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

Percentage Accurate: 66.7% → 99.9%

Time: 12.4s

Alternatives: 11

Speedup: 2.1×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 66.7% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.9% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{1 - x}{y}\\ \mathbf{if}\;y \leq -66000000 \lor \neg \left(y \leq 14000\right):\\ \;\;\;\;x + \left(\left(\frac{1 - x}{{y}^{3}} + t_0\right) + \frac{-1}{y} \cdot t_0\right)\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{y}{y + 1} \cdot \left(x + -1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (/ (- 1.0 x) y)))
   (if (or (<= y -66000000.0) (not (<= y 14000.0)))
     (+ x (+ (+ (/ (- 1.0 x) (pow y 3.0)) t_0) (* (/ -1.0 y) t_0)))
     (+ 1.0 (* (/ y (+ y 1.0)) (+ x -1.0))))))

C

double code(double x, double y) {
	double t_0 = (1.0 - x) / y;
	double tmp;
	if ((y <= -66000000.0) || !(y <= 14000.0)) {
		tmp = x + ((((1.0 - x) / pow(y, 3.0)) + t_0) + ((-1.0 / y) * t_0));
	} else {
		tmp = 1.0 + ((y / (y + 1.0)) * (x + -1.0));
	}
	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 - x) / y
    if ((y <= (-66000000.0d0)) .or. (.not. (y <= 14000.0d0))) then
        tmp = x + ((((1.0d0 - x) / (y ** 3.0d0)) + t_0) + (((-1.0d0) / y) * t_0))
    else
        tmp = 1.0d0 + ((y / (y + 1.0d0)) * (x + (-1.0d0)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double t_0 = (1.0 - x) / y;
	double tmp;
	if ((y <= -66000000.0) || !(y <= 14000.0)) {
		tmp = x + ((((1.0 - x) / Math.pow(y, 3.0)) + t_0) + ((-1.0 / y) * t_0));
	} else {
		tmp = 1.0 + ((y / (y + 1.0)) * (x + -1.0));
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = (1.0 - x) / y
	tmp = 0
	if (y <= -66000000.0) or not (y <= 14000.0):
		tmp = x + ((((1.0 - x) / math.pow(y, 3.0)) + t_0) + ((-1.0 / y) * t_0))
	else:
		tmp = 1.0 + ((y / (y + 1.0)) * (x + -1.0))
	return tmp

Julia

function code(x, y)
	t_0 = Float64(Float64(1.0 - x) / y)
	tmp = 0.0
	if ((y <= -66000000.0) || !(y <= 14000.0))
		tmp = Float64(x + Float64(Float64(Float64(Float64(1.0 - x) / (y ^ 3.0)) + t_0) + Float64(Float64(-1.0 / y) * t_0)));
	else
		tmp = Float64(1.0 + Float64(Float64(y / Float64(y + 1.0)) * Float64(x + -1.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = (1.0 - x) / y;
	tmp = 0.0;
	if ((y <= -66000000.0) || ~((y <= 14000.0)))
		tmp = x + ((((1.0 - x) / (y ^ 3.0)) + t_0) + ((-1.0 / y) * t_0));
	else
		tmp = 1.0 + ((y / (y + 1.0)) * (x + -1.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(N[(1.0 - x), $MachinePrecision] / y), $MachinePrecision]}, If[Or[LessEqual[y, -66000000.0], N[Not[LessEqual[y, 14000.0]], $MachinePrecision]], N[(x + N[(N[(N[(N[(1.0 - x), $MachinePrecision] / N[Power[y, 3.0], $MachinePrecision]), $MachinePrecision] + t$95$0), $MachinePrecision] + N[(N[(-1.0 / y), $MachinePrecision] * t$95$0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(1.0 + N[(N[(y / N[(y + 1.0), $MachinePrecision]), $MachinePrecision] * N[(x + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -6.6e7 or 14000 < y

   1. Initial program 35.8%

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

      1. *-commutative 35.8%

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

      2. associate-*l/ 51.0%

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

      3. +-commutative 51.0%

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

   3. Simplified 51.0%

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

   4. Taylor expanded in y around -inf 100.0%

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

      1. associate--l+ 100.0%

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

      2. associate-+r+ 100.0%

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

      3. associate--l+ 100.0%

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

   6. Simplified 100.0%

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

      1. *-un-lft-identity 100.0%

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

      2. unpow2 100.0%

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

      3. times-frac 100.0%

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

   8. Applied egg-rr 100.0%

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

   if -6.6e7 < y < 14000

   1. Initial program 99.3%

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

      1. *-commutative 99.3%

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

      2. associate-*l/ 100.0%

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

      3. +-commutative 100.0%

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

   3. Simplified 100.0%

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

4. Final simplification 100.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -66000000 \lor \neg \left(y \leq 14000\right):\\ \;\;\;\;x + \left(\left(\frac{1 - x}{{y}^{3}} + \frac{1 - x}{y}\right) + \frac{-1}{y} \cdot \frac{1 - x}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{y}{y + 1} \cdot \left(x + -1\right)\\ \end{array} \]

Alternative 2: 99.7% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{y \cdot \left(1 - x\right)}{y + 1}\\ \mathbf{if}\;t_0 \leq 0.004 \lor \neg \left(t_0 \leq 1.2\right):\\ \;\;\;\;1 + \frac{y}{y + 1} \cdot \left(x + -1\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(\frac{-1}{y} \cdot \frac{1 - x}{y} + \left(\frac{1}{y} + \frac{1}{{y}^{3}}\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (/ (* y (- 1.0 x)) (+ y 1.0))))
   (if (or (<= t_0 0.004) (not (<= t_0 1.2)))
     (+ 1.0 (* (/ y (+ y 1.0)) (+ x -1.0)))
     (+
      x
      (+ (* (/ -1.0 y) (/ (- 1.0 x) y)) (+ (/ 1.0 y) (/ 1.0 (pow y 3.0))))))))

C

double code(double x, double y) {
	double t_0 = (y * (1.0 - x)) / (y + 1.0);
	double tmp;
	if ((t_0 <= 0.004) || !(t_0 <= 1.2)) {
		tmp = 1.0 + ((y / (y + 1.0)) * (x + -1.0));
	} else {
		tmp = x + (((-1.0 / y) * ((1.0 - x) / y)) + ((1.0 / y) + (1.0 / pow(y, 3.0))));
	}
	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 = (y * (1.0d0 - x)) / (y + 1.0d0)
    if ((t_0 <= 0.004d0) .or. (.not. (t_0 <= 1.2d0))) then
        tmp = 1.0d0 + ((y / (y + 1.0d0)) * (x + (-1.0d0)))
    else
        tmp = x + ((((-1.0d0) / y) * ((1.0d0 - x) / y)) + ((1.0d0 / y) + (1.0d0 / (y ** 3.0d0))))
    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 <= 0.004) || !(t_0 <= 1.2)) {
		tmp = 1.0 + ((y / (y + 1.0)) * (x + -1.0));
	} else {
		tmp = x + (((-1.0 / y) * ((1.0 - x) / y)) + ((1.0 / y) + (1.0 / Math.pow(y, 3.0))));
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = (y * (1.0 - x)) / (y + 1.0)
	tmp = 0
	if (t_0 <= 0.004) or not (t_0 <= 1.2):
		tmp = 1.0 + ((y / (y + 1.0)) * (x + -1.0))
	else:
		tmp = x + (((-1.0 / y) * ((1.0 - x) / y)) + ((1.0 / y) + (1.0 / math.pow(y, 3.0))))
	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 <= 0.004) || !(t_0 <= 1.2))
		tmp = Float64(1.0 + Float64(Float64(y / Float64(y + 1.0)) * Float64(x + -1.0)));
	else
		tmp = Float64(x + Float64(Float64(Float64(-1.0 / y) * Float64(Float64(1.0 - x) / y)) + Float64(Float64(1.0 / y) + Float64(1.0 / (y ^ 3.0)))));
	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 <= 0.004) || ~((t_0 <= 1.2)))
		tmp = 1.0 + ((y / (y + 1.0)) * (x + -1.0));
	else
		tmp = x + (((-1.0 / y) * ((1.0 - x) / y)) + ((1.0 / y) + (1.0 / (y ^ 3.0))));
	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, 0.004], N[Not[LessEqual[t$95$0, 1.2]], $MachinePrecision]], N[(1.0 + N[(N[(y / N[(y + 1.0), $MachinePrecision]), $MachinePrecision] * N[(x + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(N[(-1.0 / y), $MachinePrecision] * N[(N[(1.0 - x), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision] + N[(N[(1.0 / y), $MachinePrecision] + N[(1.0 / N[Power[y, 3.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 (-.f64 1 x) y) (+.f64 y 1)) < 0.0040000000000000001 or 1.19999999999999996 < (/.f64 (*.f64 (-.f64 1 x) y) (+.f64 y 1))

   1. Initial program 88.3%

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

      1. *-commutative 88.3%

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

      2. associate-*l/ 100.0%

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

      3. +-commutative 100.0%

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

   3. Simplified 100.0%

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

   if 0.0040000000000000001 < (/.f64 (*.f64 (-.f64 1 x) y) (+.f64 y 1)) < 1.19999999999999996

   1. Initial program 10.6%

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

      1. *-commutative 10.6%

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

      2. associate-*l/ 10.6%

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

      3. +-commutative 10.6%

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

   3. Simplified 10.6%

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

   4. Taylor expanded in y around -inf 100.0%

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

      1. associate--l+ 100.0%

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

      2. associate-+r+ 100.0%

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

      3. associate--l+ 100.0%

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

   6. Simplified 100.0%

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

      1. *-un-lft-identity 100.0%

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

      2. unpow2 100.0%

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

      3. times-frac 100.0%

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

   8. Applied egg-rr 100.0%

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

   9. Taylor expanded in x around 0 100.0%

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

4. Final simplification 100.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y \cdot \left(1 - x\right)}{y + 1} \leq 0.004 \lor \neg \left(\frac{y \cdot \left(1 - x\right)}{y + 1} \leq 1.2\right):\\ \;\;\;\;1 + \frac{y}{y + 1} \cdot \left(x + -1\right)\\ \mathbf{else}:\\ \;\;\;\;x + \left(\frac{-1}{y} \cdot \frac{1 - x}{y} + \left(\frac{1}{y} + \frac{1}{{y}^{3}}\right)\right)\\ \end{array} \]

Alternative 3: 99.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{1 - x}{y}\\ \mathbf{if}\;y \leq -66000000 \lor \neg \left(y \leq 415000\right):\\ \;\;\;\;\frac{-1}{y} \cdot t_0 + \left(x + t_0\right)\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{y}{y + 1} \cdot \left(x + -1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (/ (- 1.0 x) y)))
   (if (or (<= y -66000000.0) (not (<= y 415000.0)))
     (+ (* (/ -1.0 y) t_0) (+ x t_0))
     (+ 1.0 (* (/ y (+ y 1.0)) (+ x -1.0))))))

C

double code(double x, double y) {
	double t_0 = (1.0 - x) / y;
	double tmp;
	if ((y <= -66000000.0) || !(y <= 415000.0)) {
		tmp = ((-1.0 / y) * t_0) + (x + t_0);
	} else {
		tmp = 1.0 + ((y / (y + 1.0)) * (x + -1.0));
	}
	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 - x) / y
    if ((y <= (-66000000.0d0)) .or. (.not. (y <= 415000.0d0))) then
        tmp = (((-1.0d0) / y) * t_0) + (x + t_0)
    else
        tmp = 1.0d0 + ((y / (y + 1.0d0)) * (x + (-1.0d0)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double t_0 = (1.0 - x) / y;
	double tmp;
	if ((y <= -66000000.0) || !(y <= 415000.0)) {
		tmp = ((-1.0 / y) * t_0) + (x + t_0);
	} else {
		tmp = 1.0 + ((y / (y + 1.0)) * (x + -1.0));
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = (1.0 - x) / y
	tmp = 0
	if (y <= -66000000.0) or not (y <= 415000.0):
		tmp = ((-1.0 / y) * t_0) + (x + t_0)
	else:
		tmp = 1.0 + ((y / (y + 1.0)) * (x + -1.0))
	return tmp

Julia

function code(x, y)
	t_0 = Float64(Float64(1.0 - x) / y)
	tmp = 0.0
	if ((y <= -66000000.0) || !(y <= 415000.0))
		tmp = Float64(Float64(Float64(-1.0 / y) * t_0) + Float64(x + t_0));
	else
		tmp = Float64(1.0 + Float64(Float64(y / Float64(y + 1.0)) * Float64(x + -1.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = (1.0 - x) / y;
	tmp = 0.0;
	if ((y <= -66000000.0) || ~((y <= 415000.0)))
		tmp = ((-1.0 / y) * t_0) + (x + t_0);
	else
		tmp = 1.0 + ((y / (y + 1.0)) * (x + -1.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(N[(1.0 - x), $MachinePrecision] / y), $MachinePrecision]}, If[Or[LessEqual[y, -66000000.0], N[Not[LessEqual[y, 415000.0]], $MachinePrecision]], N[(N[(N[(-1.0 / y), $MachinePrecision] * t$95$0), $MachinePrecision] + N[(x + t$95$0), $MachinePrecision]), $MachinePrecision], N[(1.0 + N[(N[(y / N[(y + 1.0), $MachinePrecision]), $MachinePrecision] * N[(x + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if y < -6.6e7 or 415000 < y

   1. Initial program 35.8%

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

      1. *-commutative 35.8%

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

      2. associate-*l/ 51.0%

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

      3. +-commutative 51.0%

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

   3. Simplified 51.0%

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

   4. Taylor expanded in y around -inf 99.8%

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

      1. associate-+r+ 99.8%

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

      2. associate--l+ 99.8%

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

      3. mul-1-neg 99.8%

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

      4. unsub-neg 99.8%

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

      5. sub-neg 99.8%

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

      6. metadata-eval 99.8%

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

      7. div-sub 99.8%

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

      8. sub-neg 99.8%

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

      9. metadata-eval 99.8%

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

   6. Simplified 99.8%

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

      1. *-un-lft-identity 100.0%

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

      2. unpow2 100.0%

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

      3. times-frac 100.0%

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

   8. Applied egg-rr 99.8%

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

   if -6.6e7 < y < 415000

   1. Initial program 99.3%

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

      1. *-commutative 99.3%

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

      2. associate-*l/ 100.0%

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

      3. +-commutative 100.0%

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

   3. Simplified 100.0%

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

4. Final simplification 99.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -66000000 \lor \neg \left(y \leq 415000\right):\\ \;\;\;\;\frac{-1}{y} \cdot \frac{1 - x}{y} + \left(x + \frac{1 - x}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{y}{y + 1} \cdot \left(x + -1\right)\\ \end{array} \]

Alternative 4: 99.7% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -132000000 \lor \neg \left(y \leq 220000000\right):\\ \;\;\;\;x + \frac{1 - x}{y}\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{y}{y + 1} \cdot \left(x + -1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= y -132000000.0) (not (<= y 220000000.0)))
   (+ x (/ (- 1.0 x) y))
   (+ 1.0 (* (/ y (+ y 1.0)) (+ x -1.0)))))

C

double code(double x, double y) {
	double tmp;
	if ((y <= -132000000.0) || !(y <= 220000000.0)) {
		tmp = x + ((1.0 - x) / y);
	} else {
		tmp = 1.0 + ((y / (y + 1.0)) * (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 <= (-132000000.0d0)) .or. (.not. (y <= 220000000.0d0))) then
        tmp = x + ((1.0d0 - x) / y)
    else
        tmp = 1.0d0 + ((y / (y + 1.0d0)) * (x + (-1.0d0)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((y <= -132000000.0) || !(y <= 220000000.0)) {
		tmp = x + ((1.0 - x) / y);
	} else {
		tmp = 1.0 + ((y / (y + 1.0)) * (x + -1.0));
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (y <= -132000000.0) or not (y <= 220000000.0):
		tmp = x + ((1.0 - x) / y)
	else:
		tmp = 1.0 + ((y / (y + 1.0)) * (x + -1.0))
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((y <= -132000000.0) || !(y <= 220000000.0))
		tmp = Float64(x + Float64(Float64(1.0 - x) / y));
	else
		tmp = Float64(1.0 + Float64(Float64(y / Float64(y + 1.0)) * Float64(x + -1.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((y <= -132000000.0) || ~((y <= 220000000.0)))
		tmp = x + ((1.0 - x) / y);
	else
		tmp = 1.0 + ((y / (y + 1.0)) * (x + -1.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[y, -132000000.0], N[Not[LessEqual[y, 220000000.0]], $MachinePrecision]], N[(x + N[(N[(1.0 - x), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], N[(1.0 + N[(N[(y / N[(y + 1.0), $MachinePrecision]), $MachinePrecision] * N[(x + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.32e8 or 2.2e8 < y

   1. Initial program 35.3%

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

      1. *-commutative 35.3%

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

      2. associate-*l/ 50.7%

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

      3. +-commutative 50.7%

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

   3. Simplified 50.7%

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

   4. Taylor expanded in y around -inf 99.4%

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

      1. mul-1-neg 99.4%

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

      2. unsub-neg 99.4%

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

      3. sub-neg 99.4%

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

      4. metadata-eval 99.4%

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

   6. Simplified 99.4%

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

   if -1.32e8 < y < 2.2e8

   1. Initial program 98.8%

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

      1. *-commutative 98.8%

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

      2. associate-*l/ 99.5%

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

      3. +-commutative 99.5%

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

   3. Simplified 99.5%

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

4. Final simplification 99.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -132000000 \lor \neg \left(y \leq 220000000\right):\\ \;\;\;\;x + \frac{1 - x}{y}\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{y}{y + 1} \cdot \left(x + -1\right)\\ \end{array} \]

Alternative 5: 98.2% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

2. if y < -1 or 0.80000000000000004 < y

   1. Initial program 38.0%

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

      1. *-commutative 38.0%

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

      2. associate-*l/ 53.1%

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

      3. +-commutative 53.1%

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

   3. Simplified 53.1%

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

   4. Taylor expanded in y around -inf 96.4%

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

      1. mul-1-neg 96.4%

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

      2. unsub-neg 96.4%

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

      3. sub-neg 96.4%

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

      4. metadata-eval 96.4%

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

   6. Simplified 96.4%

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

   7. Taylor expanded in x around 0 95.2%

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

   if -1 < y < 0.80000000000000004

   1. Initial program 100.0%

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

      1. *-commutative 100.0%

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

      2. associate-*l/ 100.0%

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

      3. +-commutative 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in y around 0 99.5%

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

4. Final simplification 97.1%

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

Alternative 6: 98.5% accurate, 1.0× 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. *-commutative 38.0%

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

      2. associate-*l/ 53.1%

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

      3. +-commutative 53.1%

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

   3. Simplified 53.1%

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

   4. Taylor expanded in y around -inf 96.4%

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

      1. mul-1-neg 96.4%

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

      2. unsub-neg 96.4%

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

      3. sub-neg 96.4%

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

      4. metadata-eval 96.4%

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

   6. Simplified 96.4%

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

   if -1 < y < 1

   1. Initial program 100.0%

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

      1. *-commutative 100.0%

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

      2. associate-*l/ 100.0%

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

      3. +-commutative 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in y around 0 99.5%

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

4. Final simplification 97.8%

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

Alternative 7: 97.9% accurate, 1.2× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

2. if y < -1 or 1 < y

   1. Initial program 38.0%

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

      1. *-commutative 38.0%

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

      2. associate-*l/ 53.1%

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

      3. +-commutative 53.1%

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

   3. Simplified 53.1%

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

   4. Taylor expanded in y around -inf 96.4%

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

      1. mul-1-neg 96.4%

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

      2. unsub-neg 96.4%

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

      3. sub-neg 96.4%

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

      4. metadata-eval 96.4%

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

   6. Simplified 96.4%

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

   7. Taylor expanded in x around 0 95.2%

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

   if -1 < y < 1

   1. Initial program 100.0%

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

      1. *-commutative 100.0%

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

      2. associate-*l/ 100.0%

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

      3. +-commutative 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in y around 0 99.5%

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

   5. Taylor expanded in x around inf 99.0%

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

      1. associate-*r* 99.0%

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

      2. mul-1-neg 99.0%

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

   7. Simplified 99.0%

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

   8. Taylor expanded in x around 0 99.0%

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

      1. *-commutative 99.0%

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

   10. Simplified 99.0%

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

4. Final simplification 96.9%

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

Alternative 8: 86.1% accurate, 1.2× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 860000:\\ \;\;\;\;1 + y \cdot x\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -1.0) x (if (<= y 860000.0) (+ 1.0 (* y x)) x)))

C

double code(double x, double y) {
	double tmp;
	if (y <= -1.0) {
		tmp = x;
	} else if (y <= 860000.0) {
		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 <= 860000.0d0) 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 <= 860000.0) {
		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 <= 860000.0:
		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 <= 860000.0)
		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 <= 860000.0)
		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, 860000.0], N[(1.0 + N[(y * x), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if y < -1 or 8.6e5 < y

   1. Initial program 37.2%

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

      1. *-commutative 37.2%

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

      2. associate-*l/ 52.5%

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

      3. +-commutative 52.5%

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

   3. Simplified 52.5%

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

   4. Taylor expanded in y around inf 70.5%

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

   if -1 < y < 8.6e5

   1. Initial program 99.8%

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

      1. *-commutative 99.8%

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

      2. associate-*l/ 99.8%

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

      3. +-commutative 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in y around 0 98.0%

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

   5. Taylor expanded in x around inf 97.6%

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

      1. associate-*r* 97.6%

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

      2. mul-1-neg 97.6%

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

   7. Simplified 97.6%

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

   8. Taylor expanded in x 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 82.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 860000:\\ \;\;\;\;1 + y \cdot x\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 9: 73.9% accurate, 1.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 0.172:\\ \;\;\;\;1 - y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -1.0) x (if (<= y 0.172) (- 1.0 y) x)))

C

double code(double x, double y) {
	double tmp;
	if (y <= -1.0) {
		tmp = x;
	} else if (y <= 0.172) {
		tmp = 1.0 - y;
	} else {
		tmp = x;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (y <= (-1.0d0)) then
        tmp = x
    else if (y <= 0.172d0) then
        tmp = 1.0d0 - y
    else
        tmp = x
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (y <= -1.0) {
		tmp = x;
	} else if (y <= 0.172) {
		tmp = 1.0 - y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -1.0:
		tmp = x
	elif y <= 0.172:
		tmp = 1.0 - y
	else:
		tmp = x
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -1.0)
		tmp = x;
	elseif (y <= 0.172)
		tmp = Float64(1.0 - y);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -1.0)
		tmp = x;
	elseif (y <= 0.172)
		tmp = 1.0 - y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -1.0], x, If[LessEqual[y, 0.172], N[(1.0 - y), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if y < -1 or 0.17199999999999999 < y

   1. Initial program 38.0%

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

      1. *-commutative 38.0%

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

      2. associate-*l/ 53.1%

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

      3. +-commutative 53.1%

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

   3. Simplified 53.1%

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

   4. Taylor expanded in y around inf 69.7%

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

   if -1 < y < 0.17199999999999999

   1. Initial program 100.0%

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

      1. *-commutative 100.0%

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

      2. associate-*l/ 100.0%

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

      3. +-commutative 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in y around 0 99.5%

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

   5. Taylor expanded in x around 0 81.0%

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

4. Final simplification 74.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 0.172:\\ \;\;\;\;1 - y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 10: 73.6% accurate, 2.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 0.156:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (if (<= y -1.0) x (if (<= y 0.156) 1.0 x)))

C

double code(double x, double y) {
	double tmp;
	if (y <= -1.0) {
		tmp = x;
	} else if (y <= 0.156) {
		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 <= 0.156d0) 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 <= 0.156) {
		tmp = 1.0;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -1.0:
		tmp = x
	elif y <= 0.156:
		tmp = 1.0
	else:
		tmp = x
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -1.0)
		tmp = x;
	elseif (y <= 0.156)
		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 <= 0.156)
		tmp = 1.0;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -1.0], x, If[LessEqual[y, 0.156], 1.0, x]]

Derivation

1. Split input into 2 regimes

2. if y < -1 or 0.156 < y

   1. Initial program 38.0%

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

      1. *-commutative 38.0%

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

      2. associate-*l/ 53.1%

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

      3. +-commutative 53.1%

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

   3. Simplified 53.1%

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

   4. Taylor expanded in y around inf 69.7%

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

   if -1 < y < 0.156

   1. Initial program 100.0%

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

      1. *-commutative 100.0%

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

      2. associate-*l/ 100.0%

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

      3. +-commutative 100.0%

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

   3. Simplified 100.0%

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

   4. Taylor expanded in y around 0 80.7%

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

4. Final simplification 74.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 0.156:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]

Alternative 11: 39.5% 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 65.8%

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

   1. *-commutative 65.8%

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

   2. associate-*l/ 74.1%

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

   3. +-commutative 74.1%

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

3. Simplified 74.1%

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

4. Taylor expanded in y around 0 38.3%

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

5. Final simplification 38.3%

   \[\leadsto 1 \]

Developer target: 99.6% accurate, 0.7× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2023335 
(FPCore (x y)
  :name "Diagrams.Trail:splitAtParam  from diagrams-lib-1.3.0.3, D"
  :precision binary64

  :herbie-target
  (if (< y -3693.8482788297247) (- (/ 1.0 y) (- (/ x y) x)) (if (< y 6799310503.41891) (- 1.0 (/ (* (- 1.0 x) y) (+ y 1.0))) (- (/ 1.0 y) (- (/ x y) x))))

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