) / 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 <= (-11800.0d0)) then
        tmp = x + ((1.0d0 / y) + ((((((1.0d0 - x) / y) + (x + (-1.0d0))) / y) - x) / y))
    else if (y <= 250000.0d0) then
        tmp = 1.0d0 - ((1.0d0 - x) * (y / (y + 1.0d0)))
    else
        tmp = x + (((1.0d0 - x) + (((1.0d0 / y) + (-1.0d0)) / y)) / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (y <= -11800.0) {
		tmp = x + ((1.0 / y) + ((((((1.0 - x) / y) + (x + -1.0)) / y) - x) / y));
	} else if (y <= 250000.0) {
		tmp = 1.0 - ((1.0 - x) * (y / (y + 1.0)));
	} else {
		tmp = x + (((1.0 - x) + (((1.0 / y) + -1.0) / y)) / y);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -11800.0:
		tmp = x + ((1.0 / y) + ((((((1.0 - x) / y) + (x + -1.0)) / y) - x) / y))
	elif y <= 250000.0:
		tmp = 1.0 - ((1.0 - x) * (y / (y + 1.0)))
	else:
		tmp = x + (((1.0 - x) + (((1.0 / y) + -1.0) / y)) / y)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -11800.0)
		tmp = Float64(x + Float64(Float64(1.0 / y) + Float64(Float64(Float64(Float64(Float64(Float64(1.0 - x) / y) + Float64(x + -1.0)) / y) - x) / y)));
	elseif (y <= 250000.0)
		tmp = Float64(1.0 - Float64(Float64(1.0 - x) * Float64(y / Float64(y + 1.0))));
	else
		tmp = Float64(x + Float64(Float64(Float64(1.0 - x) + Float64(Float64(Float64(1.0 / y) + -1.0) / y)) / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -11800.0)
		tmp = x + ((1.0 / y) + ((((((1.0 - x) / y) + (x + -1.0)) / y) - x) / y));
	elseif (y <= 250000.0)
		tmp = 1.0 - ((1.0 - x) * (y / (y + 1.0)));
	else
		tmp = x + (((1.0 - x) + (((1.0 / y) + -1.0) / y)) / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -11800.0], N[(x + N[(N[(1.0 / y), $MachinePrecision] + N[(N[(N[(N[(N[(N[(1.0 - x), $MachinePrecision] / y), $MachinePrecision] + N[(x + -1.0), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision] - x), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 250000.0], N[(1.0 - N[(N[(1.0 - x), $MachinePrecision] * N[(y / N[(y + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(N[(1.0 - x), $MachinePrecision] + N[(N[(N[(1.0 / y), $MachinePrecision] + -1.0), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -11800

   1. Initial program 37.4%

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

      1. associate-/l* 58.0%

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

      2. +-commutative 58.0%

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

   3. Simplified 58.0%

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

   5. Taylor expanded in y around -inf 99.9%

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

   7. Simplified 99.9%

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

      1. associate-+l- 99.9%

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

      2. div-sub 100.0%

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

      3. +-commutative 100.0%

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

   9. Applied egg-rr 100.0%

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

   if -11800 < y < 2.5e5

   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

   if 2.5e5 < y

   1. Initial program 31.7%

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

      1. associate-/l* 53.4%

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

      2. +-commutative 53.4%

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

   3. Simplified 53.4%

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

   5. Taylor expanded in y around -inf 100.0%

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

   7. Simplified 100.0%

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

   8. Taylor expanded in x around 0 100.0%

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

4. Final simplification 100.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -11800:\\ \;\;\;\;x + \left(\frac{1}{y} + \frac{\frac{\frac{1 - x}{y} + \left(x + -1\right)}{y} - x}{y}\right)\\ \mathbf{elif}\;y \leq 250000:\\ \;\;\;\;1 - \left(1 - x\right) \cdot \frac{y}{y + 1}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{\left(1 - x\right) + \frac{\frac{1}{y} + -1}{y}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 99.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -175000 \lor \neg \left(y \leq 320000\right):\\ \;\;\;\;x + \frac{\left(1 - x\right) + \frac{\frac{1}{y} + -1}{y}}{y}\\ \mathbf{else}:\\ \;\;\;\;1 - \left(1 - x\right) \cdot \frac{y}{y + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= y -175000.0) (not (<= y 320000.0)))
   (+ x (/ (+ (- 1.0 x) (/ (+ (/ 1.0 y) -1.0) y)) y))
   (- 1.0 (* (- 1.0 x) (/ y (+ y 1.0))))))

C

double code(double x, double y) {
	double tmp;
	if ((y <= -175000.0) || !(y <= 320000.0)) {
		tmp = x + (((1.0 - x) + (((1.0 / y) + -1.0) / y)) / y);
	} else {
		tmp = 1.0 - ((1.0 - x) * (y / (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 <= (-175000.0d0)) .or. (.not. (y <= 320000.0d0))) then
        tmp = x + (((1.0d0 - x) + (((1.0d0 / y) + (-1.0d0)) / y)) / y)
    else
        tmp = 1.0d0 - ((1.0d0 - x) * (y / (y + 1.0d0)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((y <= -175000.0) || !(y <= 320000.0)) {
		tmp = x + (((1.0 - x) + (((1.0 / y) + -1.0) / y)) / y);
	} else {
		tmp = 1.0 - ((1.0 - x) * (y / (y + 1.0)));
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (y <= -175000.0) or not (y <= 320000.0):
		tmp = x + (((1.0 - x) + (((1.0 / y) + -1.0) / y)) / y)
	else:
		tmp = 1.0 - ((1.0 - x) * (y / (y + 1.0)))
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((y <= -175000.0) || !(y <= 320000.0))
		tmp = Float64(x + Float64(Float64(Float64(1.0 - x) + Float64(Float64(Float64(1.0 / y) + -1.0) / y)) / y));
	else
		tmp = Float64(1.0 - Float64(Float64(1.0 - x) * Float64(y / Float64(y + 1.0))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((y <= -175000.0) || ~((y <= 320000.0)))
		tmp = x + (((1.0 - x) + (((1.0 / y) + -1.0) / y)) / y);
	else
		tmp = 1.0 - ((1.0 - x) * (y / (y + 1.0)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[y, -175000.0], N[Not[LessEqual[y, 320000.0]], $MachinePrecision]], N[(x + N[(N[(N[(1.0 - x), $MachinePrecision] + N[(N[(N[(1.0 / y), $MachinePrecision] + -1.0), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], N[(1.0 - N[(N[(1.0 - x), $MachinePrecision] * N[(y / N[(y + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -175000 or 3.2e5 < y

   1. Initial program 33.8%

      \[1 - \frac{\left(1 - x\right) \cdot y}{y + 1} \]
   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 100.0%

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

   7. Simplified 100.0%

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

   8. Taylor expanded in x around 0 100.0%

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

   if -175000 < y < 3.2e5

   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
3. Recombined 2 regimes into one program.

4. Final simplification 100.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -175000 \lor \neg \left(y \leq 320000\right):\\ \;\;\;\;x + \frac{\left(1 - x\right) + \frac{\frac{1}{y} + -1}{y}}{y}\\ \mathbf{else}:\\ \;\;\;\;1 - \left(1 - x\right) \cdot \frac{y}{y + 1}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 99.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -11800:\\ \;\;\;\;x + \frac{\left(1 - x\right) + \frac{\frac{1 - x}{y} + \left(x + -1\right)}{y}}{y}\\ \mathbf{elif}\;y \leq 120000:\\ \;\;\;\;1 - \left(1 - x\right) \cdot \frac{y}{y + 1}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{\left(1 - x\right) + \frac{\frac{1}{y} + -1}{y}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -11800.0)
   (+ x (/ (+ (- 1.0 x) (/ (+ (/ (- 1.0 x) y) (+ x -1.0)) y)) y))
   (if (<= y 120000.0)
     (- 1.0 (* (- 1.0 x) (/ y (+ y 1.0))))
     (+ x (/ (+ (- 1.0 x) (/ (+ (/ 1.0 y) -1.0) y)) y)))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -11800.0) {
		tmp = x + (((1.0 - x) + ((((1.0 - x) / y) + (x + -1.0)) / y)) / y);
	} else if (y <= 120000.0) {
		tmp = 1.0 - ((1.0 - x) * (y / (y + 1.0)));
	} else {
		tmp = x + (((1.0 - x) + (((1.0 / y) + -1.0) / y)) / 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 <= (-11800.0d0)) then
        tmp = x + (((1.0d0 - x) + ((((1.0d0 - x) / y) + (x + (-1.0d0))) / y)) / y)
    else if (y <= 120000.0d0) then
        tmp = 1.0d0 - ((1.0d0 - x) * (y / (y + 1.0d0)))
    else
        tmp = x + (((1.0d0 - x) + (((1.0d0 / y) + (-1.0d0)) / y)) / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (y <= -11800.0) {
		tmp = x + (((1.0 - x) + ((((1.0 - x) / y) + (x + -1.0)) / y)) / y);
	} else if (y <= 120000.0) {
		tmp = 1.0 - ((1.0 - x) * (y / (y + 1.0)));
	} else {
		tmp = x + (((1.0 - x) + (((1.0 / y) + -1.0) / y)) / y);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -11800.0:
		tmp = x + (((1.0 - x) + ((((1.0 - x) / y) + (x + -1.0)) / y)) / y)
	elif y <= 120000.0:
		tmp = 1.0 - ((1.0 - x) * (y / (y + 1.0)))
	else:
		tmp = x + (((1.0 - x) + (((1.0 / y) + -1.0) / y)) / y)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -11800.0)
		tmp = Float64(x + Float64(Float64(Float64(1.0 - x) + Float64(Float64(Float64(Float64(1.0 - x) / y) + Float64(x + -1.0)) / y)) / y));
	elseif (y <= 120000.0)
		tmp = Float64(1.0 - Float64(Float64(1.0 - x) * Float64(y / Float64(y + 1.0))));
	else
		tmp = Float64(x + Float64(Float64(Float64(1.0 - x) + Float64(Float64(Float64(1.0 / y) + -1.0) / y)) / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -11800.0)
		tmp = x + (((1.0 - x) + ((((1.0 - x) / y) + (x + -1.0)) / y)) / y);
	elseif (y <= 120000.0)
		tmp = 1.0 - ((1.0 - x) * (y / (y + 1.0)));
	else
		tmp = x + (((1.0 - x) + (((1.0 / y) + -1.0) / y)) / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -11800.0], N[(x + N[(N[(N[(1.0 - x), $MachinePrecision] + N[(N[(N[(N[(1.0 - x), $MachinePrecision] / y), $MachinePrecision] + N[(x + -1.0), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 120000.0], N[(1.0 - N[(N[(1.0 - x), $MachinePrecision] * N[(y / N[(y + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(N[(1.0 - x), $MachinePrecision] + N[(N[(N[(1.0 / y), $MachinePrecision] + -1.0), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -11800

   1. Initial program 37.4%

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

      1. associate-/l* 58.0%

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

      2. +-commutative 58.0%

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

   3. Simplified 58.0%

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

   5. Taylor expanded in y around -inf 99.9%

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

   7. Simplified 99.9%

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

   if -11800 < y < 1.2e5

   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

   if 1.2e5 < y

   1. Initial program 31.7%

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

      1. associate-/l* 53.4%

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

      2. +-commutative 53.4%

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

   3. Simplified 53.4%

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

   5. Taylor expanded in y around -inf 100.0%

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

   7. Simplified 100.0%

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

   8. Taylor expanded in x around 0 100.0%

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

4. Final simplification 100.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -11800:\\ \;\;\;\;x + \frac{\left(1 - x\right) + \frac{\frac{1 - x}{y} + \left(x + -1\right)}{y}}{y}\\ \mathbf{elif}\;y \leq 120000:\\ \;\;\;\;1 - \left(1 - x\right) \cdot \frac{y}{y + 1}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{\left(1 - x\right) + \frac{\frac{1}{y} + -1}{y}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 85.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x + \frac{1 - x}{y}\\ \mathbf{if}\;y \leq -1:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq -5.4 \cdot 10^{-79}:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;y \leq 0.95:\\ \;\;\;\;1 - y\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (+ x (/ (- 1.0 x) y))))
   (if (<= y -1.0)
     t_0
     (if (<= y -5.4e-79) (* y x) (if (<= y 0.95) (- 1.0 y) t_0)))))

C

double code(double x, double y) {
	double t_0 = x + ((1.0 - x) / y);
	double tmp;
	if (y <= -1.0) {
		tmp = t_0;
	} else if (y <= -5.4e-79) {
		tmp = y * x;
	} else if (y <= 0.95) {
		tmp = 1.0 - y;
	} 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 = x + ((1.0d0 - x) / y)
    if (y <= (-1.0d0)) then
        tmp = t_0
    else if (y <= (-5.4d-79)) then
        tmp = y * x
    else if (y <= 0.95d0) then
        tmp = 1.0d0 - y
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double t_0 = x + ((1.0 - x) / y);
	double tmp;
	if (y <= -1.0) {
		tmp = t_0;
	} else if (y <= -5.4e-79) {
		tmp = y * x;
	} else if (y <= 0.95) {
		tmp = 1.0 - y;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = x + ((1.0 - x) / y)
	tmp = 0
	if y <= -1.0:
		tmp = t_0
	elif y <= -5.4e-79:
		tmp = y * x
	elif y <= 0.95:
		tmp = 1.0 - y
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y)
	t_0 = Float64(x + Float64(Float64(1.0 - x) / y))
	tmp = 0.0
	if (y <= -1.0)
		tmp = t_0;
	elseif (y <= -5.4e-79)
		tmp = Float64(y * x);
	elseif (y <= 0.95)
		tmp = Float64(1.0 - y);
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = x + ((1.0 - x) / y);
	tmp = 0.0;
	if (y <= -1.0)
		tmp = t_0;
	elseif (y <= -5.4e-79)
		tmp = y * x;
	elseif (y <= 0.95)
		tmp = 1.0 - y;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(x + N[(N[(1.0 - x), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.0], t$95$0, If[LessEqual[y, -5.4e-79], N[(y * x), $MachinePrecision], If[LessEqual[y, 0.95], N[(1.0 - y), $MachinePrecision], t$95$0]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1 or 0.94999999999999996 < y

   1. Initial program 34.9%

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

      1. associate-/l* 55.9%

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

      2. +-commutative 55.9%

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

   3. Simplified 55.9%

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

   5. Taylor expanded in y around inf 97.7%

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

      1. associate--l+ 97.7%

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

      2. div-sub 97.7%

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

   7. Simplified 97.7%

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

   if -1 < y < -5.4000000000000004e-79

   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 67.2%

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

   6. Taylor expanded in y around 0 65.2%

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

      1. *-commutative 65.2%

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

   8. Simplified 65.2%

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

   if -5.4000000000000004e-79 < y < 0.94999999999999996

   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 0 100.0%

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

   6. Taylor expanded in x around 0 81.3%

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

Alternative 7: 99.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -2650000 \lor \neg \left(y \leq 560000\right):\\ \;\;\;\;x + \frac{\left(\frac{-1}{y} - -1\right) - x}{y}\\ \mathbf{else}:\\ \;\;\;\;1 + \left(1 - x\right) \cdot \frac{y}{-1 - y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= y -2650000.0) (not (<= y 560000.0)))
   (+ x (/ (- (- (/ -1.0 y) -1.0) x) y))
   (+ 1.0 (* (- 1.0 x) (/ y (- -1.0 y))))))

C

double code(double x, double y) {
	double tmp;
	if ((y <= -2650000.0) || !(y <= 560000.0)) {
		tmp = x + ((((-1.0 / y) - -1.0) - x) / y);
	} else {
		tmp = 1.0 + ((1.0 - x) * (y / (-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 <= (-2650000.0d0)) .or. (.not. (y <= 560000.0d0))) then
        tmp = x + (((((-1.0d0) / y) - (-1.0d0)) - x) / y)
    else
        tmp = 1.0d0 + ((1.0d0 - x) * (y / ((-1.0d0) - y)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((y <= -2650000.0) || !(y <= 560000.0)) {
		tmp = x + ((((-1.0 / y) - -1.0) - x) / y);
	} else {
		tmp = 1.0 + ((1.0 - x) * (y / (-1.0 - y)));
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (y <= -2650000.0) or not (y <= 560000.0):
		tmp = x + ((((-1.0 / y) - -1.0) - x) / y)
	else:
		tmp = 1.0 + ((1.0 - x) * (y / (-1.0 - y)))
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((y <= -2650000.0) || !(y <= 560000.0))
		tmp = Float64(x + Float64(Float64(Float64(Float64(-1.0 / y) - -1.0) - x) / y));
	else
		tmp = Float64(1.0 + Float64(Float64(1.0 - x) * Float64(y / Float64(-1.0 - y))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((y <= -2650000.0) || ~((y <= 560000.0)))
		tmp = x + ((((-1.0 / y) - -1.0) - x) / y);
	else
		tmp = 1.0 + ((1.0 - x) * (y / (-1.0 - y)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[y, -2650000.0], N[Not[LessEqual[y, 560000.0]], $MachinePrecision]], N[(x + N[(N[(N[(N[(-1.0 / y), $MachinePrecision] - -1.0), $MachinePrecision] - x), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], N[(1.0 + N[(N[(1.0 - x), $MachinePrecision] * N[(y / N[(-1.0 - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -2.65e6 or 5.6e5 < y

   1. Initial program 33.4%

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

      1. associate-/l* 55.0%

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

      2. +-commutative 55.0%

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

   3. Simplified 55.0%

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

   5. Taylor expanded in y around -inf 100.0%

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

   7. Simplified 100.0%

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

   8. Taylor expanded in x around 0 100.0%

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

   9. Taylor expanded in y around inf 99.8%

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

       1. associate--l+ 99.8%

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

       2. +-commutative 99.8%

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

       3. associate--r+ 99.8%

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

       4. div-sub 99.8%

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

       5. unpow2 99.8%

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

       6. associate-/r* 99.8%

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

       7. div-sub 99.8%

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

   11. Simplified 99.8%

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

   if -2.65e6 < y < 5.6e5

   1. Initial program 99.8%

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

      1. associate-/l* 99.8%

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

      2. +-commutative 99.8%

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

   3. Simplified 99.8%

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

4. Final simplification 99.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -2650000 \lor \neg \left(y \leq 560000\right):\\ \;\;\;\;x + \frac{\left(\frac{-1}{y} - -1\right) - x}{y}\\ \mathbf{else}:\\ \;\;\;\;1 + \left(1 - x\right) \cdot \frac{y}{-1 - y}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 99.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -3.6 \cdot 10^{+25} \lor \neg \left(y \leq 78000000\right):\\ \;\;\;\;x + \frac{1 - x}{y}\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{y \cdot \left(1 - x\right)}{-1 - y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= y -3.6e+25) (not (<= y 78000000.0)))
   (+ x (/ (- 1.0 x) y))
   (+ 1.0 (/ (* y (- 1.0 x)) (- -1.0 y)))))

C

double code(double x, double y) {
	double tmp;
	if ((y <= -3.6e+25) || !(y <= 78000000.0)) {
		tmp = x + ((1.0 - x) / y);
	} else {
		tmp = 1.0 + ((y * (1.0 - 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 <= (-3.6d+25)) .or. (.not. (y <= 78000000.0d0))) then
        tmp = x + ((1.0d0 - x) / y)
    else
        tmp = 1.0d0 + ((y * (1.0d0 - x)) / ((-1.0d0) - y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((y <= -3.6e+25) || !(y <= 78000000.0)) {
		tmp = x + ((1.0 - x) / y);
	} else {
		tmp = 1.0 + ((y * (1.0 - x)) / (-1.0 - y));
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (y <= -3.6e+25) or not (y <= 78000000.0):
		tmp = x + ((1.0 - x) / y)
	else:
		tmp = 1.0 + ((y * (1.0 - x)) / (-1.0 - y))
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((y <= -3.6e+25) || !(y <= 78000000.0))
		tmp = Float64(x + Float64(Float64(1.0 - x) / y));
	else
		tmp = Float64(1.0 + Float64(Float64(y * Float64(1.0 - x)) / Float64(-1.0 - y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((y <= -3.6e+25) || ~((y <= 78000000.0)))
		tmp = x + ((1.0 - x) / y);
	else
		tmp = 1.0 + ((y * (1.0 - x)) / (-1.0 - y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[y, -3.6e+25], N[Not[LessEqual[y, 78000000.0]], $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[(-1.0 - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -3.60000000000000015e25 or 7.8e7 < y

   1. Initial program 30.4%

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

      1. associate-/l* 53.1%

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

      2. +-commutative 53.1%

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

   3. Simplified 53.1%

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

   5. Taylor expanded in y around inf 99.8%

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

      1. associate--l+ 99.8%

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

      2. div-sub 99.8%

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

   7. Simplified 99.8%

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

   if -3.60000000000000015e25 < y < 7.8e7

   1. Initial program 99.4%

      \[1 - \frac{\left(1 - x\right) \cdot y}{y + 1} \]
   2. Add Preprocessing
3. Recombined 2 regimes into one program.

4. Final simplification 99.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.6 \cdot 10^{+25} \lor \neg \left(y \leq 78000000\right):\\ \;\;\;\;x + \frac{1 - x}{y}\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{y \cdot \left(1 - x\right)}{-1 - y}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 99.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -170000000 \lor \neg \left(y \leq 160000000\right):\\ \;\;\;\;x + \frac{1 - x}{y}\\ \mathbf{else}:\\ \;\;\;\;1 + \left(1 - x\right) \cdot \frac{y}{-1 - y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= y -170000000.0) (not (<= y 160000000.0)))
   (+ x (/ (- 1.0 x) y))
   (+ 1.0 (* (- 1.0 x) (/ y (- -1.0 y))))))

C

double code(double x, double y) {
	double tmp;
	if ((y <= -170000000.0) || !(y <= 160000000.0)) {
		tmp = x + ((1.0 - x) / y);
	} else {
		tmp = 1.0 + ((1.0 - x) * (y / (-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 <= (-170000000.0d0)) .or. (.not. (y <= 160000000.0d0))) then
        tmp = x + ((1.0d0 - x) / y)
    else
        tmp = 1.0d0 + ((1.0d0 - x) * (y / ((-1.0d0) - y)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((y <= -170000000.0) || !(y <= 160000000.0)) {
		tmp = x + ((1.0 - x) / y);
	} else {
		tmp = 1.0 + ((1.0 - x) * (y / (-1.0 - y)));
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (y <= -170000000.0) or not (y <= 160000000.0):
		tmp = x + ((1.0 - x) / y)
	else:
		tmp = 1.0 + ((1.0 - x) * (y / (-1.0 - y)))
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((y <= -170000000.0) || !(y <= 160000000.0))
		tmp = Float64(x + Float64(Float64(1.0 - x) / y));
	else
		tmp = Float64(1.0 + Float64(Float64(1.0 - x) * Float64(y / Float64(-1.0 - y))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((y <= -170000000.0) || ~((y <= 160000000.0)))
		tmp = x + ((1.0 - x) / y);
	else
		tmp = 1.0 + ((1.0 - x) * (y / (-1.0 - y)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[y, -170000000.0], N[Not[LessEqual[y, 160000000.0]], $MachinePrecision]], N[(x + N[(N[(1.0 - x), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], N[(1.0 + N[(N[(1.0 - x), $MachinePrecision] * N[(y / N[(-1.0 - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.7e8 or 1.6e8 < y

   1. Initial program 32.8%

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

      1. associate-/l* 54.7%

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

      2. +-commutative 54.7%

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

   3. Simplified 54.7%

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

   5. Taylor expanded in y around inf 99.8%

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

      1. associate--l+ 99.8%

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

      2. div-sub 99.8%

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

   7. Simplified 99.8%

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

   if -1.7e8 < y < 1.6e8

   1. Initial program 99.4%

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

      1. associate-/l* 99.4%

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

      2. +-commutative 99.4%

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

   3. Simplified 99.4%

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

4. Final simplification 99.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -170000000 \lor \neg \left(y \leq 160000000\right):\\ \;\;\;\;x + \frac{1 - x}{y}\\ \mathbf{else}:\\ \;\;\;\;1 + \left(1 - x\right) \cdot \frac{y}{-1 - y}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 73.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x - \frac{x}{y}\\ \mathbf{if}\;y \leq -1:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq -5.5 \cdot 10^{-79}:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;y \leq 270000000000:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (- x (/ x y))))
   (if (<= y -1.0)
     t_0
     (if (<= y -5.5e-79) (* y x) (if (<= y 270000000000.0) 1.0 t_0)))))

C

double code(double x, double y) {
	double t_0 = x - (x / y);
	double tmp;
	if (y <= -1.0) {
		tmp = t_0;
	} else if (y <= -5.5e-79) {
		tmp = y * x;
	} else if (y <= 270000000000.0) {
		tmp = 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 = x - (x / y)
    if (y <= (-1.0d0)) then
        tmp = t_0
    else if (y <= (-5.5d-79)) then
        tmp = y * x
    else if (y <= 270000000000.0d0) then
        tmp = 1.0d0
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double t_0 = x - (x / y);
	double tmp;
	if (y <= -1.0) {
		tmp = t_0;
	} else if (y <= -5.5e-79) {
		tmp = y * x;
	} else if (y <= 270000000000.0) {
		tmp = 1.0;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = x - (x / y)
	tmp = 0
	if y <= -1.0:
		tmp = t_0
	elif y <= -5.5e-79:
		tmp = y * x
	elif y <= 270000000000.0:
		tmp = 1.0
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y)
	t_0 = Float64(x - Float64(x / y))
	tmp = 0.0
	if (y <= -1.0)
		tmp = t_0;
	elseif (y <= -5.5e-79)
		tmp = Float64(y * x);
	elseif (y <= 270000000000.0)
		tmp = 1.0;
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = x - (x / y);
	tmp = 0.0;
	if (y <= -1.0)
		tmp = t_0;
	elseif (y <= -5.5e-79)
		tmp = y * x;
	elseif (y <= 270000000000.0)
		tmp = 1.0;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(x - N[(x / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.0], t$95$0, If[LessEqual[y, -5.5e-79], N[(y * x), $MachinePrecision], If[LessEqual[y, 270000000000.0], 1.0, t$95$0]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1 or 2.7e11 < y

   1. Initial program 34.1%

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

      1. associate-/l* 55.6%

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

      2. +-commutative 55.6%

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

   3. Simplified 55.6%

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

   5. Taylor expanded in y around inf 98.7%

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

      1. associate--l+ 98.7%

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

      2. div-sub 98.7%

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

   7. Simplified 98.7%

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

   8. Taylor expanded in x around -inf 74.6%

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

      1. associate-*r* 74.6%

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

      2. neg-mul-1 74.6%

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

      3. sub-neg 74.6%

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

      4. metadata-eval 74.6%

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

      5. distribute-lft-in 74.6%

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

      6. /-rgt-identity 74.6%

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

      7. distribute-neg-frac2 74.6%

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

      8. metadata-eval 74.6%

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

      9. times-frac 74.6%

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

      10. *-rgt-identity 74.6%

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

      11. neg-mul-1 74.6%

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

      12. distribute-neg-frac2 74.6%

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

      13. distribute-lft-neg-in 74.6%

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

      14. *-commutative 74.6%

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

      15. neg-mul-1 74.6%

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

      16. remove-double-neg 74.6%

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

      17. +-commutative 74.6%

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

      18. unsub-neg 74.6%

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

   10. Simplified 74.6%

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

   if -1 < y < -5.4999999999999997e-79

   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 67.2%

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

   6. Taylor expanded in y around 0 65.2%

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

      1. *-commutative 65.2%

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

   8. Simplified 65.2%

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

   if -5.4999999999999997e-79 < y < 2.7e11

   1. Initial program 99.1%

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

      1. associate-/l* 99.1%

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

      2. +-commutative 99.1%

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

   3. Simplified 99.1%

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

   5. Taylor expanded in y around 0 79.6%

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

Alternative 11: 98.4% 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 34.9%

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

      1. associate-/l* 55.9%

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

      2. +-commutative 55.9%

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

   3. Simplified 55.9%

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

   5. Taylor expanded in y around inf 97.7%

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

      1. associate--l+ 97.7%

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

      2. div-sub 97.7%

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

   7. Simplified 97.7%

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

   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* 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 99.7%

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

4. Final simplification 98.7%

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

Alternative 12: 73.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -5.5 \cdot 10^{-79}:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;y \leq 270000000000:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -1.0)
   x
   (if (<= y -5.5e-79) (* y x) (if (<= y 270000000000.0) 1.0 x))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -1.0) {
		tmp = x;
	} else if (y <= -5.5e-79) {
		tmp = y * x;
	} else if (y <= 270000000000.0) {
		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 <= (-5.5d-79)) then
        tmp = y * x
    else if (y <= 270000000000.0d0) 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 <= -5.5e-79) {
		tmp = y * x;
	} else if (y <= 270000000000.0) {
		tmp = 1.0;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -1.0:
		tmp = x
	elif y <= -5.5e-79:
		tmp = y * x
	elif y <= 270000000000.0:
		tmp = 1.0
	else:
		tmp = x
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -1.0)
		tmp = x;
	elseif (y <= -5.5e-79)
		tmp = Float64(y * x);
	elseif (y <= 270000000000.0)
		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 <= -5.5e-79)
		tmp = y * x;
	elseif (y <= 270000000000.0)
		tmp = 1.0;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -1.0], x, If[LessEqual[y, -5.5e-79], N[(y * x), $MachinePrecision], If[LessEqual[y, 270000000000.0], 1.0, x]]]

Derivation

1. Split input into 3 regimes

2. if y < -1 or 2.7e11 < y

   1. Initial program 34.1%

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

      1. associate-/l* 55.6%

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

      2. +-commutative 55.6%

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

   3. Simplified 55.6%

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

   5. Taylor expanded in y around inf 73.7%

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

   if -1 < y < -5.4999999999999997e-79

   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 67.2%

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

   6. Taylor expanded in y around 0 65.2%

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

      1. *-commutative 65.2%

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

   8. Simplified 65.2%

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

   if -5.4999999999999997e-79 < y < 2.7e11

   1. Initial program 99.1%

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

      1. associate-/l* 99.1%

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

      2. +-commutative 99.1%

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

   3. Simplified 99.1%

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

   5. Taylor expanded in y around 0 79.6%

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

Alternative 13: 73.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 270000000000:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -1.0) x (if (<= y 270000000000.0) 1.0 x)))

C

double code(double x, double y) {
	double tmp;
	if (y <= -1.0) {
		tmp = x;
	} else if (y <= 270000000000.0) {
		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 <= 270000000000.0d0) 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 <= 270000000000.0) {
		tmp = 1.0;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -1.0:
		tmp = x
	elif y <= 270000000000.0:
		tmp = 1.0
	else:
		tmp = x
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -1.0)
		tmp = x;
	elseif (y <= 270000000000.0)
		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 <= 270000000000.0)
		tmp = 1.0;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -1.0], x, If[LessEqual[y, 270000000000.0], 1.0, x]]

Derivation

1. Split input into 2 regimes

2. if y < -1 or 2.7e11 < y

   1. Initial program 34.1%

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

      1. associate-/l* 55.6%

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

      2. +-commutative 55.6%

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

   3. Simplified 55.6%

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

   5. Taylor expanded in y around inf 73.7%

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

   if -1 < y < 2.7e11

   1. Initial program 99.2%

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

      1. associate-/l* 99.2%

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

      2. +-commutative 99.2%

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

   3. Simplified 99.2%

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

   5. Taylor expanded in y around 0 73.4%

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

Alternative 14: 38.8% 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 69.2%

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

   1. associate-/l* 79.1%

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

   2. +-commutative 79.1%

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

3. Simplified 79.1%

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

5. Taylor expanded in y around 0 41.5%

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

Developer target: 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 2024089 
(FPCore (x y)
  :name "Diagrams.Trail:splitAtParam  from diagrams-lib-1.3.0.3, D"
  :precision binary64

  :alt
  (if (< y -3693.8482788297247) (- (/ 1.0 y) (- (/ x y) x)) (if (< y 6799310503.41891) (- 1.0 (/ (* (- 1.0 x) y) (+ y 1.0))) (- (/ 1.0 y) (- (/ x y) x))))

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