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

Percentage Accurate: 66.2% → 99.9%

Time: 11.1s

Alternatives: 13

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

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{1 - x}{y}\\ \mathbf{if}\;y \leq -11800:\\ \;\;\;\;x + \left(\frac{\frac{\left(x + -1\right) + t\_0}{y}}{y} + t\_0\right)\\ \mathbf{elif}\;y \leq 12500:\\ \;\;\;\;\mathsf{fma}\left(1 - x, \frac{y}{-1 - y}, 1\right)\\ \mathbf{else}:\\ \;\;\;\;x - \left(\left(\frac{-1}{y} + \frac{-1}{{y}^{3}}\right) - \left(\frac{x + -1}{{y}^{2}} - \left(\frac{x}{y} + \frac{x}{{y}^{3}}\right)\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (/ (- 1.0 x) y)))
   (if (<= y -11800.0)
     (+ x (+ (/ (/ (+ (+ x -1.0) t_0) y) y) t_0))
     (if (<= y 12500.0)
       (fma (- 1.0 x) (/ y (- -1.0 y)) 1.0)
       (-
        x
        (-
         (+ (/ -1.0 y) (/ -1.0 (pow y 3.0)))
         (- (/ (+ x -1.0) (pow y 2.0)) (+ (/ x y) (/ x (pow y 3.0))))))))))

C

double code(double x, double y) {
	double t_0 = (1.0 - x) / y;
	double tmp;
	if (y <= -11800.0) {
		tmp = x + (((((x + -1.0) + t_0) / y) / y) + t_0);
	} else if (y <= 12500.0) {
		tmp = fma((1.0 - x), (y / (-1.0 - y)), 1.0);
	} else {
		tmp = x - (((-1.0 / y) + (-1.0 / pow(y, 3.0))) - (((x + -1.0) / pow(y, 2.0)) - ((x / y) + (x / pow(y, 3.0)))));
	}
	return tmp;
}

Julia

function code(x, y)
	t_0 = Float64(Float64(1.0 - x) / y)
	tmp = 0.0
	if (y <= -11800.0)
		tmp = Float64(x + Float64(Float64(Float64(Float64(Float64(x + -1.0) + t_0) / y) / y) + t_0));
	elseif (y <= 12500.0)
		tmp = fma(Float64(1.0 - x), Float64(y / Float64(-1.0 - y)), 1.0);
	else
		tmp = Float64(x - Float64(Float64(Float64(-1.0 / y) + Float64(-1.0 / (y ^ 3.0))) - Float64(Float64(Float64(x + -1.0) / (y ^ 2.0)) - Float64(Float64(x / y) + Float64(x / (y ^ 3.0))))));
	end
	return tmp
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(N[(1.0 - x), $MachinePrecision] / y), $MachinePrecision]}, If[LessEqual[y, -11800.0], N[(x + N[(N[(N[(N[(N[(x + -1.0), $MachinePrecision] + t$95$0), $MachinePrecision] / y), $MachinePrecision] / y), $MachinePrecision] + t$95$0), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 12500.0], N[(N[(1.0 - x), $MachinePrecision] * N[(y / N[(-1.0 - y), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision], N[(x - N[(N[(N[(-1.0 / y), $MachinePrecision] + N[(-1.0 / N[Power[y, 3.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - N[(N[(N[(x + -1.0), $MachinePrecision] / N[Power[y, 2.0], $MachinePrecision]), $MachinePrecision] - N[(N[(x / y), $MachinePrecision] + N[(x / N[Power[y, 3.0], $MachinePrecision]), $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%

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

      1. div-sub 100.0%

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

      2. +-commutative 100.0%

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

      3. +-commutative 100.0%

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

      4. +-commutative 100.0%

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

   9. Applied egg-rr 100.0%

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

   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. sub-neg 100.0%

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

      2. +-commutative 100.0%

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

      3. associate-/l* 100.0%

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

      4. distribute-rgt-neg-in 100.0%

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

      5. fma-define 100.0%

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

      6. distribute-neg-frac2 100.0%

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

      7. +-commutative 100.0%

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

      8. distribute-neg-in 100.0%

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

      9. metadata-eval 100.0%

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

      10. unsub-neg 100.0%

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

   3. Simplified 100.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(1 - x, \frac{y}{-1 - y}, 1\right)} \]
   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. +-commutative 100.0%

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

      3. +-commutative 100.0%

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

      4. associate-+l+ 100.0%

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

      5. mul-1-neg 100.0%

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

      6. sub-neg 100.0%

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

      7. div-sub 100.0%

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

   7. Simplified 100.0%

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

4. Final simplification 100.0%

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

Alternative 2: 99.9% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{1 - x}{y}\\ \mathbf{if}\;y \leq -11800:\\ \;\;\;\;x + \left(\frac{\frac{\left(x + -1\right) + t\_0}{y}}{y} + t\_0\right)\\ \mathbf{elif}\;y \leq 250000:\\ \;\;\;\;\mathsf{fma}\left(1 - x, \frac{y}{-1 - y}, 1\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{\left(1 - x\right) + \frac{-1 + \frac{1}{y}}{y}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (/ (- 1.0 x) y)))
   (if (<= y -11800.0)
     (+ x (+ (/ (/ (+ (+ x -1.0) t_0) y) y) t_0))
     (if (<= y 250000.0)
       (fma (- 1.0 x) (/ y (- -1.0 y)) 1.0)
       (+ x (/ (+ (- 1.0 x) (/ (+ -1.0 (/ 1.0 y)) y)) y))))))

C

double code(double x, double y) {
	double t_0 = (1.0 - x) / y;
	double tmp;
	if (y <= -11800.0) {
		tmp = x + (((((x + -1.0) + t_0) / y) / y) + t_0);
	} else if (y <= 250000.0) {
		tmp = fma((1.0 - x), (y / (-1.0 - y)), 1.0);
	} else {
		tmp = x + (((1.0 - x) + ((-1.0 + (1.0 / y)) / y)) / y);
	}
	return tmp;
}

Julia

function code(x, y)
	t_0 = Float64(Float64(1.0 - x) / y)
	tmp = 0.0
	if (y <= -11800.0)
		tmp = Float64(x + Float64(Float64(Float64(Float64(Float64(x + -1.0) + t_0) / y) / y) + t_0));
	elseif (y <= 250000.0)
		tmp = fma(Float64(1.0 - x), Float64(y / Float64(-1.0 - y)), 1.0);
	else
		tmp = Float64(x + Float64(Float64(Float64(1.0 - x) + Float64(Float64(-1.0 + Float64(1.0 / y)) / y)) / y));
	end
	return tmp
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(N[(1.0 - x), $MachinePrecision] / y), $MachinePrecision]}, If[LessEqual[y, -11800.0], N[(x + N[(N[(N[(N[(N[(x + -1.0), $MachinePrecision] + t$95$0), $MachinePrecision] / y), $MachinePrecision] / y), $MachinePrecision] + t$95$0), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 250000.0], N[(N[(1.0 - x), $MachinePrecision] * N[(y / N[(-1.0 - y), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision], N[(x + N[(N[(N[(1.0 - x), $MachinePrecision] + N[(N[(-1.0 + N[(1.0 / y), $MachinePrecision]), $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%

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

      1. div-sub 100.0%

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

      2. +-commutative 100.0%

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

      3. +-commutative 100.0%

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

      4. +-commutative 100.0%

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

   9. Applied egg-rr 100.0%

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

   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. sub-neg 100.0%

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

      2. +-commutative 100.0%

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

      3. associate-/l* 100.0%

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

      4. distribute-rgt-neg-in 100.0%

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

      5. fma-define 100.0%

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

      6. distribute-neg-frac2 100.0%

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

      7. +-commutative 100.0%

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

      8. distribute-neg-in 100.0%

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

      9. metadata-eval 100.0%

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

      10. unsub-neg 100.0%

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

   3. Simplified 100.0%

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

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

   8. Taylor expanded in x around 0 100.0%

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

4. Final simplification 100.0%

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

Alternative 3: 99.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{1 - x}{y}\\ \mathbf{if}\;y \leq -11800:\\ \;\;\;\;x + \left(\frac{\frac{\left(x + -1\right) + t\_0}{y}}{y} + t\_0\right)\\ \mathbf{elif}\;y \leq 120000:\\ \;\;\;\;1 + \left(1 - x\right) \cdot \frac{y}{-1 - y}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{\left(1 - x\right) + \frac{-1 + \frac{1}{y}}{y}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (/ (- 1.0 x) y)))
   (if (<= y -11800.0)
     (+ x (+ (/ (/ (+ (+ x -1.0) t_0) y) y) t_0))
     (if (<= y 120000.0)
       (+ 1.0 (* (- 1.0 x) (/ y (- -1.0 y))))
       (+ x (/ (+ (- 1.0 x) (/ (+ -1.0 (/ 1.0 y)) y)) y))))))

C

double code(double x, double y) {
	double t_0 = (1.0 - x) / y;
	double tmp;
	if (y <= -11800.0) {
		tmp = x + (((((x + -1.0) + t_0) / y) / y) + t_0);
	} else if (y <= 120000.0) {
		tmp = 1.0 + ((1.0 - x) * (y / (-1.0 - y)));
	} else {
		tmp = x + (((1.0 - x) + ((-1.0 + (1.0 / y)) / 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 = (1.0d0 - x) / y
    if (y <= (-11800.0d0)) then
        tmp = x + (((((x + (-1.0d0)) + t_0) / y) / y) + t_0)
    else if (y <= 120000.0d0) then
        tmp = 1.0d0 + ((1.0d0 - x) * (y / ((-1.0d0) - y)))
    else
        tmp = x + (((1.0d0 - x) + (((-1.0d0) + (1.0d0 / y)) / y)) / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double t_0 = (1.0 - x) / y;
	double tmp;
	if (y <= -11800.0) {
		tmp = x + (((((x + -1.0) + t_0) / y) / y) + t_0);
	} else if (y <= 120000.0) {
		tmp = 1.0 + ((1.0 - x) * (y / (-1.0 - y)));
	} else {
		tmp = x + (((1.0 - x) + ((-1.0 + (1.0 / y)) / y)) / y);
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = (1.0 - x) / y
	tmp = 0
	if y <= -11800.0:
		tmp = x + (((((x + -1.0) + t_0) / y) / y) + t_0)
	elif y <= 120000.0:
		tmp = 1.0 + ((1.0 - x) * (y / (-1.0 - y)))
	else:
		tmp = x + (((1.0 - x) + ((-1.0 + (1.0 / y)) / y)) / y)
	return tmp

Julia

function code(x, y)
	t_0 = Float64(Float64(1.0 - x) / y)
	tmp = 0.0
	if (y <= -11800.0)
		tmp = Float64(x + Float64(Float64(Float64(Float64(Float64(x + -1.0) + t_0) / y) / y) + t_0));
	elseif (y <= 120000.0)
		tmp = Float64(1.0 + Float64(Float64(1.0 - x) * Float64(y / Float64(-1.0 - y))));
	else
		tmp = Float64(x + Float64(Float64(Float64(1.0 - x) + Float64(Float64(-1.0 + Float64(1.0 / y)) / y)) / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = (1.0 - x) / y;
	tmp = 0.0;
	if (y <= -11800.0)
		tmp = x + (((((x + -1.0) + t_0) / y) / y) + t_0);
	elseif (y <= 120000.0)
		tmp = 1.0 + ((1.0 - x) * (y / (-1.0 - y)));
	else
		tmp = x + (((1.0 - x) + ((-1.0 + (1.0 / y)) / y)) / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(N[(1.0 - x), $MachinePrecision] / y), $MachinePrecision]}, If[LessEqual[y, -11800.0], N[(x + N[(N[(N[(N[(N[(x + -1.0), $MachinePrecision] + t$95$0), $MachinePrecision] / y), $MachinePrecision] / y), $MachinePrecision] + t$95$0), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 120000.0], N[(1.0 + N[(N[(1.0 - x), $MachinePrecision] * N[(y / N[(-1.0 - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(N[(1.0 - x), $MachinePrecision] + N[(N[(-1.0 + N[(1.0 / y), $MachinePrecision]), $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%

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

      1. div-sub 100.0%

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

      2. +-commutative 100.0%

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

      3. +-commutative 100.0%

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

      4. +-commutative 100.0%

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

   9. Applied egg-rr 100.0%

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

   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%

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

   8. Taylor expanded in x around 0 100.0%

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

4. Final simplification 100.0%

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

Alternative 4: 99.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -420000 \lor \neg \left(y \leq 290000\right):\\ \;\;\;\;x + \frac{\left(1 - x\right) + \frac{-1 + \frac{1}{y}}{y}}{y}\\ \mathbf{else}:\\ \;\;\;\;1 + \left(1 - x\right) \cdot \frac{y}{-1 - y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= y -420000.0) (not (<= y 290000.0)))
   (+ x (/ (+ (- 1.0 x) (/ (+ -1.0 (/ 1.0 y)) y)) y))
   (+ 1.0 (* (- 1.0 x) (/ y (- -1.0 y))))))

C

double code(double x, double y) {
	double tmp;
	if ((y <= -420000.0) || !(y <= 290000.0)) {
		tmp = x + (((1.0 - x) + ((-1.0 + (1.0 / y)) / y)) / 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 <= (-420000.0d0)) .or. (.not. (y <= 290000.0d0))) then
        tmp = x + (((1.0d0 - x) + (((-1.0d0) + (1.0d0 / y)) / y)) / 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 <= -420000.0) || !(y <= 290000.0)) {
		tmp = x + (((1.0 - x) + ((-1.0 + (1.0 / y)) / y)) / y);
	} else {
		tmp = 1.0 + ((1.0 - x) * (y / (-1.0 - y)));
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (y <= -420000.0) or not (y <= 290000.0):
		tmp = x + (((1.0 - x) + ((-1.0 + (1.0 / y)) / y)) / y)
	else:
		tmp = 1.0 + ((1.0 - x) * (y / (-1.0 - y)))
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((y <= -420000.0) || !(y <= 290000.0))
		tmp = Float64(x + Float64(Float64(Float64(1.0 - x) + Float64(Float64(-1.0 + Float64(1.0 / y)) / y)) / 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 <= -420000.0) || ~((y <= 290000.0)))
		tmp = x + (((1.0 - x) + ((-1.0 + (1.0 / y)) / y)) / 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, -420000.0], N[Not[LessEqual[y, 290000.0]], $MachinePrecision]], N[(x + N[(N[(N[(1.0 - x), $MachinePrecision] + N[(N[(-1.0 + N[(1.0 / y), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $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 < -4.2e5 or 2.9e5 < 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%

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

   8. Taylor expanded in x around 0 100.0%

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

   if -4.2e5 < y < 2.9e5

   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%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -420000 \lor \neg \left(y \leq 290000\right):\\ \;\;\;\;x + \frac{\left(1 - x\right) + \frac{-1 + \frac{1}{y}}{y}}{y}\\ \mathbf{else}:\\ \;\;\;\;1 + \left(1 - x\right) \cdot \frac{y}{-1 - y}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 99.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{-1 + \frac{1}{y}}{y}\\ \mathbf{if}\;y \leq -175000:\\ \;\;\;\;x + \left(\frac{t\_0}{y} + \frac{1 - x}{y}\right)\\ \mathbf{elif}\;y \leq 320000:\\ \;\;\;\;1 + \left(1 - x\right) \cdot \frac{y}{-1 - y}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{\left(1 - x\right) + t\_0}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (/ (+ -1.0 (/ 1.0 y)) y)))
   (if (<= y -175000.0)
     (+ x (+ (/ t_0 y) (/ (- 1.0 x) y)))
     (if (<= y 320000.0)
       (+ 1.0 (* (- 1.0 x) (/ y (- -1.0 y))))
       (+ x (/ (+ (- 1.0 x) t_0) y))))))

C

double code(double x, double y) {
	double t_0 = (-1.0 + (1.0 / y)) / y;
	double tmp;
	if (y <= -175000.0) {
		tmp = x + ((t_0 / y) + ((1.0 - x) / y));
	} else if (y <= 320000.0) {
		tmp = 1.0 + ((1.0 - x) * (y / (-1.0 - y)));
	} else {
		tmp = x + (((1.0 - x) + t_0) / 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 = ((-1.0d0) + (1.0d0 / y)) / y
    if (y <= (-175000.0d0)) then
        tmp = x + ((t_0 / y) + ((1.0d0 - x) / y))
    else if (y <= 320000.0d0) then
        tmp = 1.0d0 + ((1.0d0 - x) * (y / ((-1.0d0) - y)))
    else
        tmp = x + (((1.0d0 - x) + t_0) / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double t_0 = (-1.0 + (1.0 / y)) / y;
	double tmp;
	if (y <= -175000.0) {
		tmp = x + ((t_0 / y) + ((1.0 - x) / y));
	} else if (y <= 320000.0) {
		tmp = 1.0 + ((1.0 - x) * (y / (-1.0 - y)));
	} else {
		tmp = x + (((1.0 - x) + t_0) / y);
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = (-1.0 + (1.0 / y)) / y
	tmp = 0
	if y <= -175000.0:
		tmp = x + ((t_0 / y) + ((1.0 - x) / y))
	elif y <= 320000.0:
		tmp = 1.0 + ((1.0 - x) * (y / (-1.0 - y)))
	else:
		tmp = x + (((1.0 - x) + t_0) / y)
	return tmp

Julia

function code(x, y)
	t_0 = Float64(Float64(-1.0 + Float64(1.0 / y)) / y)
	tmp = 0.0
	if (y <= -175000.0)
		tmp = Float64(x + Float64(Float64(t_0 / y) + Float64(Float64(1.0 - x) / y)));
	elseif (y <= 320000.0)
		tmp = Float64(1.0 + Float64(Float64(1.0 - x) * Float64(y / Float64(-1.0 - y))));
	else
		tmp = Float64(x + Float64(Float64(Float64(1.0 - x) + t_0) / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = (-1.0 + (1.0 / y)) / y;
	tmp = 0.0;
	if (y <= -175000.0)
		tmp = x + ((t_0 / y) + ((1.0 - x) / y));
	elseif (y <= 320000.0)
		tmp = 1.0 + ((1.0 - x) * (y / (-1.0 - y)));
	else
		tmp = x + (((1.0 - x) + t_0) / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(N[(-1.0 + N[(1.0 / y), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]}, If[LessEqual[y, -175000.0], N[(x + N[(N[(t$95$0 / y), $MachinePrecision] + N[(N[(1.0 - x), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 320000.0], N[(1.0 + N[(N[(1.0 - x), $MachinePrecision] * N[(y / N[(-1.0 - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(N[(1.0 - x), $MachinePrecision] + t$95$0), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if y < -175000

   1. Initial program 36.2%

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

      1. associate-/l* 57.2%

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

      2. +-commutative 57.2%

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

   3. Simplified 57.2%

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

   5. Taylor expanded in y around -inf 99.9%

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

   7. Simplified 99.9%

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

      1. div-sub 100.0%

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

      2. +-commutative 100.0%

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

      3. +-commutative 100.0%

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

      4. +-commutative 100.0%

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

   9. Applied egg-rr 100.0%

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

   10. Taylor expanded in x around 0 100.0%

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

   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

   if 3.2e5 < 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%

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

   8. Taylor expanded in x around 0 100.0%

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

4. Final simplification 100.0%

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

Alternative 6: 99.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -300000 \lor \neg \left(y \leq 340000\right):\\ \;\;\;\;x + \frac{\frac{x + -1}{y} + \left(1 - x\right)}{y}\\ \mathbf{else}:\\ \;\;\;\;1 + \left(1 - x\right) \cdot \frac{y}{-1 - y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= y -300000.0) (not (<= y 340000.0)))
   (+ x (/ (+ (/ (+ 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 <= -300000.0) || !(y <= 340000.0)) {
		tmp = x + ((((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 <= (-300000.0d0)) .or. (.not. (y <= 340000.0d0))) then
        tmp = x + ((((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 <= -300000.0) || !(y <= 340000.0)) {
		tmp = x + ((((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 <= -300000.0) or not (y <= 340000.0):
		tmp = x + ((((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 <= -300000.0) || !(y <= 340000.0))
		tmp = Float64(x + Float64(Float64(Float64(Float64(x + -1.0) / y) + 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 <= -300000.0) || ~((y <= 340000.0)))
		tmp = x + ((((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, -300000.0], N[Not[LessEqual[y, 340000.0]], $MachinePrecision]], N[(x + N[(N[(N[(N[(x + -1.0), $MachinePrecision] / y), $MachinePrecision] + N[(1.0 - x), $MachinePrecision]), $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 < -3e5 or 3.4e5 < 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 99.8%

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

   7. Simplified 99.8%

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

   if -3e5 < y < 3.4e5

   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%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -300000 \lor \neg \left(y \leq 340000\right):\\ \;\;\;\;x + \frac{\frac{x + -1}{y} + \left(1 - x\right)}{y}\\ \mathbf{else}:\\ \;\;\;\;1 + \left(1 - x\right) \cdot \frac{y}{-1 - y}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 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%

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

      3. sub-neg 99.8%

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

      4. +-commutative 99.8%

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

      5. neg-sub0 99.8%

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

      6. associate-+l- 99.8%

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

      7. neg-sub0 99.8%

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

      8. distribute-frac-neg 99.8%

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

      9. unsub-neg 99.8%

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

      10. sub-neg 99.8%

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

      11. metadata-eval 99.8%

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

   7. Simplified 99.8%

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

   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 8: 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 x around inf 53.3%

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

      1. *-commutative 53.3%

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

   7. Simplified 53.3%

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

   8. Taylor expanded in y around inf 74.6%

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

      1. mul-1-neg 74.6%

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

      2. 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 y around 0 97.9%

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

   6. Taylor expanded in x around inf 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. Final simplification 76.3%

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

Alternative 9: 86.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1 \lor \neg \left(y \leq 1.05\right):\\ \;\;\;\;x - \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;1 + y \cdot \left(x + -1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= y -1.0) (not (<= y 1.05)))
   (- x (/ x y))
   (+ 1.0 (* y (+ x -1.0)))))

C

double code(double x, double y) {
	double tmp;
	if ((y <= -1.0) || !(y <= 1.05)) {
		tmp = x - (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 <= 1.05d0))) then
        tmp = x - (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 <= 1.05)) {
		tmp = x - (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 <= 1.05):
		tmp = x - (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 <= 1.05))
		tmp = Float64(x - Float64(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 <= 1.05)))
		tmp = x - (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, 1.05]], $MachinePrecision]], N[(x - N[(x / 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 1.05000000000000004 < 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 x around inf 52.1%

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

      1. *-commutative 52.1%

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

   7. Simplified 52.1%

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

   8. Taylor expanded in y around inf 72.8%

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

      1. mul-1-neg 72.8%

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

      2. unsub-neg 72.8%

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

   10. Simplified 72.8%

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

   if -1 < y < 1.05000000000000004

   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 87.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1 \lor \neg \left(y \leq 1.05\right):\\ \;\;\;\;x - \frac{x}{y}\\ \mathbf{else}:\\ \;\;\;\;1 + y \cdot \left(x + -1\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 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%

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

      3. sub-neg 97.7%

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

      4. +-commutative 97.7%

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

      5. neg-sub0 97.7%

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

      6. associate-+l- 97.7%

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

      7. neg-sub0 97.7%

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

      8. distribute-frac-neg 97.7%

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

      9. unsub-neg 97.7%

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

      10. sub-neg 97.7%

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

      11. metadata-eval 97.7%

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

   7. Simplified 97.7%

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

   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 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 11: 73.0% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -5.3 \cdot 10^{-79}:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;y \leq 270000000000:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -1.0)
   x
   (if (<= y -5.3e-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 <= -5.3e-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 <= (-5.3d-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 <= -5.3e-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 <= -5.3e-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 <= -5.3e-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 <= -5.3e-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, -5.3e-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 < -5.2999999999999998e-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 y around 0 97.9%

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

   6. Taylor expanded in x around inf 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 -5.2999999999999998e-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. Final simplification 75.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -5.3 \cdot 10^{-79}:\\ \;\;\;\;y \cdot x\\ \mathbf{elif}\;y \leq 270000000000:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 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. Final simplification 73.5%

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

Alternative 13: 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. Final simplification 41.5%

   \[\leadsto 1 \]
7. 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))))