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

Percentage Accurate: 66.2% → 99.8%

Time: 8.1s

Alternatives: 11

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 66.2% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.8% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1250000000:\\ \;\;\;\;x + \frac{-1}{y} \cdot \left(-1 + \frac{1}{y}\right)\\ \mathbf{elif}\;y \leq 420000:\\ \;\;\;\;1 + \left(1 - x\right) \cdot \frac{y}{-1 - y}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{\left(1 - x\right) + \frac{x + -1}{y}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -1250000000.0)
   (+ x (* (/ -1.0 y) (+ -1.0 (/ 1.0 y))))
   (if (<= y 420000.0)
     (+ 1.0 (* (- 1.0 x) (/ y (- -1.0 y))))
     (+ x (/ (+ (- 1.0 x) (/ (+ x -1.0) y)) y)))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -1250000000.0) {
		tmp = x + ((-1.0 / y) * (-1.0 + (1.0 / y)));
	} else if (y <= 420000.0) {
		tmp = 1.0 + ((1.0 - x) * (y / (-1.0 - y)));
	} else {
		tmp = x + (((1.0 - x) + ((x + -1.0) / y)) / y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (y <= (-1250000000.0d0)) then
        tmp = x + (((-1.0d0) / y) * ((-1.0d0) + (1.0d0 / y)))
    else if (y <= 420000.0d0) then
        tmp = 1.0d0 + ((1.0d0 - x) * (y / ((-1.0d0) - y)))
    else
        tmp = x + (((1.0d0 - x) + ((x + (-1.0d0)) / y)) / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (y <= -1250000000.0) {
		tmp = x + ((-1.0 / y) * (-1.0 + (1.0 / y)));
	} else if (y <= 420000.0) {
		tmp = 1.0 + ((1.0 - x) * (y / (-1.0 - y)));
	} else {
		tmp = x + (((1.0 - x) + ((x + -1.0) / y)) / y);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -1250000000.0:
		tmp = x + ((-1.0 / y) * (-1.0 + (1.0 / y)))
	elif y <= 420000.0:
		tmp = 1.0 + ((1.0 - x) * (y / (-1.0 - y)))
	else:
		tmp = x + (((1.0 - x) + ((x + -1.0) / y)) / y)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -1250000000.0)
		tmp = Float64(x + Float64(Float64(-1.0 / y) * Float64(-1.0 + Float64(1.0 / y))));
	elseif (y <= 420000.0)
		tmp = Float64(1.0 + Float64(Float64(1.0 - x) * Float64(y / Float64(-1.0 - y))));
	else
		tmp = Float64(x + Float64(Float64(Float64(1.0 - x) + Float64(Float64(x + -1.0) / y)) / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -1250000000.0)
		tmp = x + ((-1.0 / y) * (-1.0 + (1.0 / y)));
	elseif (y <= 420000.0)
		tmp = 1.0 + ((1.0 - x) * (y / (-1.0 - y)));
	else
		tmp = x + (((1.0 - x) + ((x + -1.0) / y)) / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -1250000000.0], N[(x + N[(N[(-1.0 / y), $MachinePrecision] * N[(-1.0 + N[(1.0 / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 420000.0], N[(1.0 + N[(N[(1.0 - x), $MachinePrecision] * N[(y / N[(-1.0 - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(N[(1.0 - x), $MachinePrecision] + N[(N[(x + -1.0), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.25e9

   1. Initial program 26.8%

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

      1. associate-/l* 56.6%

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

      2. +-commutative 56.6%

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

   3. Simplified 56.6%

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

   5. Taylor expanded in y around -inf 100.0%

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

      1. mul-1-neg 100.0%

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

      2. unsub-neg 100.0%

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

      3. mul-1-neg 100.0%

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

      4. neg-sub0 100.0%

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

      5. associate-+l- 100.0%

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

      6. neg-sub0 100.0%

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

      7. +-commutative 100.0%

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

      8. sub-neg 100.0%

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

      9. unsub-neg 100.0%

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

      10. neg-mul-1 100.0%

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

      11. +-commutative 100.0%

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

   7. Simplified 100.0%

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

   8. Taylor expanded in x around 0 100.0%

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

      1. frac-2neg 100.0%

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

      2. div-inv 100.0%

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

      3. sub-neg 100.0%

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

      4. metadata-eval 100.0%

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

      5. distribute-neg-in 100.0%

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

      6. mul-1-neg 100.0%

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

      7. div-inv 100.0%

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

      8. add-sqr-sqrt 100.0%

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

      9. sqrt-unprod 100.0%

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

      10. frac-times 100.0%

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

      11. metadata-eval 100.0%

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

      12. metadata-eval 100.0%

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

      13. frac-times 100.0%

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

      14. sqrt-unprod 0.0%

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

      15. add-sqr-sqrt 99.6%

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

      16. metadata-eval 99.6%

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

      17. +-commutative 99.6%

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

      18. add-sqr-sqrt 0.0%

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

      19. sqrt-unprod 100.0%

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

      20. frac-times 100.0%

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

      21. metadata-eval 100.0%

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

      22. metadata-eval 100.0%

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

      23. frac-times 100.0%

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

      24. sqrt-unprod 100.0%

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

      25. add-sqr-sqrt 100.0%

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

   10. Applied egg-rr 100.0%

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

   if -1.25e9 < y < 4.2e5

   1. Initial program 99.9%

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

      1. associate-/l* 99.9%

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

      2. +-commutative 99.9%

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

   3. Simplified 99.9%

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

   if 4.2e5 < y

   1. Initial program 27.6%

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

      1. associate-/l* 52.3%

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

      2. +-commutative 52.3%

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

   3. Simplified 52.3%

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

   5. Taylor expanded in y around -inf 100.0%

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

      1. mul-1-neg 100.0%

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

      2. unsub-neg 100.0%

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

      3. mul-1-neg 100.0%

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

      4. neg-sub0 100.0%

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

      5. associate-+l- 100.0%

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

      6. neg-sub0 100.0%

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

      7. +-commutative 100.0%

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

      8. sub-neg 100.0%

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

      9. unsub-neg 100.0%

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

      10. neg-mul-1 100.0%

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

      11. +-commutative 100.0%

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

   7. Simplified 100.0%

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

4. Final simplification 100.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1250000000:\\ \;\;\;\;x + \frac{-1}{y} \cdot \left(-1 + \frac{1}{y}\right)\\ \mathbf{elif}\;y \leq 420000:\\ \;\;\;\;1 + \left(1 - x\right) \cdot \frac{y}{-1 - y}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{\left(1 - x\right) + \frac{x + -1}{y}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 99.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{y \cdot \left(1 - x\right)}{y + 1}\\ \mathbf{if}\;t\_0 \leq 0.999 \lor \neg \left(t\_0 \leq 2\right):\\ \;\;\;\;1 + \left(1 - x\right) \cdot \frac{y}{-1 - y}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{-1}{y} \cdot \left(-1 + \frac{1}{y}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (/ (* y (- 1.0 x)) (+ y 1.0))))
   (if (or (<= t_0 0.999) (not (<= t_0 2.0)))
     (+ 1.0 (* (- 1.0 x) (/ y (- -1.0 y))))
     (+ x (* (/ -1.0 y) (+ -1.0 (/ 1.0 y)))))))

C

double code(double x, double y) {
	double t_0 = (y * (1.0 - x)) / (y + 1.0);
	double tmp;
	if ((t_0 <= 0.999) || !(t_0 <= 2.0)) {
		tmp = 1.0 + ((1.0 - x) * (y / (-1.0 - y)));
	} else {
		tmp = x + ((-1.0 / y) * (-1.0 + (1.0 / 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 = (y * (1.0d0 - x)) / (y + 1.0d0)
    if ((t_0 <= 0.999d0) .or. (.not. (t_0 <= 2.0d0))) then
        tmp = 1.0d0 + ((1.0d0 - x) * (y / ((-1.0d0) - y)))
    else
        tmp = x + (((-1.0d0) / y) * ((-1.0d0) + (1.0d0 / y)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double t_0 = (y * (1.0 - x)) / (y + 1.0);
	double tmp;
	if ((t_0 <= 0.999) || !(t_0 <= 2.0)) {
		tmp = 1.0 + ((1.0 - x) * (y / (-1.0 - y)));
	} else {
		tmp = x + ((-1.0 / y) * (-1.0 + (1.0 / y)));
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = (y * (1.0 - x)) / (y + 1.0)
	tmp = 0
	if (t_0 <= 0.999) or not (t_0 <= 2.0):
		tmp = 1.0 + ((1.0 - x) * (y / (-1.0 - y)))
	else:
		tmp = x + ((-1.0 / y) * (-1.0 + (1.0 / y)))
	return tmp

Julia

function code(x, y)
	t_0 = Float64(Float64(y * Float64(1.0 - x)) / Float64(y + 1.0))
	tmp = 0.0
	if ((t_0 <= 0.999) || !(t_0 <= 2.0))
		tmp = Float64(1.0 + Float64(Float64(1.0 - x) * Float64(y / Float64(-1.0 - y))));
	else
		tmp = Float64(x + Float64(Float64(-1.0 / y) * Float64(-1.0 + Float64(1.0 / y))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = (y * (1.0 - x)) / (y + 1.0);
	tmp = 0.0;
	if ((t_0 <= 0.999) || ~((t_0 <= 2.0)))
		tmp = 1.0 + ((1.0 - x) * (y / (-1.0 - y)));
	else
		tmp = x + ((-1.0 / y) * (-1.0 + (1.0 / y)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(N[(y * N[(1.0 - x), $MachinePrecision]), $MachinePrecision] / N[(y + 1.0), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$0, 0.999], N[Not[LessEqual[t$95$0, 2.0]], $MachinePrecision]], N[(1.0 + N[(N[(1.0 - x), $MachinePrecision] * N[(y / N[(-1.0 - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(-1.0 / y), $MachinePrecision] * N[(-1.0 + N[(1.0 / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 (-.f64 #s(literal 1 binary64) x) y) (+.f64 y #s(literal 1 binary64))) < 0.998999999999999999 or 2 < (/.f64 (*.f64 (-.f64 #s(literal 1 binary64) x) y) (+.f64 y #s(literal 1 binary64)))

   1. Initial program 79.5%

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

      1. associate-/l* 99.9%

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

      2. +-commutative 99.9%

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

   3. Simplified 99.9%

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

   if 0.998999999999999999 < (/.f64 (*.f64 (-.f64 #s(literal 1 binary64) x) y) (+.f64 y #s(literal 1 binary64))) < 2

   1. Initial program 7.7%

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

      1. associate-/l* 7.8%

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

      2. +-commutative 7.8%

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

   3. Simplified 7.8%

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

   5. Taylor expanded in y around -inf 100.0%

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

      1. mul-1-neg 100.0%

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

      2. unsub-neg 100.0%

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

      3. mul-1-neg 100.0%

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

      4. neg-sub0 100.0%

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

      5. associate-+l- 100.0%

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

      6. neg-sub0 100.0%

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

      7. +-commutative 100.0%

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

      8. sub-neg 100.0%

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

      9. unsub-neg 100.0%

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

      10. neg-mul-1 100.0%

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

      11. +-commutative 100.0%

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

   7. Simplified 100.0%

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

   8. Taylor expanded in x around 0 100.0%

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

      1. frac-2neg 100.0%

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

      2. div-inv 100.0%

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

      3. sub-neg 100.0%

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

      4. metadata-eval 100.0%

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

      5. distribute-neg-in 100.0%

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

      6. mul-1-neg 100.0%

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

      7. div-inv 100.0%

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

      8. add-sqr-sqrt 49.3%

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

      9. sqrt-unprod 99.7%

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

      10. frac-times 99.7%

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

      11. metadata-eval 99.7%

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

      12. metadata-eval 99.7%

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

      13. frac-times 99.7%

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

      14. sqrt-unprod 50.4%

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

      15. add-sqr-sqrt 99.2%

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

      16. metadata-eval 99.2%

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

      17. +-commutative 99.2%

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

      18. add-sqr-sqrt 50.4%

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

      19. sqrt-unprod 99.7%

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

      20. frac-times 99.7%

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

      21. metadata-eval 99.7%

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

      22. metadata-eval 99.7%

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

      23. frac-times 99.7%

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

      24. sqrt-unprod 49.3%

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

      25. add-sqr-sqrt 100.0%

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

   10. Applied egg-rr 100.0%

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

4. Final simplification 99.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y \cdot \left(1 - x\right)}{y + 1} \leq 0.999 \lor \neg \left(\frac{y \cdot \left(1 - x\right)}{y + 1} \leq 2\right):\\ \;\;\;\;1 + \left(1 - x\right) \cdot \frac{y}{-1 - y}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{-1}{y} \cdot \left(-1 + \frac{1}{y}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 99.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{y \cdot \left(1 - x\right)}{y + 1}\\ \mathbf{if}\;t\_0 \leq 0.999 \lor \neg \left(t\_0 \leq 2\right):\\ \;\;\;\;1 + \left(1 - x\right) \cdot \frac{y}{-1 - y}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{-1 + \frac{1}{y}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (/ (* y (- 1.0 x)) (+ y 1.0))))
   (if (or (<= t_0 0.999) (not (<= t_0 2.0)))
     (+ 1.0 (* (- 1.0 x) (/ y (- -1.0 y))))
     (- x (/ (+ -1.0 (/ 1.0 y)) y)))))

C

double code(double x, double y) {
	double t_0 = (y * (1.0 - x)) / (y + 1.0);
	double tmp;
	if ((t_0 <= 0.999) || !(t_0 <= 2.0)) {
		tmp = 1.0 + ((1.0 - x) * (y / (-1.0 - y)));
	} else {
		tmp = x - ((-1.0 + (1.0 / y)) / y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: t_0
    real(8) :: tmp
    t_0 = (y * (1.0d0 - x)) / (y + 1.0d0)
    if ((t_0 <= 0.999d0) .or. (.not. (t_0 <= 2.0d0))) then
        tmp = 1.0d0 + ((1.0d0 - x) * (y / ((-1.0d0) - y)))
    else
        tmp = x - (((-1.0d0) + (1.0d0 / y)) / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double t_0 = (y * (1.0 - x)) / (y + 1.0);
	double tmp;
	if ((t_0 <= 0.999) || !(t_0 <= 2.0)) {
		tmp = 1.0 + ((1.0 - x) * (y / (-1.0 - y)));
	} else {
		tmp = x - ((-1.0 + (1.0 / y)) / y);
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = (y * (1.0 - x)) / (y + 1.0)
	tmp = 0
	if (t_0 <= 0.999) or not (t_0 <= 2.0):
		tmp = 1.0 + ((1.0 - x) * (y / (-1.0 - y)))
	else:
		tmp = x - ((-1.0 + (1.0 / y)) / y)
	return tmp

Julia

function code(x, y)
	t_0 = Float64(Float64(y * Float64(1.0 - x)) / Float64(y + 1.0))
	tmp = 0.0
	if ((t_0 <= 0.999) || !(t_0 <= 2.0))
		tmp = Float64(1.0 + Float64(Float64(1.0 - x) * Float64(y / Float64(-1.0 - y))));
	else
		tmp = Float64(x - Float64(Float64(-1.0 + Float64(1.0 / y)) / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = (y * (1.0 - x)) / (y + 1.0);
	tmp = 0.0;
	if ((t_0 <= 0.999) || ~((t_0 <= 2.0)))
		tmp = 1.0 + ((1.0 - x) * (y / (-1.0 - y)));
	else
		tmp = x - ((-1.0 + (1.0 / y)) / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(N[(y * N[(1.0 - x), $MachinePrecision]), $MachinePrecision] / N[(y + 1.0), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$0, 0.999], N[Not[LessEqual[t$95$0, 2.0]], $MachinePrecision]], N[(1.0 + N[(N[(1.0 - x), $MachinePrecision] * N[(y / N[(-1.0 - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x - N[(N[(-1.0 + N[(1.0 / y), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 (-.f64 #s(literal 1 binary64) x) y) (+.f64 y #s(literal 1 binary64))) < 0.998999999999999999 or 2 < (/.f64 (*.f64 (-.f64 #s(literal 1 binary64) x) y) (+.f64 y #s(literal 1 binary64)))

   1. Initial program 79.5%

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

      1. associate-/l* 99.9%

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

      2. +-commutative 99.9%

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

   3. Simplified 99.9%

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

   if 0.998999999999999999 < (/.f64 (*.f64 (-.f64 #s(literal 1 binary64) x) y) (+.f64 y #s(literal 1 binary64))) < 2

   1. Initial program 7.7%

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

      1. associate-/l* 7.8%

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

      2. +-commutative 7.8%

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

   3. Simplified 7.8%

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

   5. Taylor expanded in y around -inf 100.0%

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

      1. mul-1-neg 100.0%

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

      2. unsub-neg 100.0%

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

      3. mul-1-neg 100.0%

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

      4. neg-sub0 100.0%

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

      5. associate-+l- 100.0%

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

      6. neg-sub0 100.0%

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

      7. +-commutative 100.0%

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

      8. sub-neg 100.0%

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

      9. unsub-neg 100.0%

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

      10. neg-mul-1 100.0%

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

      11. +-commutative 100.0%

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

   7. Simplified 100.0%

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

   8. Taylor expanded in x around 0 100.0%

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

4. Final simplification 99.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y \cdot \left(1 - x\right)}{y + 1} \leq 0.999 \lor \neg \left(\frac{y \cdot \left(1 - x\right)}{y + 1} \leq 2\right):\\ \;\;\;\;1 + \left(1 - x\right) \cdot \frac{y}{-1 - y}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{-1 + \frac{1}{y}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 98.1% accurate, 0.6× speedup

Math

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

FPCore

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

C

double code(double x, double y) {
	double tmp;
	if ((y <= -1.0) || !(y <= 0.8)) {
		tmp = x + (1.0 / y);
	} else {
		tmp = 1.0 + (y * (x + -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 <= 0.8d0))) 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 <= 0.8)) {
		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 <= 0.8):
		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 <= 0.8))
		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 <= 0.8)))
		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, 0.8]], $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 0.80000000000000004 < y

   1. Initial program 27.6%

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

      1. associate-/l* 54.8%

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

      2. +-commutative 54.8%

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

   3. Simplified 54.8%

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

   5. Taylor expanded in y around inf 99.1%

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

      1. associate--l+ 99.1%

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

      2. div-sub 99.1%

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

      3. sub-neg 99.1%

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

      4. +-commutative 99.1%

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

      5. neg-sub0 99.1%

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

      6. associate-+l- 99.1%

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

      7. neg-sub0 99.1%

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

      8. mul-1-neg 99.1%

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

      9. associate-*r/ 99.1%

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

      10. mul-1-neg 99.1%

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

      11. unsub-neg 99.1%

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

      12. sub-neg 99.1%

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

      13. metadata-eval 99.1%

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

   7. Simplified 99.1%

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

   8. Taylor expanded in x around 0 98.8%

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

   if -1 < y < 0.80000000000000004

   1. Initial program 100.0%

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

      1. associate-/l* 100.0%

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

      2. +-commutative 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in y around 0 98.6%

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

4. Final simplification 98.7%

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

Alternative 5: 98.4% accurate, 0.6× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 3 regimes

2. if y < -1

   1. Initial program 26.8%

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

      1. associate-/l* 56.6%

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

      2. +-commutative 56.6%

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

   3. Simplified 56.6%

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

   5. Taylor expanded in y around -inf 100.0%

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

      1. mul-1-neg 100.0%

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

      2. unsub-neg 100.0%

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

      3. mul-1-neg 100.0%

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

      4. neg-sub0 100.0%

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

      5. associate-+l- 100.0%

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

      6. neg-sub0 100.0%

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

      7. +-commutative 100.0%

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

      8. sub-neg 100.0%

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

      9. unsub-neg 100.0%

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

      10. neg-mul-1 100.0%

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

      11. +-commutative 100.0%

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

   7. Simplified 100.0%

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

   8. Taylor expanded in x around 0 100.0%

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

   if -1 < y < 1

   1. Initial program 100.0%

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

      1. associate-/l* 100.0%

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

      2. +-commutative 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in y around 0 98.6%

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

   if 1 < y

   1. Initial program 28.5%

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

      1. associate-/l* 52.8%

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

      2. +-commutative 52.8%

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

   3. Simplified 52.8%

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

   5. Taylor expanded in y around inf 98.5%

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

      1. associate--l+ 98.5%

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

      2. div-sub 98.5%

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

      3. sub-neg 98.5%

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

      4. +-commutative 98.5%

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

      5. neg-sub0 98.5%

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

      6. associate-+l- 98.5%

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

      7. neg-sub0 98.5%

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

      8. mul-1-neg 98.5%

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

      9. associate-*r/ 98.5%

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

      10. mul-1-neg 98.5%

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

      11. unsub-neg 98.5%

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

      12. sub-neg 98.5%

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

      13. metadata-eval 98.5%

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

   7. Simplified 98.5%

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

4. Final simplification 99.0%

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

Alternative 6: 98.2% accurate, 0.6× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 3 regimes

2. if y < -1

   1. Initial program 26.8%

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

      1. associate-/l* 56.6%

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

      2. +-commutative 56.6%

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

   3. Simplified 56.6%

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

   5. Taylor expanded in y around inf 99.6%

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

      1. associate--l+ 99.6%

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

      2. div-sub 99.6%

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

      3. sub-neg 99.6%

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

      4. +-commutative 99.6%

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

      5. neg-sub0 99.6%

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

      6. associate-+l- 99.6%

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

      7. neg-sub0 99.6%

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

      8. mul-1-neg 99.6%

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

      9. associate-*r/ 99.6%

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

      10. mul-1-neg 99.6%

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

      11. unsub-neg 99.6%

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

      12. sub-neg 99.6%

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

      13. metadata-eval 99.6%

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

   7. Simplified 99.6%

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

   8. Taylor expanded in x around 0 99.6%

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

   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. associate-/l* 100.0%

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

      2. +-commutative 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in y around 0 98.6%

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

   if 1 < y

   1. Initial program 28.5%

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

      1. associate-/l* 52.8%

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

      2. +-commutative 52.8%

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

   3. Simplified 52.8%

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

   5. Taylor expanded in y around inf 98.5%

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

      1. associate--l+ 98.5%

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

      2. div-sub 98.5%

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

      3. sub-neg 98.5%

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

      4. +-commutative 98.5%

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

      5. neg-sub0 98.5%

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

      6. associate-+l- 98.5%

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

      7. neg-sub0 98.5%

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

      8. mul-1-neg 98.5%

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

      9. associate-*r/ 98.5%

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

      10. mul-1-neg 98.5%

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

      11. unsub-neg 98.5%

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

      12. sub-neg 98.5%

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

      13. metadata-eval 98.5%

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

   7. Simplified 98.5%

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

4. Final simplification 98.9%

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

Alternative 7: 97.9% accurate, 0.7× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

2. if y < -1 or 1 < y

   1. Initial program 27.6%

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

      1. associate-/l* 54.8%

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

      2. +-commutative 54.8%

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

   3. Simplified 54.8%

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

   5. Taylor expanded in y around inf 99.1%

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

      1. associate--l+ 99.1%

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

      2. div-sub 99.1%

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

      3. sub-neg 99.1%

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

      4. +-commutative 99.1%

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

      5. neg-sub0 99.1%

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

      6. associate-+l- 99.1%

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

      7. neg-sub0 99.1%

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

      8. mul-1-neg 99.1%

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

      9. associate-*r/ 99.1%

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

      10. mul-1-neg 99.1%

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

      11. unsub-neg 99.1%

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

      12. sub-neg 99.1%

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

      13. metadata-eval 99.1%

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

   7. Simplified 99.1%

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

   8. 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. associate-/l* 100.0%

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

      2. +-commutative 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in y around 0 98.6%

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

   6. Taylor expanded in x around inf 97.9%

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

      1. neg-mul-1 97.9%

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

   8. Simplified 97.9%

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

      1. cancel-sign-sub 97.9%

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

      2. add-sqr-sqrt 55.7%

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

      3. sqrt-unprod 68.3%

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

      4. sqr-neg 68.3%

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

      5. sqrt-unprod 29.7%

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

      6. add-sqr-sqrt 73.1%

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

      7. *-commutative 73.1%

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

      8. add-sqr-sqrt 29.7%

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

      9. sqrt-unprod 68.3%

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

      10. sqr-neg 68.3%

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

      11. sqrt-unprod 55.7%

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

      12. add-sqr-sqrt 97.9%

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

   10. Applied egg-rr 97.9%

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

4. Final simplification 98.4%

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

Alternative 8: 86.1% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 550:\\ \;\;\;\;1 + y \cdot x\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -1.0) x (if (<= y 550.0) (+ 1.0 (* y x)) x)))

C

double code(double x, double y) {
	double tmp;
	if (y <= -1.0) {
		tmp = x;
	} else if (y <= 550.0) {
		tmp = 1.0 + (y * x);
	} 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 <= 550.0d0) then
        tmp = 1.0d0 + (y * x)
    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 <= 550.0) {
		tmp = 1.0 + (y * x);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -1.0:
		tmp = x
	elif y <= 550.0:
		tmp = 1.0 + (y * x)
	else:
		tmp = x
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -1.0)
		tmp = x;
	elseif (y <= 550.0)
		tmp = Float64(1.0 + Float64(y * x));
	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 <= 550.0)
		tmp = 1.0 + (y * x);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -1.0], x, If[LessEqual[y, 550.0], N[(1.0 + N[(y * x), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if y < -1 or 550 < y

   1. Initial program 27.1%

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

      1. associate-/l* 54.5%

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

      2. +-commutative 54.5%

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

   3. Simplified 54.5%

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

   5. Taylor expanded in y around inf 74.5%

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

   if -1 < y < 550

   1. Initial program 99.9%

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

      1. associate-/l* 99.9%

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

      2. +-commutative 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in y around 0 97.8%

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

   6. Taylor expanded in x around inf 97.2%

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

      1. neg-mul-1 97.2%

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

   8. Simplified 97.2%

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

      1. cancel-sign-sub 97.2%

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

      2. add-sqr-sqrt 55.3%

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

      3. sqrt-unprod 67.8%

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

      4. sqr-neg 67.8%

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

      5. sqrt-unprod 29.4%

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

      6. add-sqr-sqrt 72.5%

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

      7. *-commutative 72.5%

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

      8. add-sqr-sqrt 29.4%

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

      9. sqrt-unprod 67.8%

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

      10. sqr-neg 67.8%

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

      11. sqrt-unprod 55.3%

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

      12. add-sqr-sqrt 97.2%

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

   10. Applied egg-rr 97.2%

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

Alternative 9: 74.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 0.98:\\ \;\;\;\;1 - y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -1.0) x (if (<= y 0.98) (- 1.0 y) x)))

C

double code(double x, double y) {
	double tmp;
	if (y <= -1.0) {
		tmp = x;
	} else if (y <= 0.98) {
		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 <= 0.98d0) 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 <= 0.98) {
		tmp = 1.0 - y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -1.0:
		tmp = x
	elif y <= 0.98:
		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 <= 0.98)
		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 <= 0.98)
		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, 0.98], N[(1.0 - y), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if y < -1 or 0.97999999999999998 < y

   1. Initial program 27.6%

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

      1. associate-/l* 54.8%

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

      2. +-commutative 54.8%

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

   3. Simplified 54.8%

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

   5. Taylor expanded in y around inf 74.0%

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

   if -1 < y < 0.97999999999999998

   1. Initial program 100.0%

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

      1. associate-/l* 100.0%

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

      2. +-commutative 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in y around 0 98.6%

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

   6. Taylor expanded in x around 0 74.3%

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

Alternative 10: 73.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 550:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (if (<= y -1.0) x (if (<= y 550.0) 1.0 x)))

C

double code(double x, double y) {
	double tmp;
	if (y <= -1.0) {
		tmp = x;
	} else if (y <= 550.0) {
		tmp = 1.0;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (y <= (-1.0d0)) then
        tmp = x
    else if (y <= 550.0d0) then
        tmp = 1.0d0
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (y <= -1.0) {
		tmp = x;
	} else if (y <= 550.0) {
		tmp = 1.0;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -1.0:
		tmp = x
	elif y <= 550.0:
		tmp = 1.0
	else:
		tmp = x
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -1.0)
		tmp = x;
	elseif (y <= 550.0)
		tmp = 1.0;
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -1.0)
		tmp = x;
	elseif (y <= 550.0)
		tmp = 1.0;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -1.0], x, If[LessEqual[y, 550.0], 1.0, x]]

Derivation

1. Split input into 2 regimes

2. if y < -1 or 550 < y

   1. Initial program 27.1%

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

      1. associate-/l* 54.5%

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

      2. +-commutative 54.5%

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

   3. Simplified 54.5%

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

   5. Taylor expanded in y around inf 74.5%

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

   if -1 < y < 550

   1. Initial program 99.9%

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

      1. associate-/l* 99.9%

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

      2. +-commutative 99.9%

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

   3. Simplified 99.9%

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

   5. Taylor expanded in y around 0 73.1%

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

Alternative 11: 38.7% 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 60.1%

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

   1. associate-/l* 75.1%

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

   2. +-commutative 75.1%

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

3. Simplified 75.1%

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

5. Taylor expanded in y around 0 35.1%

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

Developer Target 1: 99.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{1}{y} - \left(\frac{x}{y} - x\right)\\ \mathbf{if}\;y < -3693.8482788297247:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y < 6799310503.41891:\\ \;\;\;\;1 - \frac{\left(1 - x\right) \cdot y}{y + 1}\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (- (/ 1.0 y) (- (/ x y) x))))
   (if (< y -3693.8482788297247)
     t_0
     (if (< y 6799310503.41891) (- 1.0 (/ (* (- 1.0 x) y) (+ y 1.0))) t_0))))

C

double code(double x, double y) {
	double t_0 = (1.0 / y) - ((x / y) - x);
	double tmp;
	if (y < -3693.8482788297247) {
		tmp = t_0;
	} else if (y < 6799310503.41891) {
		tmp = 1.0 - (((1.0 - x) * y) / (y + 1.0));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: t_0
    real(8) :: tmp
    t_0 = (1.0d0 / y) - ((x / y) - x)
    if (y < (-3693.8482788297247d0)) then
        tmp = t_0
    else if (y < 6799310503.41891d0) then
        tmp = 1.0d0 - (((1.0d0 - x) * y) / (y + 1.0d0))
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double t_0 = (1.0 / y) - ((x / y) - x);
	double tmp;
	if (y < -3693.8482788297247) {
		tmp = t_0;
	} else if (y < 6799310503.41891) {
		tmp = 1.0 - (((1.0 - x) * y) / (y + 1.0));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = (1.0 / y) - ((x / y) - x)
	tmp = 0
	if y < -3693.8482788297247:
		tmp = t_0
	elif y < 6799310503.41891:
		tmp = 1.0 - (((1.0 - x) * y) / (y + 1.0))
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y)
	t_0 = Float64(Float64(1.0 / y) - Float64(Float64(x / y) - x))
	tmp = 0.0
	if (y < -3693.8482788297247)
		tmp = t_0;
	elseif (y < 6799310503.41891)
		tmp = Float64(1.0 - Float64(Float64(Float64(1.0 - x) * y) / Float64(y + 1.0)));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = (1.0 / y) - ((x / y) - x);
	tmp = 0.0;
	if (y < -3693.8482788297247)
		tmp = t_0;
	elseif (y < 6799310503.41891)
		tmp = 1.0 - (((1.0 - x) * y) / (y + 1.0));
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(N[(1.0 / y), $MachinePrecision] - N[(N[(x / y), $MachinePrecision] - x), $MachinePrecision]), $MachinePrecision]}, If[Less[y, -3693.8482788297247], t$95$0, If[Less[y, 6799310503.41891], N[(1.0 - N[(N[(N[(1.0 - x), $MachinePrecision] * y), $MachinePrecision] / N[(y + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$0]]]

Reproduce

herbie shell --seed 2024137 
(FPCore (x y)
  :name "Diagrams.Trail:splitAtParam  from diagrams-lib-1.3.0.3, D"
  :precision binary64

  :alt
  (! :herbie-platform default (if (< y -36938482788297247/10000000000000) (- (/ 1 y) (- (/ x y) x)) (if (< y 679931050341891/100000) (- 1 (/ (* (- 1 x) y) (+ y 1))) (- (/ 1 y) (- (/ x y) x)))))

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