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

Percentage Accurate: 65.6% → 99.9%

Time: 8.1s

Alternatives: 13

Speedup: 2.0×

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: 65.6% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.9% accurate, 0.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x - \frac{\mathsf{fma}\left(\frac{1 - x}{y}, 1 - \frac{1}{y}, x - 1\right)}{y}\\ \mathbf{if}\;y \leq -13000:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq 12000:\\ \;\;\;\;\mathsf{fma}\left(y, \frac{1 - x}{-1 - y}, 1\right)\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (- x (/ (fma (/ (- 1.0 x) y) (- 1.0 (/ 1.0 y)) (- x 1.0)) y))))
   (if (<= y -13000.0)
     t_0
     (if (<= y 12000.0) (fma y (/ (- 1.0 x) (- -1.0 y)) 1.0) t_0))))

C

double code(double x, double y) {
	double t_0 = x - (fma(((1.0 - x) / y), (1.0 - (1.0 / y)), (x - 1.0)) / y);
	double tmp;
	if (y <= -13000.0) {
		tmp = t_0;
	} else if (y <= 12000.0) {
		tmp = fma(y, ((1.0 - x) / (-1.0 - y)), 1.0);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Julia

function code(x, y)
	t_0 = Float64(x - Float64(fma(Float64(Float64(1.0 - x) / y), Float64(1.0 - Float64(1.0 / y)), Float64(x - 1.0)) / y))
	tmp = 0.0
	if (y <= -13000.0)
		tmp = t_0;
	elseif (y <= 12000.0)
		tmp = fma(y, Float64(Float64(1.0 - x) / Float64(-1.0 - y)), 1.0);
	else
		tmp = t_0;
	end
	return tmp
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(x - N[(N[(N[(N[(1.0 - x), $MachinePrecision] / y), $MachinePrecision] * N[(1.0 - N[(1.0 / y), $MachinePrecision]), $MachinePrecision] + N[(x - 1.0), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -13000.0], t$95$0, If[LessEqual[y, 12000.0], N[(y * N[(N[(1.0 - x), $MachinePrecision] / N[(-1.0 - y), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if y < -13000 or 12000 < y

   1. Initial program 37.3%

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

   3. Taylor expanded in y around -inf

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

   5. Applied rewrites 99.9%

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

   if -13000 < y < 12000

   1. Initial program 100.0%

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

      1. lift--.f64 N/A

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

      2. sub-neg N/A

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

      3. +-commutative N/A

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

      4. lift-/.f64 N/A

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

      5. distribute-neg-frac2 N/A

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

      6. lift-*.f64 N/A

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

      7. *-commutative N/A

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

      8. associate-/l* N/A

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

      9. lower-fma.f64 N/A

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

      10. lower-/.f64 N/A

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

      11. lift-+.f64 N/A

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

      12. +-commutative N/A

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

      13. distribute-neg-in N/A

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

      14. metadata-eval N/A

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

      15. unsub-neg N/A

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

      16. lower--.f64 100.0

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

   4. Applied rewrites 100.0%

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

Alternative 2: 99.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \mathsf{fma}\left(\frac{1 - x}{y}, 1 - \frac{1}{y}, x\right)\\ \mathbf{if}\;y \leq -390000:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq 300000:\\ \;\;\;\;\mathsf{fma}\left(\frac{y}{\mathsf{fma}\left(y, y, -1\right)} \cdot \left(1 - x\right), 1 - y, 1\right)\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (fma (/ (- 1.0 x) y) (- 1.0 (/ 1.0 y)) x)))
   (if (<= y -390000.0)
     t_0
     (if (<= y 300000.0)
       (fma (* (/ y (fma y y -1.0)) (- 1.0 x)) (- 1.0 y) 1.0)
       t_0))))

C

double code(double x, double y) {
	double t_0 = fma(((1.0 - x) / y), (1.0 - (1.0 / y)), x);
	double tmp;
	if (y <= -390000.0) {
		tmp = t_0;
	} else if (y <= 300000.0) {
		tmp = fma(((y / fma(y, y, -1.0)) * (1.0 - x)), (1.0 - y), 1.0);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Julia

function code(x, y)
	t_0 = fma(Float64(Float64(1.0 - x) / y), Float64(1.0 - Float64(1.0 / y)), x)
	tmp = 0.0
	if (y <= -390000.0)
		tmp = t_0;
	elseif (y <= 300000.0)
		tmp = fma(Float64(Float64(y / fma(y, y, -1.0)) * Float64(1.0 - x)), Float64(1.0 - y), 1.0);
	else
		tmp = t_0;
	end
	return tmp
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(N[(N[(1.0 - x), $MachinePrecision] / y), $MachinePrecision] * N[(1.0 - N[(1.0 / y), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision]}, If[LessEqual[y, -390000.0], t$95$0, If[LessEqual[y, 300000.0], N[(N[(N[(y / N[(y * y + -1.0), $MachinePrecision]), $MachinePrecision] * N[(1.0 - x), $MachinePrecision]), $MachinePrecision] * N[(1.0 - y), $MachinePrecision] + 1.0), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if y < -3.9e5 or 3e5 < y

   1. Initial program 36.5%

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

   3. Taylor expanded in y around inf

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

      1. sub-neg N/A

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

      2. +-commutative N/A

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

      3. associate-+l+ N/A

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

      4. +-commutative N/A

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

      5. associate-+l+ N/A

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

      6. +-commutative N/A

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

      7. +-commutative N/A

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

      8. associate-+r+ N/A

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

      9. neg-sub0 N/A

         \[\leadsto -1 \cdot \frac{1 + -1 \cdot x}{{y}^{2}} + \left(\left(\color{blue}{\left(0 - \frac{x}{y}\right)} + \frac{1}{y}\right) + x\right) \]

      10. associate--r- N/A

          \[\leadsto -1 \cdot \frac{1 + -1 \cdot x}{{y}^{2}} + \left(\color{blue}{\left(0 - \left(\frac{x}{y} - \frac{1}{y}\right)\right)} + x\right) \]

      11. div-sub N/A

          \[\leadsto -1 \cdot \frac{1 + -1 \cdot x}{{y}^{2}} + \left(\left(0 - \color{blue}{\frac{x - 1}{y}}\right) + x\right) \]

      12. neg-sub0 N/A

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

      13. mul-1-neg N/A

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

      14. associate-+l+ N/A

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

   5. Applied rewrites 100.0%

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

   if -3.9e5 < y < 3e5

   1. Initial program 99.8%

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

      1. lift--.f64 N/A

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

      2. sub-neg N/A

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

      3. +-commutative N/A

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

      4. lift-/.f64 N/A

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

      5. lift-+.f64 N/A

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

      6. flip-+ N/A

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

      7. associate-/r/ N/A

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

      8. distribute-rgt-neg-in N/A

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

      9. sub-neg N/A

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

      10. metadata-eval N/A

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

      11. distribute-neg-in N/A

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

      12. metadata-eval N/A

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

      13. +-commutative N/A

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

      14. *-rgt-identity N/A

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

      15. sub-neg N/A

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

      16. metadata-eval N/A

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

      17. lower-fma.f64 N/A

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

   4. Applied rewrites 99.8%

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

4. Final simplification 99.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -390000:\\ \;\;\;\;\mathsf{fma}\left(\frac{1 - x}{y}, 1 - \frac{1}{y}, x\right)\\ \mathbf{elif}\;y \leq 300000:\\ \;\;\;\;\mathsf{fma}\left(\frac{y}{\mathsf{fma}\left(y, y, -1\right)} \cdot \left(1 - x\right), 1 - y, 1\right)\\ \mathbf{else}:\\ \;\;\;\;\mathsf{fma}\left(\frac{1 - x}{y}, 1 - \frac{1}{y}, x\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 99.9% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \mathsf{fma}\left(\frac{1 - x}{y}, 1 - \frac{1}{y}, x\right)\\ \mathbf{if}\;y \leq -290000:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq 550000:\\ \;\;\;\;\mathsf{fma}\left(y, \frac{1 - x}{-1 - y}, 1\right)\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (fma (/ (- 1.0 x) y) (- 1.0 (/ 1.0 y)) x)))
   (if (<= y -290000.0)
     t_0
     (if (<= y 550000.0) (fma y (/ (- 1.0 x) (- -1.0 y)) 1.0) t_0))))

C

double code(double x, double y) {
	double t_0 = fma(((1.0 - x) / y), (1.0 - (1.0 / y)), x);
	double tmp;
	if (y <= -290000.0) {
		tmp = t_0;
	} else if (y <= 550000.0) {
		tmp = fma(y, ((1.0 - x) / (-1.0 - y)), 1.0);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Julia

function code(x, y)
	t_0 = fma(Float64(Float64(1.0 - x) / y), Float64(1.0 - Float64(1.0 / y)), x)
	tmp = 0.0
	if (y <= -290000.0)
		tmp = t_0;
	elseif (y <= 550000.0)
		tmp = fma(y, Float64(Float64(1.0 - x) / Float64(-1.0 - y)), 1.0);
	else
		tmp = t_0;
	end
	return tmp
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(N[(N[(1.0 - x), $MachinePrecision] / y), $MachinePrecision] * N[(1.0 - N[(1.0 / y), $MachinePrecision]), $MachinePrecision] + x), $MachinePrecision]}, If[LessEqual[y, -290000.0], t$95$0, If[LessEqual[y, 550000.0], N[(y * N[(N[(1.0 - x), $MachinePrecision] / N[(-1.0 - y), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if y < -2.9e5 or 5.5e5 < y

   1. Initial program 36.5%

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

   3. Taylor expanded in y around inf

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

      1. sub-neg N/A

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

      2. +-commutative N/A

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

      3. associate-+l+ N/A

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

      4. +-commutative N/A

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

      5. associate-+l+ N/A

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

      6. +-commutative N/A

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

      7. +-commutative N/A

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

      8. associate-+r+ N/A

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

      9. neg-sub0 N/A

         \[\leadsto -1 \cdot \frac{1 + -1 \cdot x}{{y}^{2}} + \left(\left(\color{blue}{\left(0 - \frac{x}{y}\right)} + \frac{1}{y}\right) + x\right) \]

      10. associate--r- N/A

          \[\leadsto -1 \cdot \frac{1 + -1 \cdot x}{{y}^{2}} + \left(\color{blue}{\left(0 - \left(\frac{x}{y} - \frac{1}{y}\right)\right)} + x\right) \]

      11. div-sub N/A

          \[\leadsto -1 \cdot \frac{1 + -1 \cdot x}{{y}^{2}} + \left(\left(0 - \color{blue}{\frac{x - 1}{y}}\right) + x\right) \]

      12. neg-sub0 N/A

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

      13. mul-1-neg N/A

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

      14. associate-+l+ N/A

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

   5. Applied rewrites 100.0%

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

   if -2.9e5 < y < 5.5e5

   1. Initial program 99.8%

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

      1. lift--.f64 N/A

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

      2. sub-neg N/A

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

      3. +-commutative N/A

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

      4. lift-/.f64 N/A

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

      5. distribute-neg-frac2 N/A

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

      6. lift-*.f64 N/A

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

      7. *-commutative N/A

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

      8. associate-/l* N/A

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

      9. lower-fma.f64 N/A

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

      10. lower-/.f64 N/A

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

      11. lift-+.f64 N/A

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

      12. +-commutative N/A

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

      13. distribute-neg-in N/A

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

      14. metadata-eval N/A

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

      15. unsub-neg N/A

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

      16. lower--.f64 99.8

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

   4. Applied rewrites 99.8%

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

Alternative 4: 99.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x - \frac{-1}{y}\\ \mathbf{if}\;y \leq -18000000000:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq 100000000000:\\ \;\;\;\;\mathsf{fma}\left(y, \frac{1 - x}{-1 - y}, 1\right)\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (- x (/ -1.0 y))))
   (if (<= y -18000000000.0)
     t_0
     (if (<= y 100000000000.0) (fma y (/ (- 1.0 x) (- -1.0 y)) 1.0) t_0))))

C

double code(double x, double y) {
	double t_0 = x - (-1.0 / y);
	double tmp;
	if (y <= -18000000000.0) {
		tmp = t_0;
	} else if (y <= 100000000000.0) {
		tmp = fma(y, ((1.0 - x) / (-1.0 - y)), 1.0);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Julia

function code(x, y)
	t_0 = Float64(x - Float64(-1.0 / y))
	tmp = 0.0
	if (y <= -18000000000.0)
		tmp = t_0;
	elseif (y <= 100000000000.0)
		tmp = fma(y, Float64(Float64(1.0 - x) / Float64(-1.0 - y)), 1.0);
	else
		tmp = t_0;
	end
	return tmp
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(x - N[(-1.0 / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -18000000000.0], t$95$0, If[LessEqual[y, 100000000000.0], N[(y * N[(N[(1.0 - x), $MachinePrecision] / N[(-1.0 - y), $MachinePrecision]), $MachinePrecision] + 1.0), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if y < -1.8e10 or 1e11 < y

   1. Initial program 35.1%

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

   3. Taylor expanded in y around inf

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

      1. +-commutative N/A

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

      2. associate--l+ N/A

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

      3. +-commutative N/A

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

      4. associate--r- N/A

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

      5. div-sub N/A

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

      6. lower--.f64 N/A

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

      7. lower-/.f64 N/A

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

      8. lower--.f64 99.8

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

   5. Applied rewrites 99.8%

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

   6. Taylor expanded in x around 0

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

   8. Applied rewrites 99.8%

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

   if -1.8e10 < y < 1e11

   1. Initial program 99.6%

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

      1. lift--.f64 N/A

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

      2. sub-neg N/A

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

      3. +-commutative N/A

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

      4. lift-/.f64 N/A

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

      5. distribute-neg-frac2 N/A

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

      6. lift-*.f64 N/A

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

      7. *-commutative N/A

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

      8. associate-/l* N/A

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

      9. lower-fma.f64 N/A

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

      10. lower-/.f64 N/A

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

      11. lift-+.f64 N/A

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

      12. +-commutative N/A

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

      13. distribute-neg-in N/A

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

      14. metadata-eval N/A

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

      15. unsub-neg N/A

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

      16. lower--.f64 99.6

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

   4. Applied rewrites 99.6%

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

Alternative 5: 98.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x - \frac{x - 1}{y}\\ \mathbf{if}\;y \leq -7000:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq 1500000:\\ \;\;\;\;1 - \frac{x}{-1 - y} \cdot y\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (- x (/ (- x 1.0) y))))
   (if (<= y -7000.0)
     t_0
     (if (<= y 1500000.0) (- 1.0 (* (/ x (- -1.0 y)) y)) t_0))))

C

double code(double x, double y) {
	double t_0 = x - ((x - 1.0) / y);
	double tmp;
	if (y <= -7000.0) {
		tmp = t_0;
	} else if (y <= 1500000.0) {
		tmp = 1.0 - ((x / (-1.0 - y)) * y);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: t_0
    real(8) :: tmp
    t_0 = x - ((x - 1.0d0) / y)
    if (y <= (-7000.0d0)) then
        tmp = t_0
    else if (y <= 1500000.0d0) then
        tmp = 1.0d0 - ((x / ((-1.0d0) - y)) * y)
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double t_0 = x - ((x - 1.0) / y);
	double tmp;
	if (y <= -7000.0) {
		tmp = t_0;
	} else if (y <= 1500000.0) {
		tmp = 1.0 - ((x / (-1.0 - y)) * y);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = x - ((x - 1.0) / y)
	tmp = 0
	if y <= -7000.0:
		tmp = t_0
	elif y <= 1500000.0:
		tmp = 1.0 - ((x / (-1.0 - y)) * y)
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y)
	t_0 = Float64(x - Float64(Float64(x - 1.0) / y))
	tmp = 0.0
	if (y <= -7000.0)
		tmp = t_0;
	elseif (y <= 1500000.0)
		tmp = Float64(1.0 - Float64(Float64(x / Float64(-1.0 - y)) * y));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = x - ((x - 1.0) / y);
	tmp = 0.0;
	if (y <= -7000.0)
		tmp = t_0;
	elseif (y <= 1500000.0)
		tmp = 1.0 - ((x / (-1.0 - y)) * y);
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(x - N[(N[(x - 1.0), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -7000.0], t$95$0, If[LessEqual[y, 1500000.0], N[(1.0 - N[(N[(x / N[(-1.0 - y), $MachinePrecision]), $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if y < -7e3 or 1.5e6 < y

   1. Initial program 36.8%

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

   3. Taylor expanded in y around inf

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

      1. +-commutative N/A

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

      2. associate--l+ N/A

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

      3. +-commutative N/A

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

      4. associate--r- N/A

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

      5. div-sub N/A

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

      6. lower--.f64 N/A

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

      7. lower-/.f64 N/A

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

      8. lower--.f64 98.7

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

   5. Applied rewrites 98.7%

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

   if -7e3 < y < 1.5e6

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf

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

      1. mul-1-neg N/A

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

      2. *-commutative N/A

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

      3. associate-/l* N/A

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

      4. *-commutative N/A

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

      5. distribute-lft-neg-in N/A

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

      6. lower-*.f64 N/A

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

      7. distribute-frac-neg2 N/A

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

      8. lower-/.f64 N/A

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

      9. distribute-neg-in N/A

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

      10. metadata-eval N/A

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

      11. unsub-neg N/A

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

      12. lower--.f64 99.6

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

   5. Applied rewrites 99.6%

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

Alternative 6: 98.7% accurate, 0.9× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Split input into 2 regimes

2. if y < -1 or 1 < y

   1. Initial program 37.3%

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

   3. Taylor expanded in y around inf

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

      1. +-commutative N/A

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

      2. associate--l+ N/A

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

      3. +-commutative N/A

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

      4. associate--r- N/A

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

      5. div-sub N/A

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

      6. lower--.f64 N/A

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

      7. lower-/.f64 N/A

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

      8. lower--.f64 98.6

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

   5. Applied rewrites 98.6%

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

   if -1 < y < 1

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

   5. Applied rewrites 99.3%

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

4. Final simplification 99.0%

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

Alternative 7: 98.4% accurate, 0.9× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Split input into 2 regimes

2. if y < -1 or 1 < y

   1. Initial program 37.3%

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

   3. Taylor expanded in y around inf

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

      1. +-commutative N/A

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

      2. associate--l+ N/A

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

      3. +-commutative N/A

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

      4. associate--r- N/A

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

      5. div-sub N/A

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

      6. lower--.f64 N/A

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

      7. lower-/.f64 N/A

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

      8. lower--.f64 98.6

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

   5. Applied rewrites 98.6%

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

   if -1 < y < 1

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. lower--.f64 98.8

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

   5. Applied rewrites 98.8%

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

Alternative 8: 98.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x - \frac{-1}{y}\\ \mathbf{if}\;y \leq -1:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq 0.82:\\ \;\;\;\;\mathsf{fma}\left(x - 1, y, 1\right)\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (- x (/ -1.0 y))))
   (if (<= y -1.0) t_0 (if (<= y 0.82) (fma (- x 1.0) y 1.0) t_0))))

C

double code(double x, double y) {
	double t_0 = x - (-1.0 / y);
	double tmp;
	if (y <= -1.0) {
		tmp = t_0;
	} else if (y <= 0.82) {
		tmp = fma((x - 1.0), y, 1.0);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Julia

function code(x, y)
	t_0 = Float64(x - Float64(-1.0 / y))
	tmp = 0.0
	if (y <= -1.0)
		tmp = t_0;
	elseif (y <= 0.82)
		tmp = fma(Float64(x - 1.0), y, 1.0);
	else
		tmp = t_0;
	end
	return tmp
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(x - N[(-1.0 / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.0], t$95$0, If[LessEqual[y, 0.82], N[(N[(x - 1.0), $MachinePrecision] * y + 1.0), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if y < -1 or 0.819999999999999951 < y

   1. Initial program 37.3%

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

   3. Taylor expanded in y around inf

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

      1. +-commutative N/A

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

      2. associate--l+ N/A

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

      3. +-commutative N/A

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

      4. associate--r- N/A

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

      5. div-sub N/A

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

      6. lower--.f64 N/A

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

      7. lower-/.f64 N/A

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

      8. lower--.f64 98.6

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

   5. Applied rewrites 98.6%

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

   6. Taylor expanded in x around 0

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

   8. Applied rewrites 97.9%

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

   if -1 < y < 0.819999999999999951

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. lower--.f64 98.8

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

   5. Applied rewrites 98.8%

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

Alternative 9: 86.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := x - \frac{x}{y}\\ \mathbf{if}\;y \leq -1:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq 1.05:\\ \;\;\;\;\mathsf{fma}\left(x - 1, y, 1\right)\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (- x (/ x y))))
   (if (<= y -1.0) t_0 (if (<= y 1.05) (fma (- x 1.0) y 1.0) t_0))))

C

double code(double x, double y) {
	double t_0 = x - (x / y);
	double tmp;
	if (y <= -1.0) {
		tmp = t_0;
	} else if (y <= 1.05) {
		tmp = fma((x - 1.0), y, 1.0);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Julia

function code(x, y)
	t_0 = Float64(x - Float64(x / y))
	tmp = 0.0
	if (y <= -1.0)
		tmp = t_0;
	elseif (y <= 1.05)
		tmp = fma(Float64(x - 1.0), y, 1.0);
	else
		tmp = t_0;
	end
	return tmp
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(x - N[(x / y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.0], t$95$0, If[LessEqual[y, 1.05], N[(N[(x - 1.0), $MachinePrecision] * y + 1.0), $MachinePrecision], t$95$0]]]

Derivation

1. Split input into 2 regimes

2. if y < -1 or 1.05000000000000004 < y

   1. Initial program 37.3%

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

   3. Taylor expanded in y around inf

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

      1. +-commutative N/A

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

      2. associate--l+ N/A

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

      3. +-commutative N/A

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

      4. associate--r- N/A

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

      5. div-sub N/A

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

      6. lower--.f64 N/A

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

      7. lower-/.f64 N/A

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

      8. lower--.f64 98.6

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

   5. Applied rewrites 98.6%

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

   6. Taylor expanded in x around inf

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

   8. Applied rewrites 74.9%

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

   if -1 < y < 1.05000000000000004

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. lower--.f64 98.8

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

   5. Applied rewrites 98.8%

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

Alternative 10: 86.2% accurate, 1.2× speedup

Math

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

FPCore

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

C

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

Julia

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

Wolfram

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

Derivation

1. Split input into 2 regimes

2. if y < -1 or 1 < y

   1. Initial program 37.3%

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

      1. lift--.f64 N/A

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

      2. sub-neg N/A

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

      3. +-commutative N/A

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

      4. lift-/.f64 N/A

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

      5. clear-num N/A

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

      6. distribute-neg-frac N/A

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

      7. metadata-eval N/A

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

      8. lift-*.f64 N/A

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

      9. associate-/r* N/A

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

      10. associate-/r/ N/A

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

      11. lower-fma.f64 N/A

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

      12. lower-/.f64 N/A

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

      13. lower-/.f64 57.1

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

   4. Applied rewrites 57.1%

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

   5. Taylor expanded in y around inf

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

      1. mul-1-neg N/A

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

      2. sub-neg N/A

         \[\leadsto 1 + \left(\mathsf{neg}\left(\color{blue}{\left(1 + \left(\mathsf{neg}\left(x\right)\right)\right)}\right)\right) \]

      3. distribute-neg-in N/A

         \[\leadsto 1 + \color{blue}{\left(\left(\mathsf{neg}\left(1\right)\right) + \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(x\right)\right)\right)\right)\right)} \]

      4. metadata-eval N/A

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

      5. remove-double-neg N/A

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

      6. associate-+r+ N/A

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

      7. metadata-eval N/A

         \[\leadsto \color{blue}{0} + x \]

      8. remove-double-neg N/A

         \[\leadsto 0 + \color{blue}{\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(x\right)\right)\right)\right)} \]

      9. sub-neg N/A

         \[\leadsto \color{blue}{0 - \left(\mathsf{neg}\left(x\right)\right)} \]

      10. neg-sub0 N/A

          \[\leadsto \color{blue}{\mathsf{neg}\left(\left(\mathsf{neg}\left(x\right)\right)\right)} \]

      11. remove-double-neg 74.4

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

   7. Applied rewrites 74.4%

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

   if -1 < y < 1

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0

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

      1. +-commutative N/A

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

      2. *-commutative N/A

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

      3. lower-fma.f64 N/A

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

      4. lower--.f64 98.8

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

   5. Applied rewrites 98.8%

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

Alternative 11: 72.6% accurate, 1.4× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -3.8 \cdot 10^{-81}:\\ \;\;\;\;x \cdot y\\ \mathbf{elif}\;y \leq 9 \cdot 10^{-9}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -1.0) x (if (<= y -3.8e-81) (* x y) (if (<= y 9e-9) 1.0 x))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -1.0) {
		tmp = x;
	} else if (y <= -3.8e-81) {
		tmp = x * y;
	} else if (y <= 9e-9) {
		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 <= (-3.8d-81)) then
        tmp = x * y
    else if (y <= 9d-9) 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 <= -3.8e-81) {
		tmp = x * y;
	} else if (y <= 9e-9) {
		tmp = 1.0;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -1.0:
		tmp = x
	elif y <= -3.8e-81:
		tmp = x * y
	elif y <= 9e-9:
		tmp = 1.0
	else:
		tmp = x
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -1.0)
		tmp = x;
	elseif (y <= -3.8e-81)
		tmp = Float64(x * y);
	elseif (y <= 9e-9)
		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 <= -3.8e-81)
		tmp = x * y;
	elseif (y <= 9e-9)
		tmp = 1.0;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -1.0], x, If[LessEqual[y, -3.8e-81], N[(x * y), $MachinePrecision], If[LessEqual[y, 9e-9], 1.0, x]]]

Derivation

1. Split input into 3 regimes

2. if y < -1 or 8.99999999999999953e-9 < y

   1. Initial program 37.8%

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

      1. lift--.f64 N/A

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

      2. sub-neg N/A

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

      3. +-commutative N/A

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

      4. lift-/.f64 N/A

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

      5. clear-num N/A

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

      6. distribute-neg-frac N/A

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

      7. metadata-eval N/A

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

      8. lift-*.f64 N/A

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

      9. associate-/r* N/A

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

      10. associate-/r/ N/A

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

      11. lower-fma.f64 N/A

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

      12. lower-/.f64 N/A

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

      13. lower-/.f64 57.5

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

   4. Applied rewrites 57.5%

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

   5. Taylor expanded in y around inf

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

      1. mul-1-neg N/A

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

      2. sub-neg N/A

         \[\leadsto 1 + \left(\mathsf{neg}\left(\color{blue}{\left(1 + \left(\mathsf{neg}\left(x\right)\right)\right)}\right)\right) \]

      3. distribute-neg-in N/A

         \[\leadsto 1 + \color{blue}{\left(\left(\mathsf{neg}\left(1\right)\right) + \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(x\right)\right)\right)\right)\right)} \]

      4. metadata-eval N/A

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

      5. remove-double-neg N/A

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

      6. associate-+r+ N/A

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

      7. metadata-eval N/A

         \[\leadsto \color{blue}{0} + x \]

      8. remove-double-neg N/A

         \[\leadsto 0 + \color{blue}{\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(x\right)\right)\right)\right)} \]

      9. sub-neg N/A

         \[\leadsto \color{blue}{0 - \left(\mathsf{neg}\left(x\right)\right)} \]

      10. neg-sub0 N/A

          \[\leadsto \color{blue}{\mathsf{neg}\left(\left(\mathsf{neg}\left(x\right)\right)\right)} \]

      11. remove-double-neg 73.9

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

   7. Applied rewrites 73.9%

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

   if -1 < y < -3.7999999999999999e-81

   1. Initial program 100.0%

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

   3. Taylor expanded in x around inf

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

      1. *-commutative N/A

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

      2. associate-*l/ N/A

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

      3. lower-*.f64 N/A

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

      4. lower-/.f64 N/A

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

      5. +-commutative N/A

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

      6. lower-+.f64 74.3

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

   5. Applied rewrites 74.3%

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

   6. Taylor expanded in y around 0

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

   8. Applied rewrites 69.7%

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

   if -3.7999999999999999e-81 < y < 8.99999999999999953e-9

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0

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

   5. Applied rewrites 84.0%

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

Alternative 12: 73.3% accurate, 2.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 9 \cdot 10^{-9}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (if (<= y -1.0) x (if (<= y 9e-9) 1.0 x)))

C

double code(double x, double y) {
	double tmp;
	if (y <= -1.0) {
		tmp = x;
	} else if (y <= 9e-9) {
		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 <= 9d-9) 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 <= 9e-9) {
		tmp = 1.0;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -1.0:
		tmp = x
	elif y <= 9e-9:
		tmp = 1.0
	else:
		tmp = x
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -1.0)
		tmp = x;
	elseif (y <= 9e-9)
		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 <= 9e-9)
		tmp = 1.0;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -1.0], x, If[LessEqual[y, 9e-9], 1.0, x]]

Derivation

1. Split input into 2 regimes

2. if y < -1 or 8.99999999999999953e-9 < y

   1. Initial program 37.8%

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

      1. lift--.f64 N/A

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

      2. sub-neg N/A

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

      3. +-commutative N/A

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

      4. lift-/.f64 N/A

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

      5. clear-num N/A

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

      6. distribute-neg-frac N/A

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

      7. metadata-eval N/A

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

      8. lift-*.f64 N/A

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

      9. associate-/r* N/A

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

      10. associate-/r/ N/A

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

      11. lower-fma.f64 N/A

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

      12. lower-/.f64 N/A

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

      13. lower-/.f64 57.5

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

   4. Applied rewrites 57.5%

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

   5. Taylor expanded in y around inf

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

      1. mul-1-neg N/A

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

      2. sub-neg N/A

         \[\leadsto 1 + \left(\mathsf{neg}\left(\color{blue}{\left(1 + \left(\mathsf{neg}\left(x\right)\right)\right)}\right)\right) \]

      3. distribute-neg-in N/A

         \[\leadsto 1 + \color{blue}{\left(\left(\mathsf{neg}\left(1\right)\right) + \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(x\right)\right)\right)\right)\right)} \]

      4. metadata-eval N/A

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

      5. remove-double-neg N/A

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

      6. associate-+r+ N/A

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

      7. metadata-eval N/A

         \[\leadsto \color{blue}{0} + x \]

      8. remove-double-neg N/A

         \[\leadsto 0 + \color{blue}{\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(x\right)\right)\right)\right)} \]

      9. sub-neg N/A

         \[\leadsto \color{blue}{0 - \left(\mathsf{neg}\left(x\right)\right)} \]

      10. neg-sub0 N/A

          \[\leadsto \color{blue}{\mathsf{neg}\left(\left(\mathsf{neg}\left(x\right)\right)\right)} \]

      11. remove-double-neg 73.9

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

   7. Applied rewrites 73.9%

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

   if -1 < y < 8.99999999999999953e-9

   1. Initial program 100.0%

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

   3. Taylor expanded in y around 0

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

   5. Applied rewrites 76.1%

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

Alternative 13: 38.5% accurate, 26.0× speedup

Math

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

FPCore

(FPCore (x y) :precision binary64 x)

C

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

Fortran

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

Java

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

Python

def code(x, y):
	return x

Julia

function code(x, y)
	return x
end

MATLAB

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

Wolfram

code[x_, y_] := x

Derivation

1. Initial program 69.9%

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

   1. lift--.f64 N/A

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

   2. sub-neg N/A

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

   3. +-commutative N/A

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

   4. lift-/.f64 N/A

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

   5. clear-num N/A

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

   6. distribute-neg-frac N/A

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

   7. metadata-eval N/A

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

   8. lift-*.f64 N/A

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

   9. associate-/r* N/A

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

   10. associate-/r/ N/A

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

   11. lower-fma.f64 N/A

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

   12. lower-/.f64 N/A

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

   13. lower-/.f64 79.4

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

4. Applied rewrites 79.4%

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

5. Taylor expanded in y around inf

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

   1. mul-1-neg N/A

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

   2. sub-neg N/A

      \[\leadsto 1 + \left(\mathsf{neg}\left(\color{blue}{\left(1 + \left(\mathsf{neg}\left(x\right)\right)\right)}\right)\right) \]

   3. distribute-neg-in N/A

      \[\leadsto 1 + \color{blue}{\left(\left(\mathsf{neg}\left(1\right)\right) + \left(\mathsf{neg}\left(\left(\mathsf{neg}\left(x\right)\right)\right)\right)\right)} \]

   4. metadata-eval N/A

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

   5. remove-double-neg N/A

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

   6. associate-+r+ N/A

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

   7. metadata-eval N/A

      \[\leadsto \color{blue}{0} + x \]

   8. remove-double-neg N/A

      \[\leadsto 0 + \color{blue}{\left(\mathsf{neg}\left(\left(\mathsf{neg}\left(x\right)\right)\right)\right)} \]

   9. sub-neg N/A

      \[\leadsto \color{blue}{0 - \left(\mathsf{neg}\left(x\right)\right)} \]

   10. neg-sub0 N/A

       \[\leadsto \color{blue}{\mathsf{neg}\left(\left(\mathsf{neg}\left(x\right)\right)\right)} \]

   11. remove-double-neg 37.6

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

7. Applied rewrites 37.6%

   \[\leadsto \color{blue}{x} \]
8. Add Preprocessing

Developer Target 1: 99.7% accurate, 0.6× 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 2024248 
(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))))