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

Percentage Accurate: 64.9% → 99.8%

Time: 10.9s

Alternatives: 16

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: 64.9% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.8% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -350:\\ \;\;\;\;x \cdot \left(\frac{\frac{1 + \frac{-1 + \frac{\frac{-1}{y} - -1}{y}}{y}}{y}}{x} + \frac{y}{y + 1}\right)\\ \mathbf{elif}\;y \leq 160000000:\\ \;\;\;\;\mathsf{fma}\left(y, \frac{x + -1}{y + 1}, 1\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{1 - x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -350.0)
   (*
    x
    (+
     (/ (/ (+ 1.0 (/ (+ -1.0 (/ (- (/ -1.0 y) -1.0) y)) y)) y) x)
     (/ y (+ y 1.0))))
   (if (<= y 160000000.0)
     (fma y (/ (+ x -1.0) (+ y 1.0)) 1.0)
     (+ x (/ (- 1.0 x) y)))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -350.0) {
		tmp = x * ((((1.0 + ((-1.0 + (((-1.0 / y) - -1.0) / y)) / y)) / y) / x) + (y / (y + 1.0)));
	} else if (y <= 160000000.0) {
		tmp = fma(y, ((x + -1.0) / (y + 1.0)), 1.0);
	} else {
		tmp = x + ((1.0 - x) / y);
	}
	return tmp;
}

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -350.0)
		tmp = Float64(x * Float64(Float64(Float64(Float64(1.0 + Float64(Float64(-1.0 + Float64(Float64(Float64(-1.0 / y) - -1.0) / y)) / y)) / y) / x) + Float64(y / Float64(y + 1.0))));
	elseif (y <= 160000000.0)
		tmp = fma(y, Float64(Float64(x + -1.0) / Float64(y + 1.0)), 1.0);
	else
		tmp = Float64(x + Float64(Float64(1.0 - x) / y));
	end
	return tmp
end

Wolfram

code[x_, y_] := If[LessEqual[y, -350.0], N[(x * N[(N[(N[(N[(1.0 + N[(N[(-1.0 + N[(N[(N[(-1.0 / y), $MachinePrecision] - -1.0), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision] / x), $MachinePrecision] + N[(y / N[(y + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 160000000.0], N[(y * N[(N[(x + -1.0), $MachinePrecision] / N[(y + 1.0), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision], N[(x + N[(N[(1.0 - x), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -350

   1. Initial program 35.8%

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

      1. sub-neg 35.8%

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

      2. +-commutative 35.8%

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

      3. *-commutative 35.8%

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

      4. associate-/l* 61.0%

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

      5. distribute-rgt-neg-in 61.0%

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

      6. fma-define 61.1%

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

      7. distribute-frac-neg2 61.1%

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

      8. +-commutative 61.1%

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

      9. distribute-neg-in 61.1%

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

      10. metadata-eval 61.1%

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

      11. unsub-neg 61.1%

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

   3. Simplified 61.1%

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

   5. Taylor expanded in x around -inf 77.2%

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

      1. associate-*r* 77.2%

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

      2. neg-mul-1 77.2%

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

      3. distribute-lft-out 77.2%

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

      4. associate-*r* 77.2%

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

      5. distribute-lft-neg-in 77.2%

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

      6. *-commutative 77.2%

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

      7. neg-mul-1 77.2%

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

      8. remove-double-neg 77.2%

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

      9. +-commutative 77.2%

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

      10. mul-1-neg 77.2%

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

      11. sub-neg 77.2%

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

      12. sub-neg 77.2%

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

      13. distribute-frac-neg2 77.2%

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

      14. distribute-neg-in 77.2%

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

      15. metadata-eval 77.2%

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

      16. sub-neg 77.2%

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

   7. Simplified 77.2%

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

   8. Taylor expanded in y around -inf 99.9%

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

   if -350 < y < 1.6e8

   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. +-commutative 99.9%

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

      3. *-commutative 99.9%

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

      4. associate-/l* 99.9%

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

      5. distribute-rgt-neg-in 99.9%

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

      6. fma-define 99.9%

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

      7. distribute-frac-neg2 99.9%

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

      8. +-commutative 99.9%

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

      9. distribute-neg-in 99.9%

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

      10. metadata-eval 99.9%

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

      11. unsub-neg 99.9%

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

   3. Simplified 99.9%

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

   if 1.6e8 < y

   1. Initial program 37.2%

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

      1. associate-/l* 62.4%

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

      2. +-commutative 62.4%

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

   3. Simplified 62.4%

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

   5. Taylor expanded in y around inf 100.0%

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

      1. associate--l+ 100.0%

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

      2. div-sub 100.0%

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

   7. Simplified 100.0%

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

4. Final simplification 99.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -350:\\ \;\;\;\;x \cdot \left(\frac{\frac{1 + \frac{-1 + \frac{\frac{-1}{y} - -1}{y}}{y}}{y}}{x} + \frac{y}{y + 1}\right)\\ \mathbf{elif}\;y \leq 160000000:\\ \;\;\;\;\mathsf{fma}\left(y, \frac{x + -1}{y + 1}, 1\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{1 - x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 99.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{y \cdot \left(1 - x\right)}{y + 1}\\ \mathbf{if}\;t\_0 \leq 0.98 \lor \neg \left(t\_0 \leq 2\right):\\ \;\;\;\;1 - \left(1 - x\right) \cdot \frac{y}{y + 1}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{\frac{-1 + \frac{1}{y}}{y} + \left(1 - x\right)}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (/ (* y (- 1.0 x)) (+ y 1.0))))
   (if (or (<= t_0 0.98) (not (<= t_0 2.0)))
     (- 1.0 (* (- 1.0 x) (/ y (+ y 1.0))))
     (+ x (/ (+ (/ (+ -1.0 (/ 1.0 y)) y) (- 1.0 x)) y)))))

C

double code(double x, double y) {
	double t_0 = (y * (1.0 - x)) / (y + 1.0);
	double tmp;
	if ((t_0 <= 0.98) || !(t_0 <= 2.0)) {
		tmp = 1.0 - ((1.0 - x) * (y / (y + 1.0)));
	} else {
		tmp = x + ((((-1.0 + (1.0 / y)) / y) + (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) :: t_0
    real(8) :: tmp
    t_0 = (y * (1.0d0 - x)) / (y + 1.0d0)
    if ((t_0 <= 0.98d0) .or. (.not. (t_0 <= 2.0d0))) then
        tmp = 1.0d0 - ((1.0d0 - x) * (y / (y + 1.0d0)))
    else
        tmp = x + (((((-1.0d0) + (1.0d0 / y)) / y) + (1.0d0 - x)) / 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 <= 0.98) || !(t_0 <= 2.0)) {
		tmp = 1.0 - ((1.0 - x) * (y / (y + 1.0)));
	} else {
		tmp = x + ((((-1.0 + (1.0 / y)) / y) + (1.0 - x)) / y);
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = (y * (1.0 - x)) / (y + 1.0)
	tmp = 0
	if (t_0 <= 0.98) or not (t_0 <= 2.0):
		tmp = 1.0 - ((1.0 - x) * (y / (y + 1.0)))
	else:
		tmp = x + ((((-1.0 + (1.0 / y)) / y) + (1.0 - x)) / 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 <= 0.98) || !(t_0 <= 2.0))
		tmp = Float64(1.0 - Float64(Float64(1.0 - x) * Float64(y / Float64(y + 1.0))));
	else
		tmp = Float64(x + Float64(Float64(Float64(Float64(-1.0 + Float64(1.0 / y)) / y) + Float64(1.0 - x)) / 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 <= 0.98) || ~((t_0 <= 2.0)))
		tmp = 1.0 - ((1.0 - x) * (y / (y + 1.0)));
	else
		tmp = x + ((((-1.0 + (1.0 / y)) / y) + (1.0 - x)) / 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, 0.98], N[Not[LessEqual[t$95$0, 2.0]], $MachinePrecision]], N[(1.0 - N[(N[(1.0 - x), $MachinePrecision] * N[(y / N[(y + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(N[(N[(-1.0 + N[(1.0 / y), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision] + N[(1.0 - x), $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))) < 0.97999999999999998 or 2 < (/.f64 (*.f64 (-.f64 #s(literal 1 binary64) x) y) (+.f64 y #s(literal 1 binary64)))

   1. Initial program 84.5%

      \[1 - \frac{\left(1 - x\right) \cdot y}{y + 1} \]
   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 0.97999999999999998 < (/.f64 (*.f64 (-.f64 #s(literal 1 binary64) x) y) (+.f64 y #s(literal 1 binary64))) < 2

   1. Initial program 10.7%

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

      1. associate-/l* 10.7%

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

      2. +-commutative 10.7%

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

   3. Simplified 10.7%

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

   5. Taylor expanded in y around -inf 99.8%

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

   7. Simplified 99.8%

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

   8. Taylor expanded in x around 0 99.8%

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

4. Final simplification 99.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y \cdot \left(1 - x\right)}{y + 1} \leq 0.98 \lor \neg \left(\frac{y \cdot \left(1 - x\right)}{y + 1} \leq 2\right):\\ \;\;\;\;1 - \left(1 - x\right) \cdot \frac{y}{y + 1}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{\frac{-1 + \frac{1}{y}}{y} + \left(1 - x\right)}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 99.8% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{y \cdot \left(1 - x\right)}{y + 1}\\ \mathbf{if}\;t\_0 \leq 0.98 \lor \neg \left(t\_0 \leq 1.00001\right):\\ \;\;\;\;1 - \left(1 - x\right) \cdot \frac{y}{y + 1}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{-1 + \frac{1}{y}}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (/ (* y (- 1.0 x)) (+ y 1.0))))
   (if (or (<= t_0 0.98) (not (<= t_0 1.00001)))
     (- 1.0 (* (- 1.0 x) (/ y (+ y 1.0))))
     (- 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 <= 0.98) || !(t_0 <= 1.00001)) {
		tmp = 1.0 - ((1.0 - x) * (y / (y + 1.0)));
	} 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 <= 0.98d0) .or. (.not. (t_0 <= 1.00001d0))) then
        tmp = 1.0d0 - ((1.0d0 - x) * (y / (y + 1.0d0)))
    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 <= 0.98) || !(t_0 <= 1.00001)) {
		tmp = 1.0 - ((1.0 - x) * (y / (y + 1.0)));
	} 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 <= 0.98) or not (t_0 <= 1.00001):
		tmp = 1.0 - ((1.0 - x) * (y / (y + 1.0)))
	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 <= 0.98) || !(t_0 <= 1.00001))
		tmp = Float64(1.0 - Float64(Float64(1.0 - x) * Float64(y / Float64(y + 1.0))));
	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 <= 0.98) || ~((t_0 <= 1.00001)))
		tmp = 1.0 - ((1.0 - x) * (y / (y + 1.0)));
	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, 0.98], N[Not[LessEqual[t$95$0, 1.00001]], $MachinePrecision]], N[(1.0 - N[(N[(1.0 - x), $MachinePrecision] * N[(y / N[(y + 1.0), $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))) < 0.97999999999999998 or 1.0000100000000001 < (/.f64 (*.f64 (-.f64 #s(literal 1 binary64) x) y) (+.f64 y #s(literal 1 binary64)))

   1. Initial program 84.5%

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

      1. associate-/l* 99.8%

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

      2. +-commutative 99.8%

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

   3. Simplified 99.8%

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

   if 0.97999999999999998 < (/.f64 (*.f64 (-.f64 #s(literal 1 binary64) x) y) (+.f64 y #s(literal 1 binary64))) < 1.0000100000000001

   1. Initial program 7.7%

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

      1. associate-/l* 7.7%

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

      2. +-commutative 7.7%

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

   3. Simplified 7.7%

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

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

   7. Simplified 100.0%

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

   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 99.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y \cdot \left(1 - x\right)}{y + 1} \leq 0.98 \lor \neg \left(\frac{y \cdot \left(1 - x\right)}{y + 1} \leq 1.00001\right):\\ \;\;\;\;1 - \left(1 - x\right) \cdot \frac{y}{y + 1}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{-1 + \frac{1}{y}}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 99.7% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{y}{y + 1}\\ \mathbf{if}\;y \leq -1950:\\ \;\;\;\;x \cdot \left(\frac{\frac{1 + \frac{-1 + \frac{\frac{-1}{y} - -1}{y}}{y}}{y}}{x} + t\_0\right)\\ \mathbf{elif}\;y \leq 8.5 \cdot 10^{+15}:\\ \;\;\;\;1 - \left(1 - x\right) \cdot t\_0\\ \mathbf{else}:\\ \;\;\;\;x + \frac{1}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (/ y (+ y 1.0))))
   (if (<= y -1950.0)
     (* x (+ (/ (/ (+ 1.0 (/ (+ -1.0 (/ (- (/ -1.0 y) -1.0) y)) y)) y) x) t_0))
     (if (<= y 8.5e+15) (- 1.0 (* (- 1.0 x) t_0)) (+ x (/ 1.0 y))))))

C

double code(double x, double y) {
	double t_0 = y / (y + 1.0);
	double tmp;
	if (y <= -1950.0) {
		tmp = x * ((((1.0 + ((-1.0 + (((-1.0 / y) - -1.0) / y)) / y)) / y) / x) + t_0);
	} else if (y <= 8.5e+15) {
		tmp = 1.0 - ((1.0 - x) * t_0);
	} else {
		tmp = x + (1.0 / y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: t_0
    real(8) :: tmp
    t_0 = y / (y + 1.0d0)
    if (y <= (-1950.0d0)) then
        tmp = x * ((((1.0d0 + (((-1.0d0) + ((((-1.0d0) / y) - (-1.0d0)) / y)) / y)) / y) / x) + t_0)
    else if (y <= 8.5d+15) then
        tmp = 1.0d0 - ((1.0d0 - x) * t_0)
    else
        tmp = x + (1.0d0 / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double t_0 = y / (y + 1.0);
	double tmp;
	if (y <= -1950.0) {
		tmp = x * ((((1.0 + ((-1.0 + (((-1.0 / y) - -1.0) / y)) / y)) / y) / x) + t_0);
	} else if (y <= 8.5e+15) {
		tmp = 1.0 - ((1.0 - x) * t_0);
	} else {
		tmp = x + (1.0 / y);
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = y / (y + 1.0)
	tmp = 0
	if y <= -1950.0:
		tmp = x * ((((1.0 + ((-1.0 + (((-1.0 / y) - -1.0) / y)) / y)) / y) / x) + t_0)
	elif y <= 8.5e+15:
		tmp = 1.0 - ((1.0 - x) * t_0)
	else:
		tmp = x + (1.0 / y)
	return tmp

Julia

function code(x, y)
	t_0 = Float64(y / Float64(y + 1.0))
	tmp = 0.0
	if (y <= -1950.0)
		tmp = Float64(x * Float64(Float64(Float64(Float64(1.0 + Float64(Float64(-1.0 + Float64(Float64(Float64(-1.0 / y) - -1.0) / y)) / y)) / y) / x) + t_0));
	elseif (y <= 8.5e+15)
		tmp = Float64(1.0 - Float64(Float64(1.0 - x) * t_0));
	else
		tmp = Float64(x + Float64(1.0 / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = y / (y + 1.0);
	tmp = 0.0;
	if (y <= -1950.0)
		tmp = x * ((((1.0 + ((-1.0 + (((-1.0 / y) - -1.0) / y)) / y)) / y) / x) + t_0);
	elseif (y <= 8.5e+15)
		tmp = 1.0 - ((1.0 - x) * t_0);
	else
		tmp = x + (1.0 / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(y / N[(y + 1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1950.0], N[(x * N[(N[(N[(N[(1.0 + N[(N[(-1.0 + N[(N[(N[(-1.0 / y), $MachinePrecision] - -1.0), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision] / x), $MachinePrecision] + t$95$0), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 8.5e+15], N[(1.0 - N[(N[(1.0 - x), $MachinePrecision] * t$95$0), $MachinePrecision]), $MachinePrecision], N[(x + N[(1.0 / y), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1950

   1. Initial program 34.7%

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

      1. sub-neg 34.7%

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

      2. +-commutative 34.7%

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

      3. *-commutative 34.7%

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

      4. associate-/l* 60.3%

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

      5. distribute-rgt-neg-in 60.3%

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

      6. fma-define 60.4%

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

      7. distribute-frac-neg2 60.4%

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

      8. +-commutative 60.4%

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

      9. distribute-neg-in 60.4%

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

      10. metadata-eval 60.4%

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

      11. unsub-neg 60.4%

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

   3. Simplified 60.4%

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

   5. Taylor expanded in x around -inf 76.8%

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

      1. associate-*r* 76.8%

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

      2. neg-mul-1 76.8%

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

      3. distribute-lft-out 76.8%

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

      4. associate-*r* 76.8%

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

      5. distribute-lft-neg-in 76.8%

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

      6. *-commutative 76.8%

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

      7. neg-mul-1 76.8%

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

      8. remove-double-neg 76.8%

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

      9. +-commutative 76.8%

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

      10. mul-1-neg 76.8%

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

      11. sub-neg 76.8%

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

      12. sub-neg 76.8%

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

      13. distribute-frac-neg2 76.8%

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

      14. distribute-neg-in 76.8%

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

      15. metadata-eval 76.8%

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

      16. sub-neg 76.8%

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

   7. Simplified 76.8%

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

   8. Taylor expanded in y around -inf 99.9%

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

   if -1950 < y < 8.5e15

   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 8.5e15 < y

   1. Initial program 34.4%

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

      1. associate-/l* 60.7%

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

      2. +-commutative 60.7%

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

   3. Simplified 60.7%

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

   5. Taylor expanded in y around inf 100.0%

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

      1. associate--l+ 100.0%

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

      2. div-sub 100.0%

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

   7. Simplified 100.0%

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

   8. Taylor expanded in x around 0 100.0%

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

4. Final simplification 99.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1950:\\ \;\;\;\;x \cdot \left(\frac{\frac{1 + \frac{-1 + \frac{\frac{-1}{y} - -1}{y}}{y}}{y}}{x} + \frac{y}{y + 1}\right)\\ \mathbf{elif}\;y \leq 8.5 \cdot 10^{+15}:\\ \;\;\;\;1 - \left(1 - x\right) \cdot \frac{y}{y + 1}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{1}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 99.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -13600:\\ \;\;\;\;x + \frac{\left(1 - x\right) + \frac{\frac{1 - x}{y} + \left(x + -1\right)}{y}}{y}\\ \mathbf{elif}\;y \leq 8.5 \cdot 10^{+15}:\\ \;\;\;\;1 + \left(1 - x\right) \cdot \frac{y}{-1 - y}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{1}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -13600.0)
   (+ x (/ (+ (- 1.0 x) (/ (+ (/ (- 1.0 x) y) (+ x -1.0)) y)) y))
   (if (<= y 8.5e+15) (+ 1.0 (* (- 1.0 x) (/ y (- -1.0 y)))) (+ x (/ 1.0 y)))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -13600.0) {
		tmp = x + (((1.0 - x) + ((((1.0 - x) / y) + (x + -1.0)) / y)) / y);
	} else if (y <= 8.5e+15) {
		tmp = 1.0 + ((1.0 - x) * (y / (-1.0 - y)));
	} else {
		tmp = x + (1.0 / y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (y <= (-13600.0d0)) then
        tmp = x + (((1.0d0 - x) + ((((1.0d0 - x) / y) + (x + (-1.0d0))) / y)) / y)
    else if (y <= 8.5d+15) then
        tmp = 1.0d0 + ((1.0d0 - x) * (y / ((-1.0d0) - y)))
    else
        tmp = x + (1.0d0 / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (y <= -13600.0) {
		tmp = x + (((1.0 - x) + ((((1.0 - x) / y) + (x + -1.0)) / y)) / y);
	} else if (y <= 8.5e+15) {
		tmp = 1.0 + ((1.0 - x) * (y / (-1.0 - y)));
	} else {
		tmp = x + (1.0 / y);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -13600.0:
		tmp = x + (((1.0 - x) + ((((1.0 - x) / y) + (x + -1.0)) / y)) / y)
	elif y <= 8.5e+15:
		tmp = 1.0 + ((1.0 - x) * (y / (-1.0 - y)))
	else:
		tmp = x + (1.0 / y)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -13600.0)
		tmp = Float64(x + Float64(Float64(Float64(1.0 - x) + Float64(Float64(Float64(Float64(1.0 - x) / y) + Float64(x + -1.0)) / y)) / y));
	elseif (y <= 8.5e+15)
		tmp = Float64(1.0 + Float64(Float64(1.0 - x) * Float64(y / Float64(-1.0 - y))));
	else
		tmp = Float64(x + Float64(1.0 / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -13600.0)
		tmp = x + (((1.0 - x) + ((((1.0 - x) / y) + (x + -1.0)) / y)) / y);
	elseif (y <= 8.5e+15)
		tmp = 1.0 + ((1.0 - x) * (y / (-1.0 - y)));
	else
		tmp = x + (1.0 / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -13600.0], N[(x + N[(N[(N[(1.0 - x), $MachinePrecision] + N[(N[(N[(N[(1.0 - x), $MachinePrecision] / y), $MachinePrecision] + N[(x + -1.0), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 8.5e+15], N[(1.0 + N[(N[(1.0 - x), $MachinePrecision] * N[(y / N[(-1.0 - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(1.0 / y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -13600

   1. Initial program 34.7%

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

      1. associate-/l* 60.4%

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

      2. +-commutative 60.4%

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

   3. Simplified 60.4%

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

   5. Taylor expanded in y around -inf 99.8%

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

   7. Simplified 99.8%

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

   if -13600 < y < 8.5e15

   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 8.5e15 < y

   1. Initial program 34.4%

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

      1. associate-/l* 60.7%

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

      2. +-commutative 60.7%

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

   3. Simplified 60.7%

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

   5. Taylor expanded in y around inf 100.0%

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

      1. associate--l+ 100.0%

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

      2. div-sub 100.0%

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

   7. Simplified 100.0%

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

   8. Taylor expanded in x around 0 100.0%

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

4. Final simplification 99.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -13600:\\ \;\;\;\;x + \frac{\left(1 - x\right) + \frac{\frac{1 - x}{y} + \left(x + -1\right)}{y}}{y}\\ \mathbf{elif}\;y \leq 8.5 \cdot 10^{+15}:\\ \;\;\;\;1 + \left(1 - x\right) \cdot \frac{y}{-1 - y}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{1}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 99.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -270000:\\ \;\;\;\;x + \frac{\left(1 - x\right) + \frac{x + -1}{y}}{y}\\ \mathbf{elif}\;y \leq 8.5 \cdot 10^{+15}:\\ \;\;\;\;1 - \left(1 - x\right) \cdot \frac{y}{y + 1}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{1}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -270000.0)
   (+ x (/ (+ (- 1.0 x) (/ (+ x -1.0) y)) y))
   (if (<= y 8.5e+15) (- 1.0 (* (- 1.0 x) (/ y (+ y 1.0)))) (+ x (/ 1.0 y)))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -270000.0) {
		tmp = x + (((1.0 - x) + ((x + -1.0) / y)) / y);
	} else if (y <= 8.5e+15) {
		tmp = 1.0 - ((1.0 - x) * (y / (y + 1.0)));
	} else {
		tmp = x + (1.0 / y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (y <= (-270000.0d0)) then
        tmp = x + (((1.0d0 - x) + ((x + (-1.0d0)) / y)) / y)
    else if (y <= 8.5d+15) then
        tmp = 1.0d0 - ((1.0d0 - x) * (y / (y + 1.0d0)))
    else
        tmp = x + (1.0d0 / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (y <= -270000.0) {
		tmp = x + (((1.0 - x) + ((x + -1.0) / y)) / y);
	} else if (y <= 8.5e+15) {
		tmp = 1.0 - ((1.0 - x) * (y / (y + 1.0)));
	} else {
		tmp = x + (1.0 / y);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -270000.0:
		tmp = x + (((1.0 - x) + ((x + -1.0) / y)) / y)
	elif y <= 8.5e+15:
		tmp = 1.0 - ((1.0 - x) * (y / (y + 1.0)))
	else:
		tmp = x + (1.0 / y)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -270000.0)
		tmp = Float64(x + Float64(Float64(Float64(1.0 - x) + Float64(Float64(x + -1.0) / y)) / y));
	elseif (y <= 8.5e+15)
		tmp = Float64(1.0 - Float64(Float64(1.0 - x) * Float64(y / Float64(y + 1.0))));
	else
		tmp = Float64(x + Float64(1.0 / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -270000.0)
		tmp = x + (((1.0 - x) + ((x + -1.0) / y)) / y);
	elseif (y <= 8.5e+15)
		tmp = 1.0 - ((1.0 - x) * (y / (y + 1.0)));
	else
		tmp = x + (1.0 / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -270000.0], N[(x + N[(N[(N[(1.0 - x), $MachinePrecision] + N[(N[(x + -1.0), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 8.5e+15], N[(1.0 - N[(N[(1.0 - x), $MachinePrecision] * N[(y / N[(y + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(1.0 / y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -2.7e5

   1. Initial program 33.9%

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

      1. associate-/l* 60.1%

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

      2. +-commutative 60.1%

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

   3. Simplified 60.1%

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

   5. Taylor expanded in y around -inf 100.0%

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

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

   7. Simplified 100.0%

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

   if -2.7e5 < y < 8.5e15

   1. Initial program 99.7%

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

      1. associate-/l* 99.7%

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

      2. +-commutative 99.7%

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

   3. Simplified 99.7%

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

   if 8.5e15 < y

   1. Initial program 34.4%

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

      1. associate-/l* 60.7%

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

      2. +-commutative 60.7%

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

   3. Simplified 60.7%

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

   5. Taylor expanded in y around inf 100.0%

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

      1. associate--l+ 100.0%

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

      2. div-sub 100.0%

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

   7. Simplified 100.0%

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

   8. Taylor expanded in x around 0 100.0%

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

4. Final simplification 99.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -270000:\\ \;\;\;\;x + \frac{\left(1 - x\right) + \frac{x + -1}{y}}{y}\\ \mathbf{elif}\;y \leq 8.5 \cdot 10^{+15}:\\ \;\;\;\;1 - \left(1 - x\right) \cdot \frac{y}{y + 1}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{1}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 99.5% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -430000000:\\ \;\;\;\;x - \frac{-1 + \frac{1}{y}}{y}\\ \mathbf{elif}\;y \leq 8.5 \cdot 10^{+15}:\\ \;\;\;\;1 + \frac{y}{\frac{y + 1}{x + -1}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{1}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -430000000.0)
   (- x (/ (+ -1.0 (/ 1.0 y)) y))
   (if (<= y 8.5e+15) (+ 1.0 (/ y (/ (+ y 1.0) (+ x -1.0)))) (+ x (/ 1.0 y)))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -430000000.0) {
		tmp = x - ((-1.0 + (1.0 / y)) / y);
	} else if (y <= 8.5e+15) {
		tmp = 1.0 + (y / ((y + 1.0) / (x + -1.0)));
	} else {
		tmp = x + (1.0 / y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (y <= (-430000000.0d0)) then
        tmp = x - (((-1.0d0) + (1.0d0 / y)) / y)
    else if (y <= 8.5d+15) then
        tmp = 1.0d0 + (y / ((y + 1.0d0) / (x + (-1.0d0))))
    else
        tmp = x + (1.0d0 / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (y <= -430000000.0) {
		tmp = x - ((-1.0 + (1.0 / y)) / y);
	} else if (y <= 8.5e+15) {
		tmp = 1.0 + (y / ((y + 1.0) / (x + -1.0)));
	} else {
		tmp = x + (1.0 / y);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -430000000.0:
		tmp = x - ((-1.0 + (1.0 / y)) / y)
	elif y <= 8.5e+15:
		tmp = 1.0 + (y / ((y + 1.0) / (x + -1.0)))
	else:
		tmp = x + (1.0 / y)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -430000000.0)
		tmp = Float64(x - Float64(Float64(-1.0 + Float64(1.0 / y)) / y));
	elseif (y <= 8.5e+15)
		tmp = Float64(1.0 + Float64(y / Float64(Float64(y + 1.0) / Float64(x + -1.0))));
	else
		tmp = Float64(x + Float64(1.0 / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -430000000.0)
		tmp = x - ((-1.0 + (1.0 / y)) / y);
	elseif (y <= 8.5e+15)
		tmp = 1.0 + (y / ((y + 1.0) / (x + -1.0)));
	else
		tmp = x + (1.0 / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -430000000.0], N[(x - N[(N[(-1.0 + N[(1.0 / y), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 8.5e+15], N[(1.0 + N[(y / N[(N[(y + 1.0), $MachinePrecision] / N[(x + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(1.0 / y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -4.3e8

   1. Initial program 32.6%

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

      1. associate-/l* 59.3%

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

      2. +-commutative 59.3%

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

   3. Simplified 59.3%

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

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

   7. Simplified 100.0%

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

   8. Taylor expanded in x around 0 99.5%

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

   if -4.3e8 < y < 8.5e15

   1. Initial program 99.7%

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

      1. sub-neg 99.7%

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

      2. +-commutative 99.7%

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

      3. *-commutative 99.7%

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

      4. associate-/l* 99.7%

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

      5. distribute-rgt-neg-in 99.7%

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

      6. fma-define 99.7%

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

      7. distribute-frac-neg2 99.7%

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

      8. +-commutative 99.7%

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

      9. distribute-neg-in 99.7%

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

      10. metadata-eval 99.7%

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

      11. unsub-neg 99.7%

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

   3. Simplified 99.7%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y, \frac{1 - x}{-1 - y}, 1\right)} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. fma-undefine 99.7%

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

      2. clear-num 99.7%

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

      3. un-div-inv 99.7%

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

   6. Applied egg-rr 99.7%

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

   if 8.5e15 < y

   1. Initial program 34.4%

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

      1. associate-/l* 60.7%

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

      2. +-commutative 60.7%

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

   3. Simplified 60.7%

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

   5. Taylor expanded in y around inf 100.0%

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

      1. associate--l+ 100.0%

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

      2. div-sub 100.0%

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

   7. Simplified 100.0%

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

   8. Taylor expanded in x around 0 100.0%

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

4. Final simplification 99.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -430000000:\\ \;\;\;\;x - \frac{-1 + \frac{1}{y}}{y}\\ \mathbf{elif}\;y \leq 8.5 \cdot 10^{+15}:\\ \;\;\;\;1 + \frac{y}{\frac{y + 1}{x + -1}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{1}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 98.7% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -900 \lor \neg \left(y \leq 13000\right):\\ \;\;\;\;x + \frac{1 - x}{y}\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{y \cdot x}{y + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= y -900.0) (not (<= y 13000.0)))
   (+ x (/ (- 1.0 x) y))
   (+ 1.0 (/ (* y x) (+ y 1.0)))))

C

double code(double x, double y) {
	double tmp;
	if ((y <= -900.0) || !(y <= 13000.0)) {
		tmp = x + ((1.0 - x) / y);
	} else {
		tmp = 1.0 + ((y * x) / (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 <= (-900.0d0)) .or. (.not. (y <= 13000.0d0))) then
        tmp = x + ((1.0d0 - x) / y)
    else
        tmp = 1.0d0 + ((y * x) / (y + 1.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((y <= -900.0) || !(y <= 13000.0)) {
		tmp = x + ((1.0 - x) / y);
	} else {
		tmp = 1.0 + ((y * x) / (y + 1.0));
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (y <= -900.0) or not (y <= 13000.0):
		tmp = x + ((1.0 - x) / y)
	else:
		tmp = 1.0 + ((y * x) / (y + 1.0))
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((y <= -900.0) || !(y <= 13000.0))
		tmp = Float64(x + Float64(Float64(1.0 - x) / y));
	else
		tmp = Float64(1.0 + Float64(Float64(y * x) / Float64(y + 1.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((y <= -900.0) || ~((y <= 13000.0)))
		tmp = x + ((1.0 - x) / y);
	else
		tmp = 1.0 + ((y * x) / (y + 1.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[y, -900.0], N[Not[LessEqual[y, 13000.0]], $MachinePrecision]], N[(x + N[(N[(1.0 - x), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], N[(1.0 + N[(N[(y * x), $MachinePrecision] / N[(y + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -900 or 13000 < y

   1. Initial program 36.1%

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

      1. associate-/l* 61.5%

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

      2. +-commutative 61.5%

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

   3. Simplified 61.5%

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

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

   7. Simplified 99.1%

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

   if -900 < y < 13000

   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 x around inf 98.7%

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

      1. mul-1-neg 98.7%

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

      2. distribute-neg-frac2 98.7%

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

      3. *-commutative 98.7%

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

      4. distribute-neg-in 98.7%

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

      5. metadata-eval 98.7%

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

      6. sub-neg 98.7%

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

   7. Simplified 98.7%

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

4. Final simplification 98.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -900 \lor \neg \left(y \leq 13000\right):\\ \;\;\;\;x + \frac{1 - x}{y}\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{y \cdot x}{y + 1}\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 98.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -900:\\ \;\;\;\;x + \frac{\frac{-1}{y} - -1}{y}\\ \mathbf{elif}\;y \leq 130000:\\ \;\;\;\;1 + \frac{y \cdot x}{y + 1}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{1 - x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -900.0)
   (+ x (/ (- (/ -1.0 y) -1.0) y))
   (if (<= y 130000.0) (+ 1.0 (/ (* y x) (+ y 1.0))) (+ x (/ (- 1.0 x) y)))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -900.0) {
		tmp = x + (((-1.0 / y) - -1.0) / y);
	} else if (y <= 130000.0) {
		tmp = 1.0 + ((y * x) / (y + 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 <= (-900.0d0)) then
        tmp = x + ((((-1.0d0) / y) - (-1.0d0)) / y)
    else if (y <= 130000.0d0) then
        tmp = 1.0d0 + ((y * x) / (y + 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 <= -900.0) {
		tmp = x + (((-1.0 / y) - -1.0) / y);
	} else if (y <= 130000.0) {
		tmp = 1.0 + ((y * x) / (y + 1.0));
	} else {
		tmp = x + ((1.0 - x) / y);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -900.0:
		tmp = x + (((-1.0 / y) - -1.0) / y)
	elif y <= 130000.0:
		tmp = 1.0 + ((y * x) / (y + 1.0))
	else:
		tmp = x + ((1.0 - x) / y)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -900.0)
		tmp = Float64(x + Float64(Float64(Float64(-1.0 / y) - -1.0) / y));
	elseif (y <= 130000.0)
		tmp = Float64(1.0 + Float64(Float64(y * x) / Float64(y + 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 <= -900.0)
		tmp = x + (((-1.0 / y) - -1.0) / y);
	elseif (y <= 130000.0)
		tmp = 1.0 + ((y * x) / (y + 1.0));
	else
		tmp = x + ((1.0 - x) / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -900.0], N[(x + N[(N[(N[(-1.0 / y), $MachinePrecision] - -1.0), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 130000.0], N[(1.0 + N[(N[(y * x), $MachinePrecision] / N[(y + 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 < -900

   1. Initial program 34.7%

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

      1. associate-/l* 60.4%

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

      2. +-commutative 60.4%

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

   3. Simplified 60.4%

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

   5. Taylor expanded in y around -inf 99.4%

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

      1. mul-1-neg 99.4%

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

      2. unsub-neg 99.4%

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

   7. Simplified 99.4%

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

   8. Taylor expanded in x around 0 98.1%

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

   if -900 < y < 1.3e5

   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 x around inf 98.7%

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

      1. mul-1-neg 98.7%

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

      2. distribute-neg-frac2 98.7%

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

      3. *-commutative 98.7%

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

      4. distribute-neg-in 98.7%

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

      5. metadata-eval 98.7%

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

      6. sub-neg 98.7%

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

   7. Simplified 98.7%

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

   if 1.3e5 < y

   1. Initial program 37.2%

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

      1. associate-/l* 62.4%

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

      2. +-commutative 62.4%

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

   3. Simplified 62.4%

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

   5. Taylor expanded in y around inf 100.0%

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

      1. associate--l+ 100.0%

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

      2. div-sub 100.0%

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

   7. Simplified 100.0%

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

4. Final simplification 98.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -900:\\ \;\;\;\;x + \frac{\frac{-1}{y} - -1}{y}\\ \mathbf{elif}\;y \leq 130000:\\ \;\;\;\;1 + \frac{y \cdot x}{y + 1}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{1 - x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 98.3% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1700:\\ \;\;\;\;x + \frac{1 - x}{y}\\ \mathbf{elif}\;y \leq 8.5 \cdot 10^{+15}:\\ \;\;\;\;1 + \frac{y}{\frac{y + 1}{x}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{1}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -1700.0)
   (+ x (/ (- 1.0 x) y))
   (if (<= y 8.5e+15) (+ 1.0 (/ y (/ (+ y 1.0) x))) (+ x (/ 1.0 y)))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -1700.0) {
		tmp = x + ((1.0 - x) / y);
	} else if (y <= 8.5e+15) {
		tmp = 1.0 + (y / ((y + 1.0) / x));
	} else {
		tmp = x + (1.0 / y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (y <= (-1700.0d0)) then
        tmp = x + ((1.0d0 - x) / y)
    else if (y <= 8.5d+15) then
        tmp = 1.0d0 + (y / ((y + 1.0d0) / x))
    else
        tmp = x + (1.0d0 / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (y <= -1700.0) {
		tmp = x + ((1.0 - x) / y);
	} else if (y <= 8.5e+15) {
		tmp = 1.0 + (y / ((y + 1.0) / x));
	} else {
		tmp = x + (1.0 / y);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -1700.0:
		tmp = x + ((1.0 - x) / y)
	elif y <= 8.5e+15:
		tmp = 1.0 + (y / ((y + 1.0) / x))
	else:
		tmp = x + (1.0 / y)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -1700.0)
		tmp = Float64(x + Float64(Float64(1.0 - x) / y));
	elseif (y <= 8.5e+15)
		tmp = Float64(1.0 + Float64(y / Float64(Float64(y + 1.0) / x)));
	else
		tmp = Float64(x + Float64(1.0 / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -1700.0)
		tmp = x + ((1.0 - x) / y);
	elseif (y <= 8.5e+15)
		tmp = 1.0 + (y / ((y + 1.0) / x));
	else
		tmp = x + (1.0 / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -1700.0], N[(x + N[(N[(1.0 - x), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 8.5e+15], N[(1.0 + N[(y / N[(N[(y + 1.0), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(1.0 / y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -1700

   1. Initial program 34.7%

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

      1. associate-/l* 60.4%

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

      2. +-commutative 60.4%

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

   3. Simplified 60.4%

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

   5. Taylor expanded in y around inf 98.0%

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

      1. associate--l+ 98.0%

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

      2. div-sub 98.0%

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

   7. Simplified 98.0%

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

   if -1700 < y < 8.5e15

   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. +-commutative 99.9%

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

      3. *-commutative 99.9%

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

      4. associate-/l* 99.9%

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

      5. distribute-rgt-neg-in 99.9%

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

      6. fma-define 99.9%

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

      7. distribute-frac-neg2 99.9%

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

      8. +-commutative 99.9%

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

      9. distribute-neg-in 99.9%

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

      10. metadata-eval 99.9%

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

      11. unsub-neg 99.9%

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

   3. Simplified 99.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y, \frac{1 - x}{-1 - y}, 1\right)} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. fma-undefine 99.9%

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

      2. clear-num 99.9%

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

      3. un-div-inv 99.9%

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

   6. Applied egg-rr 99.9%

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

   7. Taylor expanded in x around inf 98.6%

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

   if 8.5e15 < y

   1. Initial program 34.4%

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

      1. associate-/l* 60.7%

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

      2. +-commutative 60.7%

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

   3. Simplified 60.7%

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

   5. Taylor expanded in y around inf 100.0%

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

      1. associate--l+ 100.0%

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

      2. div-sub 100.0%

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

   7. Simplified 100.0%

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

   8. Taylor expanded in x around 0 100.0%

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

4. Final simplification 98.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1700:\\ \;\;\;\;x + \frac{1 - x}{y}\\ \mathbf{elif}\;y \leq 8.5 \cdot 10^{+15}:\\ \;\;\;\;1 + \frac{y}{\frac{y + 1}{x}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{1}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 98.3% accurate, 0.6× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

2. if y < -1 or 1 < y

   1. Initial program 38.0%

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

      1. associate-/l* 62.7%

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

      2. +-commutative 62.7%

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

   3. Simplified 62.7%

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

   5. Taylor expanded in y around inf 97.0%

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

      1. associate--l+ 97.0%

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

      2. div-sub 97.0%

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

   7. Simplified 97.0%

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

   if -1 < y < 1

   1. Initial program 100.0%

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

      1. associate-/l* 100.0%

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

      2. +-commutative 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in y around 0 97.8%

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

4. Final simplification 97.4%

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

Alternative 12: 98.0% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1 \lor \neg \left(y \leq 1.22\right):\\ \;\;\;\;x + \frac{1 - x}{y}\\ \mathbf{else}:\\ \;\;\;\;1 + y \cdot x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= y -1.0) (not (<= y 1.22))) (+ x (/ (- 1.0 x) y)) (+ 1.0 (* y x))))

C

double code(double x, double y) {
	double tmp;
	if ((y <= -1.0) || !(y <= 1.22)) {
		tmp = x + ((1.0 - x) / 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 <= 1.22d0))) then
        tmp = x + ((1.0d0 - x) / 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 <= 1.22)) {
		tmp = x + ((1.0 - x) / y);
	} else {
		tmp = 1.0 + (y * x);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (y <= -1.0) or not (y <= 1.22):
		tmp = x + ((1.0 - x) / y)
	else:
		tmp = 1.0 + (y * x)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((y <= -1.0) || !(y <= 1.22))
		tmp = Float64(x + Float64(Float64(1.0 - x) / 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 <= 1.22)))
		tmp = x + ((1.0 - x) / 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, 1.22]], $MachinePrecision]], N[(x + N[(N[(1.0 - x), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], N[(1.0 + N[(y * x), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1 or 1.21999999999999997 < y

   1. Initial program 38.0%

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

      1. associate-/l* 62.7%

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

      2. +-commutative 62.7%

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

   3. Simplified 62.7%

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

   5. Taylor expanded in y around inf 97.0%

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

      1. associate--l+ 97.0%

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

      2. div-sub 97.0%

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

   7. Simplified 97.0%

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

   if -1 < y < 1.21999999999999997

   1. Initial program 100.0%

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

      1. sub-neg 100.0%

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

      2. +-commutative 100.0%

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

      3. *-commutative 100.0%

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

      4. associate-/l* 100.0%

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

      5. distribute-rgt-neg-in 100.0%

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

      6. fma-define 100.0%

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

      7. distribute-frac-neg2 100.0%

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

      8. +-commutative 100.0%

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

      9. distribute-neg-in 100.0%

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

      10. metadata-eval 100.0%

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

      11. unsub-neg 100.0%

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

   3. Simplified 100.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y, \frac{1 - x}{-1 - y}, 1\right)} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. fma-undefine 100.0%

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

      2. clear-num 99.9%

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

      3. un-div-inv 99.9%

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

   6. Applied egg-rr 99.9%

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

   7. Taylor expanded in x around inf 99.2%

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

   8. Taylor expanded in y around 0 97.6%

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

      1. *-commutative 97.6%

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

   10. Simplified 97.6%

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

4. Final simplification 97.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1 \lor \neg \left(y \leq 1.22\right):\\ \;\;\;\;x + \frac{1 - x}{y}\\ \mathbf{else}:\\ \;\;\;\;1 + y \cdot x\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 97.7% 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 38.0%

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

      1. associate-/l* 62.7%

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

      2. +-commutative 62.7%

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

   3. Simplified 62.7%

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

   5. Taylor expanded in y around inf 97.0%

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

      1. associate--l+ 97.0%

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

      2. div-sub 97.0%

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

   7. Simplified 97.0%

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

   8. Taylor expanded in x around 0 95.8%

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

   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. +-commutative 100.0%

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

      3. *-commutative 100.0%

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

      4. associate-/l* 100.0%

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

      5. distribute-rgt-neg-in 100.0%

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

      6. fma-define 100.0%

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

      7. distribute-frac-neg2 100.0%

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

      8. +-commutative 100.0%

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

      9. distribute-neg-in 100.0%

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

      10. metadata-eval 100.0%

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

      11. unsub-neg 100.0%

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

   3. Simplified 100.0%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y, \frac{1 - x}{-1 - y}, 1\right)} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. fma-undefine 100.0%

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

      2. clear-num 99.9%

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

      3. un-div-inv 99.9%

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

   6. Applied egg-rr 99.9%

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

   7. Taylor expanded in x around inf 99.2%

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

   8. Taylor expanded in y around 0 97.6%

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

      1. *-commutative 97.6%

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

   10. Simplified 97.6%

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

4. Final simplification 96.7%

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

Alternative 14: 85.8% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 38:\\ \;\;\;\;1 + y \cdot x\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -1.0) x (if (<= y 38.0) (+ 1.0 (* y x)) x)))

C

double code(double x, double y) {
	double tmp;
	if (y <= -1.0) {
		tmp = x;
	} else if (y <= 38.0) {
		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 <= 38.0d0) 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 <= 38.0) {
		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 <= 38.0:
		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 <= 38.0)
		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 <= 38.0)
		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, 38.0], N[(1.0 + N[(y * x), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if y < -1 or 38 < y

   1. Initial program 37.1%

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

      1. associate-/l* 62.1%

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

      2. +-commutative 62.1%

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

   3. Simplified 62.1%

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

   5. Taylor expanded in y around inf 77.4%

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

   if -1 < y < 38

   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. +-commutative 99.9%

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

      3. *-commutative 99.9%

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

      4. associate-/l* 99.9%

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

      5. distribute-rgt-neg-in 99.9%

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

      6. fma-define 99.9%

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

      7. distribute-frac-neg2 99.9%

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

      8. +-commutative 99.9%

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

      9. distribute-neg-in 99.9%

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

      10. metadata-eval 99.9%

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

      11. unsub-neg 99.9%

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

   3. Simplified 99.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(y, \frac{1 - x}{-1 - y}, 1\right)} \]
   4. Add Preprocessing
   5. Step-by-step derivation

      1. fma-undefine 99.9%

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

      2. clear-num 99.9%

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

      3. un-div-inv 99.8%

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

   6. Applied egg-rr 99.8%

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

   7. Taylor expanded in x around inf 98.6%

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

   8. Taylor expanded in y around 0 96.4%

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

      1. *-commutative 96.4%

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

   10. Simplified 96.4%

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

Alternative 15: 74.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 0.0076:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (if (<= y -1.0) x (if (<= y 0.0076) 1.0 x)))

C

double code(double x, double y) {
	double tmp;
	if (y <= -1.0) {
		tmp = x;
	} else if (y <= 0.0076) {
		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 <= 0.0076d0) 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 <= 0.0076) {
		tmp = 1.0;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -1.0:
		tmp = x
	elif y <= 0.0076:
		tmp = 1.0
	else:
		tmp = x
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -1.0)
		tmp = x;
	elseif (y <= 0.0076)
		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 <= 0.0076)
		tmp = 1.0;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -1.0], x, If[LessEqual[y, 0.0076], 1.0, x]]

Derivation

1. Split input into 2 regimes

2. if y < -1 or 0.00759999999999999998 < y

   1. Initial program 38.5%

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

      1. associate-/l* 63.0%

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

      2. +-commutative 63.0%

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

   3. Simplified 63.0%

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

   5. Taylor expanded in y around inf 75.9%

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

   if -1 < y < 0.00759999999999999998

   1. Initial program 100.0%

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

      1. sub-neg 100.0%

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

      2. +-commutative 100.0%

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

      3. *-commutative 100.0%

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

      4. associate-/l* 100.0%

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

      5. distribute-rgt-neg-in 100.0%

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

      6. fma-define 100.0%

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

      7. distribute-frac-neg2 100.0%

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

      8. +-commutative 100.0%

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

      9. distribute-neg-in 100.0%

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

      10. metadata-eval 100.0%

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

      11. unsub-neg 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in x around -inf 99.7%

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

      1. associate-*r* 99.7%

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

      2. neg-mul-1 99.7%

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

      3. distribute-lft-out 99.7%

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

      4. associate-*r* 99.7%

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

      5. distribute-lft-neg-in 99.7%

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

      6. *-commutative 99.7%

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

      7. neg-mul-1 99.7%

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

      8. remove-double-neg 99.7%

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

      9. +-commutative 99.7%

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

      10. mul-1-neg 99.7%

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

      11. sub-neg 99.7%

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

      12. sub-neg 99.7%

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

      13. distribute-frac-neg2 99.7%

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

      14. distribute-neg-in 99.7%

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

      15. metadata-eval 99.7%

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

      16. sub-neg 99.7%

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

   7. Simplified 99.7%

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

      1. add-cube-cbrt 99.6%

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

      2. pow3 99.5%

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

   9. Applied egg-rr 99.5%

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

   10. Taylor expanded in y around 0 78.5%

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

Alternative 16: 38.3% accurate, 11.0× speedup

Math

\[\begin{array}{l} \\ 1 \end{array} \]

FPCore

(FPCore (x y) :precision binary64 1.0)

C

double code(double x, double y) {
	return 1.0;
}

Fortran

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

Java

public static double code(double x, double y) {
	return 1.0;
}

Python

def code(x, y):
	return 1.0

Julia

function code(x, y)
	return 1.0
end

MATLAB

function tmp = code(x, y)
	tmp = 1.0;
end

Wolfram

code[x_, y_] := 1.0

Derivation

1. Initial program 69.2%

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

   1. sub-neg 69.2%

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

   2. +-commutative 69.2%

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

   3. *-commutative 69.2%

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

   4. associate-/l* 81.4%

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

   5. distribute-rgt-neg-in 81.4%

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

   6. fma-define 81.5%

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

   7. distribute-frac-neg2 81.5%

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

   8. +-commutative 81.5%

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

   9. distribute-neg-in 81.5%

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

   10. metadata-eval 81.5%

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

   11. unsub-neg 81.5%

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

3. Simplified 81.5%

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

5. Taylor expanded in x around -inf 90.5%

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

   1. associate-*r* 90.5%

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

   2. neg-mul-1 90.5%

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

   3. distribute-lft-out 90.5%

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

   4. associate-*r* 90.5%

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

   5. distribute-lft-neg-in 90.5%

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

   6. *-commutative 90.5%

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

   7. neg-mul-1 90.5%

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

   8. remove-double-neg 90.5%

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

   9. +-commutative 90.5%

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

   10. mul-1-neg 90.5%

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

   11. sub-neg 90.5%

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

   12. sub-neg 90.5%

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

   13. distribute-frac-neg2 90.5%

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

   14. distribute-neg-in 90.5%

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

   15. metadata-eval 90.5%

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

   16. sub-neg 90.5%

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

7. Simplified 90.5%

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

   1. add-cube-cbrt 89.6%

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

   2. pow3 89.6%

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

9. Applied egg-rr 89.6%

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

10. Taylor expanded in y around 0 41.1%

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

Developer Target 1: 99.6% 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 2024129 
(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))))