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

Percentage Accurate: 65.6% → 99.6%

Time: 7.7s

Alternatives: 9

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: 65.6% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{x + -1}{y}\\ \mathbf{if}\;y \leq -9 \cdot 10^{+16}:\\ \;\;\;\;x - \frac{-1}{y}\\ \mathbf{elif}\;y \leq 250000:\\ \;\;\;\;1 + y \cdot \frac{x + -1}{y + 1}\\ \mathbf{else}:\\ \;\;\;\;\left(x - t_0\right) + \frac{t_0}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (/ (+ x -1.0) y)))
   (if (<= y -9e+16)
     (- x (/ -1.0 y))
     (if (<= y 250000.0)
       (+ 1.0 (* y (/ (+ x -1.0) (+ y 1.0))))
       (+ (- x t_0) (/ t_0 y))))))

C

double code(double x, double y) {
	double t_0 = (x + -1.0) / y;
	double tmp;
	if (y <= -9e+16) {
		tmp = x - (-1.0 / y);
	} else if (y <= 250000.0) {
		tmp = 1.0 + (y * ((x + -1.0) / (y + 1.0)));
	} else {
		tmp = (x - t_0) + (t_0 / y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: t_0
    real(8) :: tmp
    t_0 = (x + (-1.0d0)) / y
    if (y <= (-9d+16)) then
        tmp = x - ((-1.0d0) / y)
    else if (y <= 250000.0d0) then
        tmp = 1.0d0 + (y * ((x + (-1.0d0)) / (y + 1.0d0)))
    else
        tmp = (x - t_0) + (t_0 / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double t_0 = (x + -1.0) / y;
	double tmp;
	if (y <= -9e+16) {
		tmp = x - (-1.0 / y);
	} else if (y <= 250000.0) {
		tmp = 1.0 + (y * ((x + -1.0) / (y + 1.0)));
	} else {
		tmp = (x - t_0) + (t_0 / y);
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = (x + -1.0) / y
	tmp = 0
	if y <= -9e+16:
		tmp = x - (-1.0 / y)
	elif y <= 250000.0:
		tmp = 1.0 + (y * ((x + -1.0) / (y + 1.0)))
	else:
		tmp = (x - t_0) + (t_0 / y)
	return tmp

Julia

function code(x, y)
	t_0 = Float64(Float64(x + -1.0) / y)
	tmp = 0.0
	if (y <= -9e+16)
		tmp = Float64(x - Float64(-1.0 / y));
	elseif (y <= 250000.0)
		tmp = Float64(1.0 + Float64(y * Float64(Float64(x + -1.0) / Float64(y + 1.0))));
	else
		tmp = Float64(Float64(x - t_0) + Float64(t_0 / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = (x + -1.0) / y;
	tmp = 0.0;
	if (y <= -9e+16)
		tmp = x - (-1.0 / y);
	elseif (y <= 250000.0)
		tmp = 1.0 + (y * ((x + -1.0) / (y + 1.0)));
	else
		tmp = (x - t_0) + (t_0 / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(N[(x + -1.0), $MachinePrecision] / y), $MachinePrecision]}, If[LessEqual[y, -9e+16], N[(x - N[(-1.0 / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 250000.0], N[(1.0 + N[(y * N[(N[(x + -1.0), $MachinePrecision] / N[(y + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[(x - t$95$0), $MachinePrecision] + N[(t$95$0 / y), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if y < -9e16

   1. Initial program 34.0%

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

      1. sub-neg 34.0%

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

      2. distribute-neg-frac 34.0%

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

      3. neg-mul-1 34.0%

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

      4. associate-*l/ 34.0%

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

      5. metadata-eval 34.0%

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

      6. associate-*l/ 34.0%

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

      7. associate-/r/ 34.0%

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

      8. metadata-eval 34.0%

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

      9. distribute-neg-frac 34.0%

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

      10. cancel-sign-sub-inv 34.0%

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

      11. associate-/r/ 34.0%

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

      12. associate-/r* 34.0%

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

      13. neg-mul-1 34.0%

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

      14. associate-/r/ 34.0%

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

      15. distribute-rgt-neg-in 34.0%

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

      16. associate-/r/ 34.0%

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

      17. distribute-neg-frac 34.0%

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

      18. metadata-eval 34.0%

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

      19. associate-/r/ 34.0%

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

   3. Simplified 51.7%

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

   4. Taylor expanded in y around inf 100.0%

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

      1. +-commutative 100.0%

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

      2. associate--l+ 100.0%

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

      3. div-sub 100.0%

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

      4. sub-neg 100.0%

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

      5. +-commutative 100.0%

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

      6. metadata-eval 100.0%

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

      7. distribute-neg-in 100.0%

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

      8. distribute-neg-frac 100.0%

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

      9. metadata-eval 100.0%

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

      10. sub-neg 100.0%

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

      11. unsub-neg 100.0%

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

      12. sub-neg 100.0%

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

      13. metadata-eval 100.0%

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

   6. Simplified 100.0%

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

   7. Taylor expanded in x around 0 100.0%

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

   if -9e16 < y < 2.5e5

   1. Initial program 99.9%

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

      1. sub-neg 99.9%

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

      2. distribute-neg-frac 99.9%

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

      3. neg-mul-1 99.9%

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

      4. associate-*l/ 99.9%

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

      5. metadata-eval 99.9%

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

      6. associate-*l/ 99.9%

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

      7. associate-/r/ 99.9%

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

      8. metadata-eval 99.9%

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

      9. distribute-neg-frac 99.9%

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

      10. cancel-sign-sub-inv 99.9%

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

      11. associate-/r/ 99.8%

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

      12. associate-/r* 99.8%

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

      13. neg-mul-1 99.8%

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

      14. associate-/r/ 99.9%

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

      15. distribute-rgt-neg-in 99.9%

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

      16. associate-/r/ 99.8%

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

      17. distribute-neg-frac 99.8%

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

      18. metadata-eval 99.8%

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

      19. associate-/r/ 99.9%

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

   3. Simplified 99.9%

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

   if 2.5e5 < y

   1. Initial program 29.0%

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

      1. sub-neg 29.0%

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

      2. distribute-neg-frac 29.0%

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

      3. neg-mul-1 29.0%

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

      4. associate-*l/ 29.2%

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

      5. metadata-eval 29.2%

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

      6. associate-*l/ 29.2%

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

      7. associate-/r/ 29.2%

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

      8. metadata-eval 29.2%

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

      9. distribute-neg-frac 29.2%

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

      10. cancel-sign-sub-inv 29.2%

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

      11. associate-/r/ 28.9%

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

      12. associate-/r* 28.9%

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

      13. neg-mul-1 28.9%

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

      14. associate-/r/ 29.2%

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

      15. distribute-rgt-neg-in 29.2%

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

      16. associate-/r/ 28.9%

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

      17. distribute-neg-frac 28.9%

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

      18. metadata-eval 28.9%

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

      19. associate-/r/ 29.2%

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

   3. Simplified 62.5%

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

   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%

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

      12. associate-/r* 100.0%

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

   6. Simplified 100.0%

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

4. Final simplification 99.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -9 \cdot 10^{+16}:\\ \;\;\;\;x - \frac{-1}{y}\\ \mathbf{elif}\;y \leq 250000:\\ \;\;\;\;1 + y \cdot \frac{x + -1}{y + 1}\\ \mathbf{else}:\\ \;\;\;\;\left(x - \frac{x + -1}{y}\right) + \frac{\frac{x + -1}{y}}{y}\\ \end{array} \]

Alternative 2: 97.0% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{y}{y + 1}\\ \mathsf{fma}\left(x, t_0, \left(y + 1\right) \cdot \frac{t_0}{y + y \cdot y}\right) \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (/ y (+ y 1.0))))
   (fma x t_0 (* (+ y 1.0) (/ t_0 (+ y (* y y)))))))

C

double code(double x, double y) {
	double t_0 = y / (y + 1.0);
	return fma(x, t_0, ((y + 1.0) * (t_0 / (y + (y * y)))));
}

Julia

function code(x, y)
	t_0 = Float64(y / Float64(y + 1.0))
	return fma(x, t_0, Float64(Float64(y + 1.0) * Float64(t_0 / Float64(y + Float64(y * y)))))
end

Wolfram

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

Derivation

1. Initial program 68.6%

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

   1. sub-neg 68.6%

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

   2. distribute-neg-frac 68.6%

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

   3. neg-mul-1 68.6%

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

   4. associate-*l/ 68.7%

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

   5. metadata-eval 68.7%

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

   6. associate-*l/ 68.7%

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

   7. associate-/r/ 68.7%

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

   8. metadata-eval 68.7%

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

   9. distribute-neg-frac 68.7%

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

   10. cancel-sign-sub-inv 68.7%

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

   11. associate-/r/ 68.6%

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

   12. associate-/r* 68.6%

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

   13. neg-mul-1 68.6%

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

   14. associate-/r/ 68.7%

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

   15. distribute-rgt-neg-in 68.7%

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

   16. associate-/r/ 68.6%

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

   17. distribute-neg-frac 68.6%

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

   18. metadata-eval 68.6%

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

   19. associate-/r/ 68.7%

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

3. Simplified 80.3%

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

   1. associate-/r/ 80.3%

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

   2. add-exp-log 58.2%

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

   3. sub-neg 58.2%

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

   4. log1p-def 58.2%

      \[\leadsto e^{\color{blue}{\mathsf{log1p}\left(-\frac{1 - x}{\frac{1 + y}{y}}\right)}} \]

   5. div-inv 58.2%

      \[\leadsto e^{\mathsf{log1p}\left(-\color{blue}{\left(1 - x\right) \cdot \frac{1}{\frac{1 + y}{y}}}\right)} \]

   6. clear-num 58.2%

      \[\leadsto e^{\mathsf{log1p}\left(-\left(1 - x\right) \cdot \color{blue}{\frac{y}{1 + y}}\right)} \]

   7. distribute-lft-neg-in 58.2%

      \[\leadsto e^{\mathsf{log1p}\left(\color{blue}{\left(-\left(1 - x\right)\right) \cdot \frac{y}{1 + y}}\right)} \]

5. Applied egg-rr 58.2%

   \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(\left(-\left(1 - x\right)\right) \cdot \frac{y}{1 + y}\right)}} \]
6. Step-by-step derivation

   1. neg-sub0 58.2%

      \[\leadsto e^{\mathsf{log1p}\left(\color{blue}{\left(0 - \left(1 - x\right)\right)} \cdot \frac{y}{1 + y}\right)} \]

   2. metadata-eval 58.2%

      \[\leadsto e^{\mathsf{log1p}\left(\left(\color{blue}{\log 1} - \left(1 - x\right)\right) \cdot \frac{y}{1 + y}\right)} \]

   3. associate--r- 58.2%

      \[\leadsto e^{\mathsf{log1p}\left(\color{blue}{\left(\left(\log 1 - 1\right) + x\right)} \cdot \frac{y}{1 + y}\right)} \]

   4. metadata-eval 58.2%

      \[\leadsto e^{\mathsf{log1p}\left(\left(\left(\color{blue}{0} - 1\right) + x\right) \cdot \frac{y}{1 + y}\right)} \]

   5. metadata-eval 58.2%

      \[\leadsto e^{\mathsf{log1p}\left(\left(\color{blue}{-1} + x\right) \cdot \frac{y}{1 + y}\right)} \]

   6. +-commutative 58.2%

      \[\leadsto e^{\mathsf{log1p}\left(\color{blue}{\left(x + -1\right)} \cdot \frac{y}{1 + y}\right)} \]

   7. associate-*r/ 53.8%

      \[\leadsto e^{\mathsf{log1p}\left(\color{blue}{\frac{\left(x + -1\right) \cdot y}{1 + y}}\right)} \]

   8. associate-*l/ 58.3%

      \[\leadsto e^{\mathsf{log1p}\left(\color{blue}{\frac{x + -1}{1 + y} \cdot y}\right)} \]

   9. *-commutative 58.3%

      \[\leadsto e^{\mathsf{log1p}\left(\color{blue}{y \cdot \frac{x + -1}{1 + y}}\right)} \]

7. Simplified 58.3%

   \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(y \cdot \frac{x + -1}{1 + y}\right)}} \]

8. Taylor expanded in x around inf 21.9%

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

   1. +-commutative 21.9%

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

   2. exp-sum 21.9%

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

   3. fma-def 21.9%

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

   4. mul-1-neg 21.9%

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

   5. log-rec 21.9%

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

   6. remove-double-neg 21.9%

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

   7. rem-exp-log 22.7%

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

   8. +-commutative 22.7%

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

   9. rem-exp-log 22.9%

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

10. Simplified 66.5%

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

    1. expm1-log1p-u 66.6%

       \[\leadsto \mathsf{fma}\left(x, \frac{y}{y + 1}, \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{1 - \frac{y}{y + 1}}{y} \cdot \frac{\left(\left(y + 1\right) \cdot x\right) \cdot \frac{y}{y + 1}}{x}\right)\right)}\right) \]

    2. expm1-udef 66.5%

       \[\leadsto \mathsf{fma}\left(x, \frac{y}{y + 1}, \color{blue}{e^{\mathsf{log1p}\left(\frac{1 - \frac{y}{y + 1}}{y} \cdot \frac{\left(\left(y + 1\right) \cdot x\right) \cdot \frac{y}{y + 1}}{x}\right)} - 1}\right) \]

    3. *-commutative 66.5%

       \[\leadsto \mathsf{fma}\left(x, \frac{y}{y + 1}, e^{\mathsf{log1p}\left(\color{blue}{\frac{\left(\left(y + 1\right) \cdot x\right) \cdot \frac{y}{y + 1}}{x} \cdot \frac{1 - \frac{y}{y + 1}}{y}}\right)} - 1\right) \]

    4. associate-/l* 68.8%

       \[\leadsto \mathsf{fma}\left(x, \frac{y}{y + 1}, e^{\mathsf{log1p}\left(\color{blue}{\frac{\left(y + 1\right) \cdot x}{\frac{x}{\frac{y}{y + 1}}}} \cdot \frac{1 - \frac{y}{y + 1}}{y}\right)} - 1\right) \]

    5. +-commutative 68.8%

       \[\leadsto \mathsf{fma}\left(x, \frac{y}{y + 1}, e^{\mathsf{log1p}\left(\frac{\color{blue}{\left(1 + y\right)} \cdot x}{\frac{x}{\frac{y}{y + 1}}} \cdot \frac{1 - \frac{y}{y + 1}}{y}\right)} - 1\right) \]

    6. +-commutative 68.8%

       \[\leadsto \mathsf{fma}\left(x, \frac{y}{y + 1}, e^{\mathsf{log1p}\left(\frac{\left(1 + y\right) \cdot x}{\frac{x}{\frac{y}{\color{blue}{1 + y}}}} \cdot \frac{1 - \frac{y}{y + 1}}{y}\right)} - 1\right) \]

    7. +-commutative 68.8%

       \[\leadsto \mathsf{fma}\left(x, \frac{y}{y + 1}, e^{\mathsf{log1p}\left(\frac{\left(1 + y\right) \cdot x}{\frac{x}{\frac{y}{1 + y}}} \cdot \frac{1 - \frac{y}{\color{blue}{1 + y}}}{y}\right)} - 1\right) \]

12. Applied egg-rr 68.8%

    \[\leadsto \mathsf{fma}\left(x, \frac{y}{y + 1}, \color{blue}{e^{\mathsf{log1p}\left(\frac{\left(1 + y\right) \cdot x}{\frac{x}{\frac{y}{1 + y}}} \cdot \frac{1 - \frac{y}{1 + y}}{y}\right)} - 1}\right) \]
13. Step-by-step derivation

    1. expm1-def 68.8%

       \[\leadsto \mathsf{fma}\left(x, \frac{y}{y + 1}, \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{\left(1 + y\right) \cdot x}{\frac{x}{\frac{y}{1 + y}}} \cdot \frac{1 - \frac{y}{1 + y}}{y}\right)\right)}\right) \]

    2. expm1-log1p 68.7%

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

    3. associate-/r/ 76.0%

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

    4. *-commutative 76.0%

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

    5. associate-*r/ 66.5%

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

    6. times-frac 67.5%

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

    7. associate-/l* 67.5%

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

    8. associate-*r/ 67.5%

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

    9. *-commutative 67.5%

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

    10. times-frac 76.1%

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

    11. associate-/l* 88.6%

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

    12. *-inverses 88.6%

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

    13. /-rgt-identity 88.6%

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

14. Simplified 88.6%

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

15. Taylor expanded in y around 0 98.0%

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

    1. unpow2 98.0%

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

17. Simplified 98.0%

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

18. Final simplification 98.0%

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

Alternative 3: 99.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -9 \cdot 10^{+16} \lor \neg \left(y \leq 33000000000\right):\\ \;\;\;\;x - \frac{-1}{y}\\ \mathbf{else}:\\ \;\;\;\;1 + y \cdot \frac{x + -1}{y + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= y -9e+16) (not (<= y 33000000000.0)))
   (- x (/ -1.0 y))
   (+ 1.0 (* y (/ (+ x -1.0) (+ y 1.0))))))

C

double code(double x, double y) {
	double tmp;
	if ((y <= -9e+16) || !(y <= 33000000000.0)) {
		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 <= (-9d+16)) .or. (.not. (y <= 33000000000.0d0))) 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 <= -9e+16) || !(y <= 33000000000.0)) {
		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 <= -9e+16) or not (y <= 33000000000.0):
		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 <= -9e+16) || !(y <= 33000000000.0))
		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 <= -9e+16) || ~((y <= 33000000000.0)))
		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, -9e+16], N[Not[LessEqual[y, 33000000000.0]], $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 < -9e16 or 3.3e10 < y

   1. Initial program 31.5%

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

      1. sub-neg 31.5%

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

      2. distribute-neg-frac 31.5%

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

      3. neg-mul-1 31.5%

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

      4. associate-*l/ 31.6%

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

      5. metadata-eval 31.6%

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

      6. associate-*l/ 31.6%

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

      7. associate-/r/ 31.6%

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

      8. metadata-eval 31.6%

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

      9. distribute-neg-frac 31.6%

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

      10. cancel-sign-sub-inv 31.6%

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

      11. associate-/r/ 31.4%

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

      12. associate-/r* 31.4%

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

      13. neg-mul-1 31.4%

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

      14. associate-/r/ 31.6%

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

      15. distribute-rgt-neg-in 31.6%

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

      16. associate-/r/ 31.4%

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

      17. distribute-neg-frac 31.4%

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

      18. metadata-eval 31.4%

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

      19. associate-/r/ 31.6%

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

   3. Simplified 57.1%

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

   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 -9e16 < y < 3.3e10

   1. Initial program 99.9%

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

      1. sub-neg 99.9%

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

      2. distribute-neg-frac 99.9%

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

      3. neg-mul-1 99.9%

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

      4. associate-*l/ 99.9%

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

      5. metadata-eval 99.9%

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

      6. associate-*l/ 99.9%

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

      7. associate-/r/ 99.9%

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

      8. metadata-eval 99.9%

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

      9. distribute-neg-frac 99.9%

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

      10. cancel-sign-sub-inv 99.9%

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

      11. associate-/r/ 99.8%

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

      12. associate-/r* 99.8%

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

      13. neg-mul-1 99.8%

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

      14. associate-/r/ 99.9%

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

      15. distribute-rgt-neg-in 99.9%

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

      16. associate-/r/ 99.8%

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

      17. distribute-neg-frac 99.8%

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

      18. metadata-eval 99.8%

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

      19. associate-/r/ 99.9%

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

   3. Simplified 99.9%

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

4. Final simplification 99.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -9 \cdot 10^{+16} \lor \neg \left(y \leq 33000000000\right):\\ \;\;\;\;x - \frac{-1}{y}\\ \mathbf{else}:\\ \;\;\;\;1 + y \cdot \frac{x + -1}{y + 1}\\ \end{array} \]

Alternative 4: 98.3% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if ((y <= (-1.0d0)) .or. (.not. (y <= 0.82d0))) then
        tmp = x - ((-1.0d0) / y)
    else
        tmp = 1.0d0 + (y * (x + (-1.0d0)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((y <= -1.0) || !(y <= 0.82)) {
		tmp = x - (-1.0 / y);
	} else {
		tmp = 1.0 + (y * (x + -1.0));
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (y <= -1.0) or not (y <= 0.82):
		tmp = x - (-1.0 / y)
	else:
		tmp = 1.0 + (y * (x + -1.0))
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((y <= -1.0) || !(y <= 0.82))
		tmp = Float64(x - Float64(-1.0 / y));
	else
		tmp = Float64(1.0 + Float64(y * Float64(x + -1.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((y <= -1.0) || ~((y <= 0.82)))
		tmp = x - (-1.0 / y);
	else
		tmp = 1.0 + (y * (x + -1.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[y, -1.0], N[Not[LessEqual[y, 0.82]], $MachinePrecision]], N[(x - N[(-1.0 / y), $MachinePrecision]), $MachinePrecision], N[(1.0 + N[(y * N[(x + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1 or 0.819999999999999951 < y

   1. Initial program 33.1%

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

      1. sub-neg 33.1%

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

      2. distribute-neg-frac 33.1%

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

      3. neg-mul-1 33.1%

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

      4. associate-*l/ 33.1%

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

      5. metadata-eval 33.1%

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

      6. associate-*l/ 33.1%

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

      7. associate-/r/ 33.1%

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

      8. metadata-eval 33.1%

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

      9. distribute-neg-frac 33.1%

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

      10. cancel-sign-sub-inv 33.1%

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

      11. associate-/r/ 33.0%

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

      12. associate-/r* 33.0%

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

      13. neg-mul-1 33.0%

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

      14. associate-/r/ 33.1%

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

      15. distribute-rgt-neg-in 33.1%

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

      16. associate-/r/ 33.0%

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

      17. distribute-neg-frac 33.0%

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

      18. metadata-eval 33.0%

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

      19. associate-/r/ 33.1%

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

   3. Simplified 58.0%

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

   4. Taylor expanded in y around inf 98.8%

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

      1. +-commutative 98.8%

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

      2. associate--l+ 98.8%

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

      3. div-sub 98.8%

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

      4. sub-neg 98.8%

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

      5. +-commutative 98.8%

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

      6. metadata-eval 98.8%

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

      7. distribute-neg-in 98.8%

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

      8. distribute-neg-frac 98.8%

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

      9. metadata-eval 98.8%

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

      10. sub-neg 98.8%

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

      11. unsub-neg 98.8%

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

      12. sub-neg 98.8%

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

      13. metadata-eval 98.8%

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

   6. Simplified 98.8%

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

   7. Taylor expanded in x around 0 98.8%

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

   if -1 < y < 0.819999999999999951

   1. Initial program 100.0%

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

      1. 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/ 100.0%

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

      12. associate-/r* 100.0%

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

      13. neg-mul-1 100.0%

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

      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/ 100.0%

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

      17. distribute-neg-frac 100.0%

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

      18. metadata-eval 100.0%

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

      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 98.7%

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

4. Final simplification 98.8%

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

Alternative 5: 86.7% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1 \lor \neg \left(y \leq 0.072\right):\\ \;\;\;\;x - \frac{-1}{y}\\ \mathbf{else}:\\ \;\;\;\;1 - y\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= y -1.0) (not (<= y 0.072))) (- x (/ -1.0 y)) (- 1.0 y)))

C

double code(double x, double y) {
	double tmp;
	if ((y <= -1.0) || !(y <= 0.072)) {
		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 <= 0.072d0))) 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 <= 0.072)) {
		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 <= 0.072):
		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 <= 0.072))
		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 <= 0.072)))
		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, 0.072]], $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 0.0719999999999999946 < y

   1. Initial program 33.1%

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

      1. sub-neg 33.1%

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

      2. distribute-neg-frac 33.1%

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

      3. neg-mul-1 33.1%

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

      4. associate-*l/ 33.1%

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

      5. metadata-eval 33.1%

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

      6. associate-*l/ 33.1%

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

      7. associate-/r/ 33.1%

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

      8. metadata-eval 33.1%

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

      9. distribute-neg-frac 33.1%

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

      10. cancel-sign-sub-inv 33.1%

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

      11. associate-/r/ 33.0%

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

      12. associate-/r* 33.0%

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

      13. neg-mul-1 33.0%

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

      14. associate-/r/ 33.1%

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

      15. distribute-rgt-neg-in 33.1%

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

      16. associate-/r/ 33.0%

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

      17. distribute-neg-frac 33.0%

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

      18. metadata-eval 33.0%

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

      19. associate-/r/ 33.1%

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

   3. Simplified 58.0%

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

   4. Taylor expanded in y around inf 98.8%

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

      1. +-commutative 98.8%

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

      2. associate--l+ 98.8%

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

      3. div-sub 98.8%

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

      4. sub-neg 98.8%

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

      5. +-commutative 98.8%

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

      6. metadata-eval 98.8%

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

      7. distribute-neg-in 98.8%

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

      8. distribute-neg-frac 98.8%

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

      9. metadata-eval 98.8%

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

      10. sub-neg 98.8%

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

      11. unsub-neg 98.8%

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

      12. sub-neg 98.8%

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

      13. metadata-eval 98.8%

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

   6. Simplified 98.8%

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

   7. Taylor expanded in x around 0 98.8%

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

   if -1 < y < 0.0719999999999999946

   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/ 100.0%

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

      12. associate-/r* 100.0%

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

      13. neg-mul-1 100.0%

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

      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/ 100.0%

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

      17. distribute-neg-frac 100.0%

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

      18. metadata-eval 100.0%

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

      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 98.7%

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

   5. Taylor expanded in x around 0 75.1%

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

4. Final simplification 86.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1 \lor \neg \left(y \leq 0.072\right):\\ \;\;\;\;x - \frac{-1}{y}\\ \mathbf{else}:\\ \;\;\;\;1 - y\\ \end{array} \]

Alternative 6: 98.0% accurate, 1.2× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

2. if y < -1 or 1 < y

   1. Initial program 33.1%

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

      1. sub-neg 33.1%

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

      2. distribute-neg-frac 33.1%

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

      3. neg-mul-1 33.1%

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

      4. associate-*l/ 33.1%

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

      5. metadata-eval 33.1%

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

      6. associate-*l/ 33.1%

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

      7. associate-/r/ 33.1%

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

      8. metadata-eval 33.1%

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

      9. distribute-neg-frac 33.1%

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

      10. cancel-sign-sub-inv 33.1%

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

      11. associate-/r/ 33.0%

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

      12. associate-/r* 33.0%

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

      13. neg-mul-1 33.0%

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

      14. associate-/r/ 33.1%

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

      15. distribute-rgt-neg-in 33.1%

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

      16. associate-/r/ 33.0%

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

      17. distribute-neg-frac 33.0%

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

      18. metadata-eval 33.0%

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

      19. associate-/r/ 33.1%

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

   3. Simplified 58.0%

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

   4. Taylor expanded in y around inf 98.8%

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

      1. +-commutative 98.8%

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

      2. associate--l+ 98.8%

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

      3. div-sub 98.8%

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

      4. sub-neg 98.8%

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

      5. +-commutative 98.8%

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

      6. metadata-eval 98.8%

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

      7. distribute-neg-in 98.8%

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

      8. distribute-neg-frac 98.8%

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

      9. metadata-eval 98.8%

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

      10. sub-neg 98.8%

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

      11. unsub-neg 98.8%

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

      12. sub-neg 98.8%

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

      13. metadata-eval 98.8%

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

   6. Simplified 98.8%

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

   7. Taylor expanded in x around 0 98.8%

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

   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/ 100.0%

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

      12. associate-/r* 100.0%

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

      13. neg-mul-1 100.0%

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

      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/ 100.0%

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

      17. distribute-neg-frac 100.0%

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

      18. metadata-eval 100.0%

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

      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 98.7%

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

   5. Taylor expanded in x around inf 97.6%

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

      1. mul-1-neg 97.6%

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

      2. distribute-rgt-neg-out 97.6%

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

   7. Simplified 97.6%

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

4. Final simplification 98.2%

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

Alternative 7: 74.8% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 0.17:\\ \;\;\;\;1 - y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -1.0) x (if (<= y 0.17) (- 1.0 y) x)))

C

double code(double x, double y) {
	double tmp;
	if (y <= -1.0) {
		tmp = x;
	} else if (y <= 0.17) {
		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 <= 0.17d0) 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 <= 0.17) {
		tmp = 1.0 - y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -1.0:
		tmp = x
	elif y <= 0.17:
		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 <= 0.17)
		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 <= 0.17)
		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, 0.17], N[(1.0 - y), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if y < -1 or 0.170000000000000012 < y

   1. Initial program 33.1%

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

      1. sub-neg 33.1%

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

      2. distribute-neg-frac 33.1%

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

      3. neg-mul-1 33.1%

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

      4. associate-*l/ 33.1%

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

      5. metadata-eval 33.1%

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

      6. associate-*l/ 33.1%

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

      7. associate-/r/ 33.1%

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

      8. metadata-eval 33.1%

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

      9. distribute-neg-frac 33.1%

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

      10. cancel-sign-sub-inv 33.1%

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

      11. associate-/r/ 33.0%

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

      12. associate-/r* 33.0%

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

      13. neg-mul-1 33.0%

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

      14. associate-/r/ 33.1%

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

      15. distribute-rgt-neg-in 33.1%

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

      16. associate-/r/ 33.0%

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

      17. distribute-neg-frac 33.0%

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

      18. metadata-eval 33.0%

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

      19. associate-/r/ 33.1%

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

   3. Simplified 58.0%

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

   4. Taylor expanded in y around inf 74.0%

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

   if -1 < y < 0.170000000000000012

   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/ 100.0%

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

      12. associate-/r* 100.0%

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

      13. neg-mul-1 100.0%

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

      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/ 100.0%

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

      17. distribute-neg-frac 100.0%

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

      18. metadata-eval 100.0%

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

      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 98.7%

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

   5. Taylor expanded in x around 0 75.1%

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

4. Final simplification 74.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 0.17:\\ \;\;\;\;1 - y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 8: 74.1% accurate, 2.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 5 \cdot 10^{+17}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (if (<= y -1.0) x (if (<= y 5e+17) 1.0 x)))

C

double code(double x, double y) {
	double tmp;
	if (y <= -1.0) {
		tmp = x;
	} else if (y <= 5e+17) {
		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 <= 5d+17) 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 <= 5e+17) {
		tmp = 1.0;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -1.0:
		tmp = x
	elif y <= 5e+17:
		tmp = 1.0
	else:
		tmp = x
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -1.0)
		tmp = x;
	elseif (y <= 5e+17)
		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 <= 5e+17)
		tmp = 1.0;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -1.0], x, If[LessEqual[y, 5e+17], 1.0, x]]

Derivation

1. Split input into 2 regimes

2. if y < -1 or 5e17 < y

   1. Initial program 32.8%

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

      1. sub-neg 32.8%

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

      2. distribute-neg-frac 32.8%

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

      3. neg-mul-1 32.8%

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

      4. associate-*l/ 32.8%

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

      5. metadata-eval 32.8%

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

      6. associate-*l/ 32.8%

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

      7. associate-/r/ 32.8%

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

      8. metadata-eval 32.8%

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

      9. distribute-neg-frac 32.8%

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

      10. cancel-sign-sub-inv 32.8%

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

      11. associate-/r/ 32.7%

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

      12. associate-/r* 32.7%

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

      13. neg-mul-1 32.7%

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

      14. associate-/r/ 32.8%

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

      15. distribute-rgt-neg-in 32.8%

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

      16. associate-/r/ 32.7%

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

      17. distribute-neg-frac 32.7%

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

      18. metadata-eval 32.7%

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

      19. associate-/r/ 32.8%

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

   3. Simplified 58.4%

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

   4. Taylor expanded in y around inf 75.7%

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

   if -1 < y < 5e17

   1. Initial program 98.8%

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

      1. sub-neg 98.8%

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

      2. distribute-neg-frac 98.8%

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

      3. neg-mul-1 98.8%

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

      4. associate-*l/ 98.8%

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

      5. metadata-eval 98.8%

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

      6. associate-*l/ 98.8%

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

      7. associate-/r/ 98.8%

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

      8. metadata-eval 98.8%

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

      9. distribute-neg-frac 98.8%

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

      10. cancel-sign-sub-inv 98.8%

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

      11. associate-/r/ 98.8%

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

      12. associate-/r* 98.8%

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

      13. neg-mul-1 98.8%

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

      14. associate-/r/ 98.8%

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

      15. distribute-rgt-neg-in 98.8%

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

      16. associate-/r/ 98.8%

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

      17. distribute-neg-frac 98.8%

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

      18. metadata-eval 98.8%

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

      19. associate-/r/ 98.8%

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

   3. Simplified 98.8%

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

   4. Taylor expanded in y around 0 72.6%

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

4. Final simplification 74.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 5 \cdot 10^{+17}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 9: 39.2% 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 68.6%

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

   1. sub-neg 68.6%

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

   2. distribute-neg-frac 68.6%

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

   3. neg-mul-1 68.6%

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

   4. associate-*l/ 68.7%

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

   5. metadata-eval 68.7%

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

   6. associate-*l/ 68.7%

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

   7. associate-/r/ 68.7%

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

   8. metadata-eval 68.7%

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

   9. distribute-neg-frac 68.7%

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

   10. cancel-sign-sub-inv 68.7%

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

   11. associate-/r/ 68.6%

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

   12. associate-/r* 68.6%

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

   13. neg-mul-1 68.6%

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

   14. associate-/r/ 68.7%

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

   15. distribute-rgt-neg-in 68.7%

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

   16. associate-/r/ 68.6%

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

   17. distribute-neg-frac 68.6%

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

   18. metadata-eval 68.6%

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

   19. associate-/r/ 68.7%

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

3. Simplified 80.3%

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

4. Taylor expanded in y around 0 41.0%

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

5. Final simplification 41.0%

   \[\leadsto 1 \]

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 2023185 
(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))))