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

Percentage Accurate: 64.9% → 99.9%

Time: 10.4s

Alternatives: 13

Speedup: 2.1×

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: 64.9% 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, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{x + -1}{y \cdot y}\\ t_1 := \frac{1 - x}{y}\\ \mathbf{if}\;y \leq -11500:\\ \;\;\;\;\left(x + \left(\frac{1 - x}{{y}^{3}} + t_1\right)\right) + t_0\\ \mathbf{elif}\;y \leq 200000:\\ \;\;\;\;\mathsf{fma}\left(\frac{x + -1}{y + 1}, y, 1\right)\\ \mathbf{else}:\\ \;\;\;\;t_0 + \left(x + t_1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (/ (+ x -1.0) (* y y))) (t_1 (/ (- 1.0 x) y)))
   (if (<= y -11500.0)
     (+ (+ x (+ (/ (- 1.0 x) (pow y 3.0)) t_1)) t_0)
     (if (<= y 200000.0)
       (fma (/ (+ x -1.0) (+ y 1.0)) y 1.0)
       (+ t_0 (+ x t_1))))))

C

double code(double x, double y) {
	double t_0 = (x + -1.0) / (y * y);
	double t_1 = (1.0 - x) / y;
	double tmp;
	if (y <= -11500.0) {
		tmp = (x + (((1.0 - x) / pow(y, 3.0)) + t_1)) + t_0;
	} else if (y <= 200000.0) {
		tmp = fma(((x + -1.0) / (y + 1.0)), y, 1.0);
	} else {
		tmp = t_0 + (x + t_1);
	}
	return tmp;
}

Julia

function code(x, y)
	t_0 = Float64(Float64(x + -1.0) / Float64(y * y))
	t_1 = Float64(Float64(1.0 - x) / y)
	tmp = 0.0
	if (y <= -11500.0)
		tmp = Float64(Float64(x + Float64(Float64(Float64(1.0 - x) / (y ^ 3.0)) + t_1)) + t_0);
	elseif (y <= 200000.0)
		tmp = fma(Float64(Float64(x + -1.0) / Float64(y + 1.0)), y, 1.0);
	else
		tmp = Float64(t_0 + Float64(x + t_1));
	end
	return tmp
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(N[(x + -1.0), $MachinePrecision] / N[(y * y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(N[(1.0 - x), $MachinePrecision] / y), $MachinePrecision]}, If[LessEqual[y, -11500.0], N[(N[(x + N[(N[(N[(1.0 - x), $MachinePrecision] / N[Power[y, 3.0], $MachinePrecision]), $MachinePrecision] + t$95$1), $MachinePrecision]), $MachinePrecision] + t$95$0), $MachinePrecision], If[LessEqual[y, 200000.0], N[(N[(N[(x + -1.0), $MachinePrecision] / N[(y + 1.0), $MachinePrecision]), $MachinePrecision] * y + 1.0), $MachinePrecision], N[(t$95$0 + N[(x + t$95$1), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -11500

   1. Initial program 23.2%

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

      1. sub-neg 23.2%

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

      2. distribute-neg-frac 23.2%

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

      3. neg-mul-1 23.2%

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

      4. associate-*l/ 22.7%

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

      5. metadata-eval 22.7%

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

      6. associate-*l/ 22.7%

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

      7. associate-/r/ 22.7%

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

      8. metadata-eval 22.7%

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

      9. distribute-neg-frac 22.7%

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

      10. cancel-sign-sub-inv 22.7%

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

      11. associate-/r/ 23.1%

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

      12. associate-/r* 23.1%

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

      13. neg-mul-1 23.1%

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

      14. associate-/r/ 22.7%

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

      15. distribute-rgt-neg-in 22.7%

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

      16. associate-/r/ 23.1%

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

      17. distribute-neg-frac 23.1%

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

      18. metadata-eval 23.1%

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

      19. associate-/r/ 22.7%

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

   3. Simplified 49.6%

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

   4. Taylor expanded in y around -inf 100.0%

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

      1. +-commutative 100.0%

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

      2. associate--l+ 100.0%

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

   6. Simplified 100.0%

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

   if -11500 < y < 2e5

   1. Initial program 99.7%

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

      1. sub-neg 99.7%

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

      2. +-commutative 99.7%

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

      3. associate-/l* 99.7%

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

      4. distribute-neg-frac 99.7%

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

      5. associate-/r/ 99.7%

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

      6. fma-def 99.8%

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

      7. neg-sub0 99.8%

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

      8. associate--r- 99.8%

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

      9. metadata-eval 99.8%

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

      10. +-commutative 99.8%

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

      11. +-commutative 99.8%

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

   3. Simplified 99.8%

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

   if 2e5 < y

   1. Initial program 36.0%

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

      1. sub-neg 36.0%

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

      2. distribute-neg-frac 36.0%

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

      3. neg-mul-1 36.0%

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

      4. associate-*l/ 36.0%

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

      5. metadata-eval 36.0%

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

      6. associate-*l/ 36.0%

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

      7. associate-/r/ 36.0%

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

      8. metadata-eval 36.0%

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

      9. distribute-neg-frac 36.0%

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

      10. cancel-sign-sub-inv 36.0%

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

      11. associate-/r/ 35.9%

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

      12. associate-/r* 35.9%

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

      13. neg-mul-1 35.9%

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

      14. associate-/r/ 36.0%

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

      15. distribute-rgt-neg-in 36.0%

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

      16. associate-/r/ 35.9%

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

      17. distribute-neg-frac 35.9%

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

      18. metadata-eval 35.9%

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

      19. associate-/r/ 36.0%

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

   3. Simplified 55.7%

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

   4. Taylor expanded in y around -inf 100.0%

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

      1. +-commutative 100.0%

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

      2. associate--l+ 100.0%

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

      3. +-commutative 100.0%

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

      4. mul-1-neg 100.0%

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

      5. unsub-neg 100.0%

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

      6. sub-neg 100.0%

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

      7. metadata-eval 100.0%

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

      8. div-sub 100.0%

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

      9. sub-neg 100.0%

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

      10. metadata-eval 100.0%

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

      11. unpow2 100.0%

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

   6. Simplified 100.0%

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

4. Final simplification 99.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -11500:\\ \;\;\;\;\left(x + \left(\frac{1 - x}{{y}^{3}} + \frac{1 - x}{y}\right)\right) + \frac{x + -1}{y \cdot y}\\ \mathbf{elif}\;y \leq 200000:\\ \;\;\;\;\mathsf{fma}\left(\frac{x + -1}{y + 1}, y, 1\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{x + -1}{y \cdot y} + \left(x + \frac{1 - x}{y}\right)\\ \end{array} \]

Alternative 2: 99.9% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -290000 \lor \neg \left(y \leq 200000\right):\\ \;\;\;\;\frac{x + -1}{y \cdot y} + \left(x + \frac{1 - x}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{x + -1}{y + 1}, y, 1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= y -290000.0) (not (<= y 200000.0)))
   (+ (/ (+ x -1.0) (* y y)) (+ x (/ (- 1.0 x) y)))
   (fma (/ (+ x -1.0) (+ y 1.0)) y 1.0)))

C

double code(double x, double y) {
	double tmp;
	if ((y <= -290000.0) || !(y <= 200000.0)) {
		tmp = ((x + -1.0) / (y * y)) + (x + ((1.0 - x) / y));
	} else {
		tmp = fma(((x + -1.0) / (y + 1.0)), y, 1.0);
	}
	return tmp;
}

Julia

function code(x, y)
	tmp = 0.0
	if ((y <= -290000.0) || !(y <= 200000.0))
		tmp = Float64(Float64(Float64(x + -1.0) / Float64(y * y)) + Float64(x + Float64(Float64(1.0 - x) / y)));
	else
		tmp = fma(Float64(Float64(x + -1.0) / Float64(y + 1.0)), y, 1.0);
	end
	return tmp
end

Wolfram

code[x_, y_] := If[Or[LessEqual[y, -290000.0], N[Not[LessEqual[y, 200000.0]], $MachinePrecision]], N[(N[(N[(x + -1.0), $MachinePrecision] / N[(y * y), $MachinePrecision]), $MachinePrecision] + N[(x + N[(N[(1.0 - x), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(N[(x + -1.0), $MachinePrecision] / N[(y + 1.0), $MachinePrecision]), $MachinePrecision] * y + 1.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -2.9e5 or 2e5 < y

   1. Initial program 29.7%

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

      1. sub-neg 29.7%

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

      2. distribute-neg-frac 29.7%

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

      3. neg-mul-1 29.7%

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

      4. associate-*l/ 29.5%

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

      5. metadata-eval 29.5%

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

      6. associate-*l/ 29.5%

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

      7. associate-/r/ 29.5%

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

      8. metadata-eval 29.5%

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

      9. distribute-neg-frac 29.5%

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

      10. cancel-sign-sub-inv 29.5%

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

      11. associate-/r/ 29.6%

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

      12. associate-/r* 29.6%

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

      13. neg-mul-1 29.6%

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

      14. associate-/r/ 29.5%

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

      15. distribute-rgt-neg-in 29.5%

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

      16. associate-/r/ 29.6%

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

      17. distribute-neg-frac 29.6%

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

      18. metadata-eval 29.6%

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

      19. associate-/r/ 29.5%

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

   3. Simplified 52.7%

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

   4. Taylor expanded in y around -inf 99.8%

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

      1. +-commutative 99.8%

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

      2. associate--l+ 99.8%

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

      3. +-commutative 99.8%

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

      4. mul-1-neg 99.8%

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

      5. unsub-neg 99.8%

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

      6. sub-neg 99.8%

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

      7. metadata-eval 99.8%

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

      8. div-sub 99.8%

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

      9. sub-neg 99.8%

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

      10. metadata-eval 99.8%

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

      11. unpow2 99.8%

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

   6. Simplified 99.8%

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

   if -2.9e5 < y < 2e5

   1. Initial program 99.7%

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

      1. sub-neg 99.7%

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

      2. +-commutative 99.7%

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

      3. associate-/l* 99.7%

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

      4. distribute-neg-frac 99.7%

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

      5. associate-/r/ 99.7%

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

      6. fma-def 99.8%

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

      7. neg-sub0 99.8%

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

      8. associate--r- 99.8%

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

      9. metadata-eval 99.8%

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

      10. +-commutative 99.8%

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

      11. +-commutative 99.8%

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

   3. Simplified 99.8%

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

4. Final simplification 99.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -290000 \lor \neg \left(y \leq 200000\right):\\ \;\;\;\;\frac{x + -1}{y \cdot y} + \left(x + \frac{1 - x}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{x + -1}{y + 1}, y, 1\right)\\ \end{array} \]

Alternative 3: 99.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -410000 \lor \neg \left(y \leq 200000\right):\\ \;\;\;\;\frac{x + -1}{y \cdot y} + \left(x + \frac{1 - x}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;1 + y \cdot \frac{x + -1}{y + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= y -410000.0) (not (<= y 200000.0)))
   (+ (/ (+ x -1.0) (* y y)) (+ x (/ (- 1.0 x) y)))
   (+ 1.0 (* y (/ (+ x -1.0) (+ y 1.0))))))

C

double code(double x, double y) {
	double tmp;
	if ((y <= -410000.0) || !(y <= 200000.0)) {
		tmp = ((x + -1.0) / (y * y)) + (x + ((1.0 - x) / y));
	} else {
		tmp = 1.0 + (y * ((x + -1.0) / (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 <= (-410000.0d0)) .or. (.not. (y <= 200000.0d0))) then
        tmp = ((x + (-1.0d0)) / (y * y)) + (x + ((1.0d0 - x) / y))
    else
        tmp = 1.0d0 + (y * ((x + (-1.0d0)) / (y + 1.0d0)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((y <= -410000.0) || !(y <= 200000.0)) {
		tmp = ((x + -1.0) / (y * y)) + (x + ((1.0 - x) / y));
	} else {
		tmp = 1.0 + (y * ((x + -1.0) / (y + 1.0)));
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (y <= -410000.0) or not (y <= 200000.0):
		tmp = ((x + -1.0) / (y * y)) + (x + ((1.0 - x) / y))
	else:
		tmp = 1.0 + (y * ((x + -1.0) / (y + 1.0)))
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((y <= -410000.0) || !(y <= 200000.0))
		tmp = Float64(Float64(Float64(x + -1.0) / Float64(y * y)) + Float64(x + Float64(Float64(1.0 - x) / y)));
	else
		tmp = Float64(1.0 + Float64(y * Float64(Float64(x + -1.0) / Float64(y + 1.0))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((y <= -410000.0) || ~((y <= 200000.0)))
		tmp = ((x + -1.0) / (y * y)) + (x + ((1.0 - x) / y));
	else
		tmp = 1.0 + (y * ((x + -1.0) / (y + 1.0)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[y, -410000.0], N[Not[LessEqual[y, 200000.0]], $MachinePrecision]], N[(N[(N[(x + -1.0), $MachinePrecision] / N[(y * y), $MachinePrecision]), $MachinePrecision] + N[(x + N[(N[(1.0 - x), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(1.0 + N[(y * N[(N[(x + -1.0), $MachinePrecision] / N[(y + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -4.1e5 or 2e5 < y

   1. Initial program 29.7%

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

      1. sub-neg 29.7%

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

      2. distribute-neg-frac 29.7%

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

      3. neg-mul-1 29.7%

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

      4. associate-*l/ 29.5%

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

      5. metadata-eval 29.5%

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

      6. associate-*l/ 29.5%

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

      7. associate-/r/ 29.5%

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

      8. metadata-eval 29.5%

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

      9. distribute-neg-frac 29.5%

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

      10. cancel-sign-sub-inv 29.5%

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

      11. associate-/r/ 29.6%

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

      12. associate-/r* 29.6%

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

      13. neg-mul-1 29.6%

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

      14. associate-/r/ 29.5%

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

      15. distribute-rgt-neg-in 29.5%

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

      16. associate-/r/ 29.6%

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

      17. distribute-neg-frac 29.6%

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

      18. metadata-eval 29.6%

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

      19. associate-/r/ 29.5%

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

   3. Simplified 52.7%

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

   4. Taylor expanded in y around -inf 99.8%

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

      1. +-commutative 99.8%

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

      2. associate--l+ 99.8%

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

      3. +-commutative 99.8%

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

      4. mul-1-neg 99.8%

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

      5. unsub-neg 99.8%

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

      6. sub-neg 99.8%

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

      7. metadata-eval 99.8%

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

      8. div-sub 99.8%

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

      9. sub-neg 99.8%

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

      10. metadata-eval 99.8%

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

      11. unpow2 99.8%

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

   6. Simplified 99.8%

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

   if -4.1e5 < y < 2e5

   1. Initial program 99.7%

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

      1. sub-neg 99.7%

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

      2. distribute-neg-frac 99.7%

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

      3. neg-mul-1 99.7%

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

      4. associate-*l/ 99.7%

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

      5. metadata-eval 99.7%

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

      6. associate-*l/ 99.7%

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

      7. associate-/r/ 99.7%

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

      8. metadata-eval 99.7%

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

      9. distribute-neg-frac 99.7%

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

      10. cancel-sign-sub-inv 99.7%

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

      11. associate-/r/ 99.7%

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

      12. associate-/r* 99.7%

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

      13. neg-mul-1 99.7%

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

      14. associate-/r/ 99.7%

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

      15. distribute-rgt-neg-in 99.7%

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

      16. associate-/r/ 99.7%

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

      17. distribute-neg-frac 99.7%

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

      18. metadata-eval 99.7%

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

      19. associate-/r/ 99.7%

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

   3. Simplified 99.7%

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

4. Final simplification 99.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -410000 \lor \neg \left(y \leq 200000\right):\\ \;\;\;\;\frac{x + -1}{y \cdot y} + \left(x + \frac{1 - x}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;1 + y \cdot \frac{x + -1}{y + 1}\\ \end{array} \]

Alternative 4: 99.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -120000000000 \lor \neg \left(y \leq 24000000000\right):\\ \;\;\;\;x - \frac{-1}{y}\\ \mathbf{else}:\\ \;\;\;\;1 + y \cdot \frac{x + -1}{y + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= y -120000000000.0) (not (<= y 24000000000.0)))
   (- x (/ -1.0 y))
   (+ 1.0 (* y (/ (+ x -1.0) (+ y 1.0))))))

C

double code(double x, double y) {
	double tmp;
	if ((y <= -120000000000.0) || !(y <= 24000000000.0)) {
		tmp = x - (-1.0 / y);
	} else {
		tmp = 1.0 + (y * ((x + -1.0) / (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 <= (-120000000000.0d0)) .or. (.not. (y <= 24000000000.0d0))) then
        tmp = x - ((-1.0d0) / y)
    else
        tmp = 1.0d0 + (y * ((x + (-1.0d0)) / (y + 1.0d0)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((y <= -120000000000.0) || !(y <= 24000000000.0)) {
		tmp = x - (-1.0 / y);
	} else {
		tmp = 1.0 + (y * ((x + -1.0) / (y + 1.0)));
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (y <= -120000000000.0) or not (y <= 24000000000.0):
		tmp = x - (-1.0 / y)
	else:
		tmp = 1.0 + (y * ((x + -1.0) / (y + 1.0)))
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((y <= -120000000000.0) || !(y <= 24000000000.0))
		tmp = Float64(x - Float64(-1.0 / y));
	else
		tmp = Float64(1.0 + Float64(y * Float64(Float64(x + -1.0) / Float64(y + 1.0))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((y <= -120000000000.0) || ~((y <= 24000000000.0)))
		tmp = x - (-1.0 / y);
	else
		tmp = 1.0 + (y * ((x + -1.0) / (y + 1.0)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[y, -120000000000.0], N[Not[LessEqual[y, 24000000000.0]], $MachinePrecision]], N[(x - N[(-1.0 / y), $MachinePrecision]), $MachinePrecision], N[(1.0 + N[(y * N[(N[(x + -1.0), $MachinePrecision] / N[(y + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.2e11 or 2.4e10 < y

   1. Initial program 28.5%

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

      1. sub-neg 28.5%

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

      2. distribute-neg-frac 28.5%

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

      3. neg-mul-1 28.5%

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

      4. associate-*l/ 28.3%

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

      5. metadata-eval 28.3%

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

      6. associate-*l/ 28.3%

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

      7. associate-/r/ 28.3%

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

      8. metadata-eval 28.3%

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

      9. distribute-neg-frac 28.3%

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

      10. cancel-sign-sub-inv 28.3%

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

      11. associate-/r/ 28.4%

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

      12. associate-/r* 28.4%

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

      13. neg-mul-1 28.4%

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

      14. associate-/r/ 28.3%

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

      15. distribute-rgt-neg-in 28.3%

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

      16. associate-/r/ 28.4%

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

      17. distribute-neg-frac 28.4%

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

      18. metadata-eval 28.4%

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

      19. associate-/r/ 28.3%

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

   3. Simplified 52.0%

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

   4. Taylor expanded in y around inf 99.9%

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

      1. +-commutative 99.9%

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

      2. associate--l+ 99.9%

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

      3. div-sub 99.9%

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

      4. sub-neg 99.9%

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

      5. +-commutative 99.9%

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

      6. metadata-eval 99.9%

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

      7. distribute-neg-in 99.9%

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

      8. distribute-neg-frac 99.9%

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

      9. metadata-eval 99.9%

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

      10. sub-neg 99.9%

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

      11. unsub-neg 99.9%

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

      12. sub-neg 99.9%

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

      13. metadata-eval 99.9%

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

   6. Simplified 99.9%

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

   7. Taylor expanded in x around 0 99.9%

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

   if -1.2e11 < y < 2.4e10

   1. Initial program 99.3%

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

      1. sub-neg 99.3%

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

      2. distribute-neg-frac 99.3%

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

      3. neg-mul-1 99.3%

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

      4. associate-*l/ 99.2%

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

      5. metadata-eval 99.2%

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

      6. associate-*l/ 99.2%

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

      7. associate-/r/ 99.2%

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

      8. metadata-eval 99.2%

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

      9. distribute-neg-frac 99.2%

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

      10. cancel-sign-sub-inv 99.2%

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

      11. associate-/r/ 99.2%

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

      12. associate-/r* 99.2%

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

      13. neg-mul-1 99.2%

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

      14. associate-/r/ 99.2%

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

      15. distribute-rgt-neg-in 99.2%

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

      16. associate-/r/ 99.2%

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

      17. distribute-neg-frac 99.2%

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

      18. metadata-eval 99.2%

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

      19. associate-/r/ 99.2%

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

   3. Simplified 99.3%

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

4. Final simplification 99.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -120000000000 \lor \neg \left(y \leq 24000000000\right):\\ \;\;\;\;x - \frac{-1}{y}\\ \mathbf{else}:\\ \;\;\;\;1 + y \cdot \frac{x + -1}{y + 1}\\ \end{array} \]

Alternative 5: 99.6% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -31000000000 \lor \neg \left(y \leq 350000000000\right):\\ \;\;\;\;x - \frac{-1}{y}\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{y \cdot \left(x + -1\right)}{y + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= y -31000000000.0) (not (<= y 350000000000.0)))
   (- x (/ -1.0 y))
   (+ 1.0 (/ (* y (+ x -1.0)) (+ y 1.0)))))

C

double code(double x, double y) {
	double tmp;
	if ((y <= -31000000000.0) || !(y <= 350000000000.0)) {
		tmp = x - (-1.0 / y);
	} else {
		tmp = 1.0 + ((y * (x + -1.0)) / (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 <= (-31000000000.0d0)) .or. (.not. (y <= 350000000000.0d0))) then
        tmp = x - ((-1.0d0) / y)
    else
        tmp = 1.0d0 + ((y * (x + (-1.0d0))) / (y + 1.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((y <= -31000000000.0) || !(y <= 350000000000.0)) {
		tmp = x - (-1.0 / y);
	} else {
		tmp = 1.0 + ((y * (x + -1.0)) / (y + 1.0));
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (y <= -31000000000.0) or not (y <= 350000000000.0):
		tmp = x - (-1.0 / y)
	else:
		tmp = 1.0 + ((y * (x + -1.0)) / (y + 1.0))
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((y <= -31000000000.0) || !(y <= 350000000000.0))
		tmp = Float64(x - Float64(-1.0 / y));
	else
		tmp = Float64(1.0 + Float64(Float64(y * Float64(x + -1.0)) / Float64(y + 1.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((y <= -31000000000.0) || ~((y <= 350000000000.0)))
		tmp = x - (-1.0 / y);
	else
		tmp = 1.0 + ((y * (x + -1.0)) / (y + 1.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[y, -31000000000.0], N[Not[LessEqual[y, 350000000000.0]], $MachinePrecision]], N[(x - N[(-1.0 / y), $MachinePrecision]), $MachinePrecision], N[(1.0 + N[(N[(y * N[(x + -1.0), $MachinePrecision]), $MachinePrecision] / N[(y + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -3.1e10 or 3.5e11 < y

   1. Initial program 28.5%

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

      1. sub-neg 28.5%

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

      2. distribute-neg-frac 28.5%

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

      3. neg-mul-1 28.5%

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

      4. associate-*l/ 28.3%

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

      5. metadata-eval 28.3%

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

      6. associate-*l/ 28.3%

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

      7. associate-/r/ 28.3%

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

      8. metadata-eval 28.3%

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

      9. distribute-neg-frac 28.3%

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

      10. cancel-sign-sub-inv 28.3%

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

      11. associate-/r/ 28.4%

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

      12. associate-/r* 28.4%

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

      13. neg-mul-1 28.4%

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

      14. associate-/r/ 28.3%

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

      15. distribute-rgt-neg-in 28.3%

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

      16. associate-/r/ 28.4%

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

      17. distribute-neg-frac 28.4%

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

      18. metadata-eval 28.4%

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

      19. associate-/r/ 28.3%

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

   3. Simplified 52.0%

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

   4. Taylor expanded in y around inf 99.9%

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

      1. +-commutative 99.9%

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

      2. associate--l+ 99.9%

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

      3. div-sub 99.9%

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

      4. sub-neg 99.9%

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

      5. +-commutative 99.9%

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

      6. metadata-eval 99.9%

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

      7. distribute-neg-in 99.9%

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

      8. distribute-neg-frac 99.9%

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

      9. metadata-eval 99.9%

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

      10. sub-neg 99.9%

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

      11. unsub-neg 99.9%

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

      12. sub-neg 99.9%

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

      13. metadata-eval 99.9%

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

   6. Simplified 99.9%

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

   7. Taylor expanded in x around 0 99.9%

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

   if -3.1e10 < y < 3.5e11

   1. Initial program 99.3%

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

4. Final simplification 99.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -31000000000 \lor \neg \left(y \leq 350000000000\right):\\ \;\;\;\;x - \frac{-1}{y}\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{y \cdot \left(x + -1\right)}{y + 1}\\ \end{array} \]

Alternative 6: 98.6% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -62:\\ \;\;\;\;x - \frac{-1}{y}\\ \mathbf{elif}\;y \leq 1000:\\ \;\;\;\;1 - \frac{y \cdot x}{-1 - y}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{1 - x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -62.0)
   (- x (/ -1.0 y))
   (if (<= y 1000.0) (- 1.0 (/ (* y x) (- -1.0 y))) (+ x (/ (- 1.0 x) y)))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -62.0) {
		tmp = x - (-1.0 / y);
	} else if (y <= 1000.0) {
		tmp = 1.0 - ((y * x) / (-1.0 - y));
	} else {
		tmp = x + ((1.0 - x) / y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (y <= (-62.0d0)) then
        tmp = x - ((-1.0d0) / y)
    else if (y <= 1000.0d0) then
        tmp = 1.0d0 - ((y * x) / ((-1.0d0) - y))
    else
        tmp = x + ((1.0d0 - x) / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (y <= -62.0) {
		tmp = x - (-1.0 / y);
	} else if (y <= 1000.0) {
		tmp = 1.0 - ((y * x) / (-1.0 - y));
	} else {
		tmp = x + ((1.0 - x) / y);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -62.0:
		tmp = x - (-1.0 / y)
	elif y <= 1000.0:
		tmp = 1.0 - ((y * x) / (-1.0 - y))
	else:
		tmp = x + ((1.0 - x) / y)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -62.0)
		tmp = Float64(x - Float64(-1.0 / y));
	elseif (y <= 1000.0)
		tmp = Float64(1.0 - Float64(Float64(y * x) / Float64(-1.0 - y)));
	else
		tmp = Float64(x + Float64(Float64(1.0 - x) / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -62.0)
		tmp = x - (-1.0 / y);
	elseif (y <= 1000.0)
		tmp = 1.0 - ((y * x) / (-1.0 - y));
	else
		tmp = x + ((1.0 - x) / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -62.0], N[(x - N[(-1.0 / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1000.0], N[(1.0 - N[(N[(y * x), $MachinePrecision] / N[(-1.0 - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(1.0 - x), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -62

   1. Initial program 23.2%

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

      1. sub-neg 23.2%

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

      2. distribute-neg-frac 23.2%

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

      3. neg-mul-1 23.2%

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

      4. associate-*l/ 22.7%

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

      5. metadata-eval 22.7%

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

      6. associate-*l/ 22.7%

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

      7. associate-/r/ 22.7%

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

      8. metadata-eval 22.7%

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

      9. distribute-neg-frac 22.7%

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

      10. cancel-sign-sub-inv 22.7%

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

      11. associate-/r/ 23.1%

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

      12. associate-/r* 23.1%

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

      13. neg-mul-1 23.1%

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

      14. associate-/r/ 22.7%

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

      15. distribute-rgt-neg-in 22.7%

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

      16. associate-/r/ 23.1%

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

      17. distribute-neg-frac 23.1%

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

      18. metadata-eval 23.1%

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

      19. associate-/r/ 22.7%

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

   3. Simplified 49.6%

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

   4. Taylor expanded in y around inf 98.5%

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

      1. +-commutative 98.5%

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

      2. associate--l+ 98.5%

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

      3. div-sub 98.5%

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

      4. sub-neg 98.5%

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

      5. +-commutative 98.5%

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

      6. metadata-eval 98.5%

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

      7. distribute-neg-in 98.5%

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

      8. distribute-neg-frac 98.5%

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

      9. metadata-eval 98.5%

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

      10. sub-neg 98.5%

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

      11. unsub-neg 98.5%

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

      12. sub-neg 98.5%

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

      13. metadata-eval 98.5%

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

   6. Simplified 98.5%

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

   7. Taylor expanded in x around 0 98.5%

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

   if -62 < y < 1e3

   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. distribute-neg-frac 100.0%

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

      3. neg-mul-1 100.0%

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

      4. associate-*l/ 100.0%

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

      5. metadata-eval 100.0%

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

      6. associate-*l/ 100.0%

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

      7. associate-/r/ 100.0%

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

      8. metadata-eval 100.0%

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

      9. distribute-neg-frac 100.0%

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

      10. cancel-sign-sub-inv 100.0%

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

      11. associate-/r/ 99.9%

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

      12. associate-/r* 99.9%

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

      13. neg-mul-1 99.9%

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

      14. associate-/r/ 100.0%

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

      15. distribute-rgt-neg-in 100.0%

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

      16. associate-/r/ 99.9%

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

      17. distribute-neg-frac 99.9%

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

      18. metadata-eval 99.9%

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

      19. associate-/r/ 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in x around inf 99.0%

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

      1. neg-mul-1 99.0%

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

      2. distribute-neg-frac 99.0%

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

   6. Simplified 99.0%

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

      1. associate-*l/ 99.0%

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

      2. frac-2neg 99.0%

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

      3. add-sqr-sqrt 61.0%

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

      4. sqrt-unprod 73.9%

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

      5. sqr-neg 73.9%

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

      6. sqrt-unprod 26.7%

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

      7. add-sqr-sqrt 73.2%

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

      8. *-commutative 73.2%

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

      9. distribute-rgt-neg-in 73.2%

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

      10. add-sqr-sqrt 46.5%

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

      11. sqrt-unprod 72.7%

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

      12. sqr-neg 72.7%

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

      13. sqrt-unprod 37.9%

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

      14. add-sqr-sqrt 99.0%

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

      15. *-commutative 99.0%

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

   8. Applied egg-rr 99.0%

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

      1. *-commutative 99.0%

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

      2. distribute-neg-in 99.0%

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

      3. metadata-eval 99.0%

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

      4. unsub-neg 99.0%

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

   10. Simplified 99.0%

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

   if 1e3 < y

   1. Initial program 37.5%

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

      1. sub-neg 37.5%

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

      2. distribute-neg-frac 37.5%

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

      3. neg-mul-1 37.5%

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

      4. associate-*l/ 37.5%

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

      5. metadata-eval 37.5%

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

      6. associate-*l/ 37.5%

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

      7. associate-/r/ 37.5%

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

      8. metadata-eval 37.5%

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

      9. distribute-neg-frac 37.5%

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

      10. cancel-sign-sub-inv 37.5%

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

      11. associate-/r/ 37.4%

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

      12. associate-/r* 37.4%

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

      13. neg-mul-1 37.4%

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

      14. associate-/r/ 37.5%

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

      15. distribute-rgt-neg-in 37.5%

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

      16. associate-/r/ 37.4%

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

      17. distribute-neg-frac 37.4%

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

      18. metadata-eval 37.4%

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

      19. associate-/r/ 37.5%

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

   3. Simplified 56.5%

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

   4. Taylor expanded in y around inf 97.4%

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

      1. +-commutative 97.4%

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

      2. associate--l+ 97.4%

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

      3. div-sub 97.4%

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

      4. sub-neg 97.4%

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

      5. +-commutative 97.4%

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

      6. metadata-eval 97.4%

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

      7. distribute-neg-in 97.4%

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

      8. distribute-neg-frac 97.4%

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

      9. metadata-eval 97.4%

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

      10. sub-neg 97.4%

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

      11. unsub-neg 97.4%

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

      12. sub-neg 97.4%

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

      13. metadata-eval 97.4%

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

   6. Simplified 97.4%

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

4. Final simplification 98.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -62:\\ \;\;\;\;x - \frac{-1}{y}\\ \mathbf{elif}\;y \leq 1000:\\ \;\;\;\;1 - \frac{y \cdot x}{-1 - y}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{1 - x}{y}\\ \end{array} \]

Alternative 7: 98.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1 \lor \neg \left(y \leq 0.8\right):\\ \;\;\;\;x - \frac{-1}{y}\\ \mathbf{else}:\\ \;\;\;\;1 + \left(y \cdot x - y\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= y -1.0) (not (<= y 0.8))) (- x (/ -1.0 y)) (+ 1.0 (- (* y x) y))))

C

double code(double x, double y) {
	double tmp;
	if ((y <= -1.0) || !(y <= 0.8)) {
		tmp = x - (-1.0 / y);
	} else {
		tmp = 1.0 + ((y * x) - y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if ((y <= (-1.0d0)) .or. (.not. (y <= 0.8d0))) then
        tmp = x - ((-1.0d0) / y)
    else
        tmp = 1.0d0 + ((y * x) - y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((y <= -1.0) || !(y <= 0.8)) {
		tmp = x - (-1.0 / y);
	} else {
		tmp = 1.0 + ((y * x) - y);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (y <= -1.0) or not (y <= 0.8):
		tmp = x - (-1.0 / y)
	else:
		tmp = 1.0 + ((y * x) - y)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((y <= -1.0) || !(y <= 0.8))
		tmp = Float64(x - Float64(-1.0 / y));
	else
		tmp = Float64(1.0 + Float64(Float64(y * x) - y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((y <= -1.0) || ~((y <= 0.8)))
		tmp = x - (-1.0 / y);
	else
		tmp = 1.0 + ((y * x) - y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[y, -1.0], N[Not[LessEqual[y, 0.8]], $MachinePrecision]], N[(x - N[(-1.0 / y), $MachinePrecision]), $MachinePrecision], N[(1.0 + N[(N[(y * x), $MachinePrecision] - y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1 or 0.80000000000000004 < y

   1. Initial program 30.6%

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

      1. sub-neg 30.6%

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

      2. distribute-neg-frac 30.6%

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

      3. neg-mul-1 30.6%

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

      4. associate-*l/ 30.3%

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

      5. metadata-eval 30.3%

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

      6. associate-*l/ 30.3%

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

      7. associate-/r/ 30.3%

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

      8. metadata-eval 30.3%

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

      9. distribute-neg-frac 30.3%

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

      10. cancel-sign-sub-inv 30.3%

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

      11. associate-/r/ 30.5%

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

      12. associate-/r* 30.5%

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

      13. neg-mul-1 30.5%

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

      14. associate-/r/ 30.3%

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

      15. distribute-rgt-neg-in 30.3%

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

      16. associate-/r/ 30.5%

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

      17. distribute-neg-frac 30.5%

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

      18. metadata-eval 30.5%

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

      19. associate-/r/ 30.3%

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

   3. Simplified 53.2%

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

   4. Taylor expanded in y around inf 97.9%

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

      1. +-commutative 97.9%

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

      2. associate--l+ 97.9%

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

      3. div-sub 97.9%

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

      4. sub-neg 97.9%

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

      5. +-commutative 97.9%

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

      6. metadata-eval 97.9%

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

      7. distribute-neg-in 97.9%

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

      8. distribute-neg-frac 97.9%

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

      9. metadata-eval 97.9%

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

      10. sub-neg 97.9%

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

      11. unsub-neg 97.9%

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

      12. sub-neg 97.9%

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

      13. metadata-eval 97.9%

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

   6. Simplified 97.9%

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

   7. Taylor expanded in x around 0 97.7%

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

   if -1 < y < 0.80000000000000004

   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. distribute-neg-frac 100.0%

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

      3. neg-mul-1 100.0%

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

      4. associate-*l/ 100.0%

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

      5. metadata-eval 100.0%

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

      6. associate-*l/ 100.0%

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

      7. associate-/r/ 100.0%

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

      8. metadata-eval 100.0%

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

      9. distribute-neg-frac 100.0%

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

      10. cancel-sign-sub-inv 100.0%

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

      11. associate-/r/ 99.9%

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

      12. associate-/r* 99.9%

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

      13. neg-mul-1 99.9%

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

      14. associate-/r/ 100.0%

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

      15. distribute-rgt-neg-in 100.0%

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

      16. associate-/r/ 99.9%

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

      17. distribute-neg-frac 99.9%

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

      18. metadata-eval 99.9%

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

      19. associate-/r/ 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in y around 0 98.1%

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

      1. sub-neg 98.1%

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

      2. distribute-lft-in 98.1%

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

      3. distribute-rgt-neg-out 98.1%

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

      4. unsub-neg 98.1%

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

      5. *-rgt-identity 98.1%

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

   6. Simplified 98.1%

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

4. Final simplification 97.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1 \lor \neg \left(y \leq 0.8\right):\\ \;\;\;\;x - \frac{-1}{y}\\ \mathbf{else}:\\ \;\;\;\;1 + \left(y \cdot x - y\right)\\ \end{array} \]

Alternative 8: 98.3% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 3 regimes

2. if y < -1

   1. Initial program 23.2%

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

      1. sub-neg 23.2%

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

      2. distribute-neg-frac 23.2%

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

      3. neg-mul-1 23.2%

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

      4. associate-*l/ 22.7%

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

      5. metadata-eval 22.7%

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

      6. associate-*l/ 22.7%

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

      7. associate-/r/ 22.7%

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

      8. metadata-eval 22.7%

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

      9. distribute-neg-frac 22.7%

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

      10. cancel-sign-sub-inv 22.7%

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

      11. associate-/r/ 23.1%

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

      12. associate-/r* 23.1%

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

      13. neg-mul-1 23.1%

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

      14. associate-/r/ 22.7%

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

      15. distribute-rgt-neg-in 22.7%

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

      16. associate-/r/ 23.1%

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

      17. distribute-neg-frac 23.1%

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

      18. metadata-eval 23.1%

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

      19. associate-/r/ 22.7%

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

   3. Simplified 49.6%

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

   4. Taylor expanded in y around inf 98.5%

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

      1. +-commutative 98.5%

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

      2. associate--l+ 98.5%

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

      3. div-sub 98.5%

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

      4. sub-neg 98.5%

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

      5. +-commutative 98.5%

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

      6. metadata-eval 98.5%

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

      7. distribute-neg-in 98.5%

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

      8. distribute-neg-frac 98.5%

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

      9. metadata-eval 98.5%

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

      10. sub-neg 98.5%

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

      11. unsub-neg 98.5%

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

      12. sub-neg 98.5%

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

      13. metadata-eval 98.5%

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

   6. Simplified 98.5%

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

   7. Taylor expanded in x around 0 98.5%

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

   if -1 < y < 1

   1. Initial program 100.0%

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

      1. sub-neg 100.0%

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

      2. distribute-neg-frac 100.0%

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

      3. neg-mul-1 100.0%

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

      4. associate-*l/ 100.0%

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

      5. metadata-eval 100.0%

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

      6. associate-*l/ 100.0%

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

      7. associate-/r/ 100.0%

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

      8. metadata-eval 100.0%

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

      9. distribute-neg-frac 100.0%

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

      10. cancel-sign-sub-inv 100.0%

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

      11. associate-/r/ 99.9%

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

      12. associate-/r* 99.9%

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

      13. neg-mul-1 99.9%

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

      14. associate-/r/ 100.0%

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

      15. distribute-rgt-neg-in 100.0%

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

      16. associate-/r/ 99.9%

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

      17. distribute-neg-frac 99.9%

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

      18. metadata-eval 99.9%

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

      19. associate-/r/ 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in y around 0 98.1%

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

      1. sub-neg 98.1%

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

      2. distribute-lft-in 98.1%

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

      3. distribute-rgt-neg-out 98.1%

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

      4. unsub-neg 98.1%

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

      5. *-rgt-identity 98.1%

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

   6. Simplified 98.1%

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

   if 1 < y

   1. Initial program 37.5%

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

      1. sub-neg 37.5%

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

      2. distribute-neg-frac 37.5%

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

      3. neg-mul-1 37.5%

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

      4. associate-*l/ 37.5%

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

      5. metadata-eval 37.5%

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

      6. associate-*l/ 37.5%

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

      7. associate-/r/ 37.5%

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

      8. metadata-eval 37.5%

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

      9. distribute-neg-frac 37.5%

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

      10. cancel-sign-sub-inv 37.5%

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

      11. associate-/r/ 37.4%

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

      12. associate-/r* 37.4%

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

      13. neg-mul-1 37.4%

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

      14. associate-/r/ 37.5%

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

      15. distribute-rgt-neg-in 37.5%

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

      16. associate-/r/ 37.4%

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

      17. distribute-neg-frac 37.4%

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

      18. metadata-eval 37.4%

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

      19. associate-/r/ 37.5%

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

   3. Simplified 56.5%

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

   4. Taylor expanded in y around inf 97.4%

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

      1. +-commutative 97.4%

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

      2. associate--l+ 97.4%

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

      3. div-sub 97.4%

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

      4. sub-neg 97.4%

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

      5. +-commutative 97.4%

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

      6. metadata-eval 97.4%

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

      7. distribute-neg-in 97.4%

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

      8. distribute-neg-frac 97.4%

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

      9. metadata-eval 97.4%

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

      10. sub-neg 97.4%

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

      11. unsub-neg 97.4%

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

      12. sub-neg 97.4%

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

      13. metadata-eval 97.4%

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

   6. Simplified 97.4%

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

4. Final simplification 98.0%

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

Alternative 9: 86.5% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1 \lor \neg \left(y \leq 0.048\right):\\ \;\;\;\;x - \frac{-1}{y}\\ \mathbf{else}:\\ \;\;\;\;1 - y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= y -1.0) (not (<= y 0.048))) (- x (/ -1.0 y)) (- 1.0 y)))

C

double code(double x, double y) {
	double tmp;
	if ((y <= -1.0) || !(y <= 0.048)) {
		tmp = x - (-1.0 / y);
	} else {
		tmp = 1.0 - y;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if ((y <= (-1.0d0)) .or. (.not. (y <= 0.048d0))) then
        tmp = x - ((-1.0d0) / y)
    else
        tmp = 1.0d0 - y
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((y <= -1.0) || !(y <= 0.048)) {
		tmp = x - (-1.0 / y);
	} else {
		tmp = 1.0 - y;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (y <= -1.0) or not (y <= 0.048):
		tmp = x - (-1.0 / y)
	else:
		tmp = 1.0 - y
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((y <= -1.0) || !(y <= 0.048))
		tmp = Float64(x - Float64(-1.0 / y));
	else
		tmp = Float64(1.0 - y);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((y <= -1.0) || ~((y <= 0.048)))
		tmp = x - (-1.0 / y);
	else
		tmp = 1.0 - y;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[y, -1.0], N[Not[LessEqual[y, 0.048]], $MachinePrecision]], N[(x - N[(-1.0 / y), $MachinePrecision]), $MachinePrecision], N[(1.0 - y), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1 or 0.048000000000000001 < y

   1. Initial program 30.6%

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

      1. sub-neg 30.6%

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

      2. distribute-neg-frac 30.6%

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

      3. neg-mul-1 30.6%

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

      4. associate-*l/ 30.3%

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

      5. metadata-eval 30.3%

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

      6. associate-*l/ 30.3%

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

      7. associate-/r/ 30.3%

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

      8. metadata-eval 30.3%

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

      9. distribute-neg-frac 30.3%

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

      10. cancel-sign-sub-inv 30.3%

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

      11. associate-/r/ 30.5%

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

      12. associate-/r* 30.5%

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

      13. neg-mul-1 30.5%

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

      14. associate-/r/ 30.3%

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

      15. distribute-rgt-neg-in 30.3%

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

      16. associate-/r/ 30.5%

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

      17. distribute-neg-frac 30.5%

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

      18. metadata-eval 30.5%

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

      19. associate-/r/ 30.3%

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

   3. Simplified 53.2%

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

   4. Taylor expanded in y around inf 97.9%

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

      1. +-commutative 97.9%

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

      2. associate--l+ 97.9%

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

      3. div-sub 97.9%

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

      4. sub-neg 97.9%

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

      5. +-commutative 97.9%

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

      6. metadata-eval 97.9%

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

      7. distribute-neg-in 97.9%

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

      8. distribute-neg-frac 97.9%

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

      9. metadata-eval 97.9%

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

      10. sub-neg 97.9%

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

      11. unsub-neg 97.9%

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

      12. sub-neg 97.9%

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

      13. metadata-eval 97.9%

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

   6. Simplified 97.9%

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

   7. Taylor expanded in x around 0 97.7%

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

   if -1 < y < 0.048000000000000001

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 74.6%

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

   3. Taylor expanded in y around 0 74.4%

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

      1. neg-mul-1 74.4%

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

      2. unsub-neg 74.4%

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

   5. Simplified 74.4%

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

4. Final simplification 85.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1 \lor \neg \left(y \leq 0.048\right):\\ \;\;\;\;x - \frac{-1}{y}\\ \mathbf{else}:\\ \;\;\;\;1 - y\\ \end{array} \]

Alternative 10: 97.9% accurate, 1.2× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

2. if y < -1 or 1 < y

   1. Initial program 30.6%

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

      1. sub-neg 30.6%

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

      2. distribute-neg-frac 30.6%

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

      3. neg-mul-1 30.6%

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

      4. associate-*l/ 30.3%

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

      5. metadata-eval 30.3%

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

      6. associate-*l/ 30.3%

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

      7. associate-/r/ 30.3%

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

      8. metadata-eval 30.3%

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

      9. distribute-neg-frac 30.3%

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

      10. cancel-sign-sub-inv 30.3%

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

      11. associate-/r/ 30.5%

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

      12. associate-/r* 30.5%

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

      13. neg-mul-1 30.5%

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

      14. associate-/r/ 30.3%

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

      15. distribute-rgt-neg-in 30.3%

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

      16. associate-/r/ 30.5%

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

      17. distribute-neg-frac 30.5%

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

      18. metadata-eval 30.5%

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

      19. associate-/r/ 30.3%

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

   3. Simplified 53.2%

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

   4. Taylor expanded in y around inf 97.9%

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

      1. +-commutative 97.9%

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

      2. associate--l+ 97.9%

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

      3. div-sub 97.9%

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

      4. sub-neg 97.9%

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

      5. +-commutative 97.9%

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

      6. metadata-eval 97.9%

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

      7. distribute-neg-in 97.9%

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

      8. distribute-neg-frac 97.9%

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

      9. metadata-eval 97.9%

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

      10. sub-neg 97.9%

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

      11. unsub-neg 97.9%

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

      12. sub-neg 97.9%

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

      13. metadata-eval 97.9%

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

   6. Simplified 97.9%

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

   7. Taylor expanded in x around 0 97.7%

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

   if -1 < y < 1

   1. Initial program 100.0%

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

      1. sub-neg 100.0%

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

      2. distribute-neg-frac 100.0%

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

      3. neg-mul-1 100.0%

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

      4. associate-*l/ 100.0%

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

      5. metadata-eval 100.0%

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

      6. associate-*l/ 100.0%

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

      7. associate-/r/ 100.0%

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

      8. metadata-eval 100.0%

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

      9. distribute-neg-frac 100.0%

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

      10. cancel-sign-sub-inv 100.0%

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

      11. associate-/r/ 99.9%

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

      12. associate-/r* 99.9%

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

      13. neg-mul-1 99.9%

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

      14. associate-/r/ 100.0%

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

      15. distribute-rgt-neg-in 100.0%

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

      16. associate-/r/ 99.9%

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

      17. distribute-neg-frac 99.9%

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

      18. metadata-eval 99.9%

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

      19. associate-/r/ 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in x around inf 99.0%

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

      1. neg-mul-1 99.0%

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

      2. distribute-neg-frac 99.0%

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

   6. Simplified 99.0%

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

   7. Taylor expanded in y around 0 97.6%

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

      1. associate-*r* 97.6%

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

      2. neg-mul-1 97.6%

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

   9. Simplified 97.6%

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

4. Final simplification 97.7%

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

Alternative 11: 73.8% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 0.96:\\ \;\;\;\;1 - y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -1.0) x (if (<= y 0.96) (- 1.0 y) x)))

C

double code(double x, double y) {
	double tmp;
	if (y <= -1.0) {
		tmp = x;
	} else if (y <= 0.96) {
		tmp = 1.0 - y;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (y <= (-1.0d0)) then
        tmp = x
    else if (y <= 0.96d0) then
        tmp = 1.0d0 - y
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (y <= -1.0) {
		tmp = x;
	} else if (y <= 0.96) {
		tmp = 1.0 - y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -1.0:
		tmp = x
	elif y <= 0.96:
		tmp = 1.0 - y
	else:
		tmp = x
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -1.0)
		tmp = x;
	elseif (y <= 0.96)
		tmp = Float64(1.0 - y);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -1.0)
		tmp = x;
	elseif (y <= 0.96)
		tmp = 1.0 - y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -1.0], x, If[LessEqual[y, 0.96], N[(1.0 - y), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if y < -1 or 0.95999999999999996 < y

   1. Initial program 30.6%

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

      1. sub-neg 30.6%

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

      2. distribute-neg-frac 30.6%

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

      3. neg-mul-1 30.6%

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

      4. associate-*l/ 30.3%

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

      5. metadata-eval 30.3%

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

      6. associate-*l/ 30.3%

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

      7. associate-/r/ 30.3%

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

      8. metadata-eval 30.3%

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

      9. distribute-neg-frac 30.3%

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

      10. cancel-sign-sub-inv 30.3%

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

      11. associate-/r/ 30.5%

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

      12. associate-/r* 30.5%

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

      13. neg-mul-1 30.5%

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

      14. associate-/r/ 30.3%

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

      15. distribute-rgt-neg-in 30.3%

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

      16. associate-/r/ 30.5%

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

      17. distribute-neg-frac 30.5%

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

      18. metadata-eval 30.5%

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

      19. associate-/r/ 30.3%

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

   3. Simplified 53.2%

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

   4. Taylor expanded in y around inf 73.6%

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

   if -1 < y < 0.95999999999999996

   1. Initial program 100.0%

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

   2. Taylor expanded in x around 0 74.6%

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

   3. Taylor expanded in y around 0 74.4%

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

      1. neg-mul-1 74.4%

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

      2. unsub-neg 74.4%

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

   5. Simplified 74.4%

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

4. Final simplification 74.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 0.96:\\ \;\;\;\;1 - y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 12: 73.5% accurate, 2.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 25000:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (if (<= y -1.0) x (if (<= y 25000.0) 1.0 x)))

C

double code(double x, double y) {
	double tmp;
	if (y <= -1.0) {
		tmp = x;
	} else if (y <= 25000.0) {
		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 <= 25000.0d0) 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 <= 25000.0) {
		tmp = 1.0;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -1.0:
		tmp = x
	elif y <= 25000.0:
		tmp = 1.0
	else:
		tmp = x
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -1.0)
		tmp = x;
	elseif (y <= 25000.0)
		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 <= 25000.0)
		tmp = 1.0;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -1.0], x, If[LessEqual[y, 25000.0], 1.0, x]]

Derivation

1. Split input into 2 regimes

2. if y < -1 or 25000 < y

   1. Initial program 29.7%

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

      1. sub-neg 29.7%

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

      2. distribute-neg-frac 29.7%

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

      3. neg-mul-1 29.7%

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

      4. associate-*l/ 29.5%

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

      5. metadata-eval 29.5%

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

      6. associate-*l/ 29.5%

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

      7. associate-/r/ 29.5%

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

      8. metadata-eval 29.5%

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

      9. distribute-neg-frac 29.5%

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

      10. cancel-sign-sub-inv 29.5%

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

      11. associate-/r/ 29.6%

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

      12. associate-/r* 29.6%

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

      13. neg-mul-1 29.6%

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

      14. associate-/r/ 29.5%

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

      15. distribute-rgt-neg-in 29.5%

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

      16. associate-/r/ 29.6%

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

      17. distribute-neg-frac 29.6%

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

      18. metadata-eval 29.6%

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

      19. associate-/r/ 29.5%

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

   3. Simplified 52.7%

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

   4. Taylor expanded in y around inf 74.8%

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

   if -1 < y < 25000

   1. Initial program 99.7%

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

      1. sub-neg 99.7%

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

      2. distribute-neg-frac 99.7%

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

      3. neg-mul-1 99.7%

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

      4. associate-*l/ 99.7%

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

      5. metadata-eval 99.7%

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

      6. associate-*l/ 99.7%

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

      7. associate-/r/ 99.7%

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

      8. metadata-eval 99.7%

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

      9. distribute-neg-frac 99.7%

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

      10. cancel-sign-sub-inv 99.7%

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

      11. associate-/r/ 99.7%

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

      12. associate-/r* 99.7%

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

      13. neg-mul-1 99.7%

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

      14. associate-/r/ 99.7%

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

      15. distribute-rgt-neg-in 99.7%

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

      16. associate-/r/ 99.7%

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

      17. distribute-neg-frac 99.7%

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

      18. metadata-eval 99.7%

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

      19. associate-/r/ 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in y around 0 73.0%

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

4. Final simplification 73.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 25000:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 13: 38.6% accurate, 11.0× speedup

Math

\[\begin{array}{l} \\ 1 \end{array} \]

FPCore

(FPCore (x y) :precision binary64 1.0)

C

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

Fortran

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

Java

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

Python

def code(x, y):
	return 1.0

Julia

function code(x, y)
	return 1.0
end

MATLAB

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

Wolfram

code[x_, y_] := 1.0

Derivation

1. Initial program 66.4%

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

   1. sub-neg 66.4%

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

   2. distribute-neg-frac 66.4%

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

   3. neg-mul-1 66.4%

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

   4. associate-*l/ 66.3%

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

   5. metadata-eval 66.3%

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

   6. associate-*l/ 66.3%

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

   7. associate-/r/ 66.3%

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

   8. metadata-eval 66.3%

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

   9. distribute-neg-frac 66.3%

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

   10. cancel-sign-sub-inv 66.3%

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

   11. associate-/r/ 66.3%

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

   12. associate-/r* 66.3%

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

   13. neg-mul-1 66.3%

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

   14. associate-/r/ 66.3%

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

   15. distribute-rgt-neg-in 66.3%

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

   16. associate-/r/ 66.3%

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

   17. distribute-neg-frac 66.3%

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

   18. metadata-eval 66.3%

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

   19. associate-/r/ 66.3%

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

3. Simplified 77.3%

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

4. Taylor expanded in y around 0 40.1%

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

5. Final simplification 40.1%

   \[\leadsto 1 \]

Developer target: 99.6% accurate, 0.7× 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 2023182 
(FPCore (x y)
  :name "Diagrams.Trail:splitAtParam  from diagrams-lib-1.3.0.3, D"
  :precision binary64

  :herbie-target
  (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))))