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

Percentage Accurate: 66.1% → 99.4%

Time: 10.5s

Alternatives: 10

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 66.1% 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: 99.4% accurate, 0.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{\left(1 - x\right) \cdot y}{1 + y}\\ t_1 := \frac{y}{1 + y}\\ \mathbf{if}\;t\_0 \leq 0.9995:\\ \;\;\;\;1 + t\_1 \cdot \left(x + -1\right)\\ \mathbf{elif}\;t\_0 \leq 1:\\ \;\;\;\;x + \frac{1 - x}{y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\frac{1}{x} - \mathsf{fma}\left(-1, t\_1, \frac{\frac{y}{x}}{1 + y}\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (/ (* (- 1.0 x) y) (+ 1.0 y))) (t_1 (/ y (+ 1.0 y))))
   (if (<= t_0 0.9995)
     (+ 1.0 (* t_1 (+ x -1.0)))
     (if (<= t_0 1.0)
       (+ x (/ (- 1.0 x) y))
       (* x (- (/ 1.0 x) (fma -1.0 t_1 (/ (/ y x) (+ 1.0 y)))))))))

C

double code(double x, double y) {
	double t_0 = ((1.0 - x) * y) / (1.0 + y);
	double t_1 = y / (1.0 + y);
	double tmp;
	if (t_0 <= 0.9995) {
		tmp = 1.0 + (t_1 * (x + -1.0));
	} else if (t_0 <= 1.0) {
		tmp = x + ((1.0 - x) / y);
	} else {
		tmp = x * ((1.0 / x) - fma(-1.0, t_1, ((y / x) / (1.0 + y))));
	}
	return tmp;
}

Julia

function code(x, y)
	t_0 = Float64(Float64(Float64(1.0 - x) * y) / Float64(1.0 + y))
	t_1 = Float64(y / Float64(1.0 + y))
	tmp = 0.0
	if (t_0 <= 0.9995)
		tmp = Float64(1.0 + Float64(t_1 * Float64(x + -1.0)));
	elseif (t_0 <= 1.0)
		tmp = Float64(x + Float64(Float64(1.0 - x) / y));
	else
		tmp = Float64(x * Float64(Float64(1.0 / x) - fma(-1.0, t_1, Float64(Float64(y / x) / Float64(1.0 + y)))));
	end
	return tmp
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(N[(N[(1.0 - x), $MachinePrecision] * y), $MachinePrecision] / N[(1.0 + y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(y / N[(1.0 + y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$0, 0.9995], N[(1.0 + N[(t$95$1 * N[(x + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$0, 1.0], N[(x + N[(N[(1.0 - x), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], N[(x * N[(N[(1.0 / x), $MachinePrecision] - N[(-1.0 * t$95$1 + N[(N[(y / x), $MachinePrecision] / N[(1.0 + y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (*.f64 (-.f64 #s(literal 1 binary64) x) y) (+.f64 y #s(literal 1 binary64))) < 0.99950000000000006

   1. Initial program 91.9%

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

      1. associate-/l* 99.9%

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

      2. +-commutative 99.9%

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

   3. Simplified 99.9%

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

   if 0.99950000000000006 < (/.f64 (*.f64 (-.f64 #s(literal 1 binary64) x) y) (+.f64 y #s(literal 1 binary64))) < 1

   1. Initial program 5.0%

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

      1. associate-/l* 5.0%

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

      2. +-commutative 5.0%

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

   3. Simplified 5.0%

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

   5. Taylor expanded in y around inf 100.0%

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

      1. associate--l+ 100.0%

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

      2. div-sub 100.0%

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

   7. Simplified 100.0%

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

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

   1. Initial program 70.0%

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

      1. associate-/l* 96.6%

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

      2. +-commutative 96.6%

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

   3. Simplified 96.6%

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

   5. Taylor expanded in x around inf 97.6%

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

      1. fma-define 97.6%

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

      2. associate-/r* 99.9%

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

   7. Simplified 99.9%

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

4. Final simplification 99.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(1 - x\right) \cdot y}{1 + y} \leq 0.9995:\\ \;\;\;\;1 + \frac{y}{1 + y} \cdot \left(x + -1\right)\\ \mathbf{elif}\;\frac{\left(1 - x\right) \cdot y}{1 + y} \leq 1:\\ \;\;\;\;x + \frac{1 - x}{y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\frac{1}{x} - \mathsf{fma}\left(-1, \frac{y}{1 + y}, \frac{\frac{y}{x}}{1 + y}\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 99.5% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{\left(1 - x\right) \cdot y}{1 + y}\\ t_1 := \frac{y}{1 + y}\\ \mathbf{if}\;t\_0 \leq 0.9995:\\ \;\;\;\;1 + t\_1 \cdot \left(x + -1\right)\\ \mathbf{elif}\;t\_0 \leq 1:\\ \;\;\;\;x + \frac{1 - x}{y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(t\_1 + \frac{1 - t\_1}{x}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (/ (* (- 1.0 x) y) (+ 1.0 y))) (t_1 (/ y (+ 1.0 y))))
   (if (<= t_0 0.9995)
     (+ 1.0 (* t_1 (+ x -1.0)))
     (if (<= t_0 1.0) (+ x (/ (- 1.0 x) y)) (* x (+ t_1 (/ (- 1.0 t_1) x)))))))

C

double code(double x, double y) {
	double t_0 = ((1.0 - x) * y) / (1.0 + y);
	double t_1 = y / (1.0 + y);
	double tmp;
	if (t_0 <= 0.9995) {
		tmp = 1.0 + (t_1 * (x + -1.0));
	} else if (t_0 <= 1.0) {
		tmp = x + ((1.0 - x) / y);
	} else {
		tmp = x * (t_1 + ((1.0 - t_1) / x));
	}
	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) :: t_1
    real(8) :: tmp
    t_0 = ((1.0d0 - x) * y) / (1.0d0 + y)
    t_1 = y / (1.0d0 + y)
    if (t_0 <= 0.9995d0) then
        tmp = 1.0d0 + (t_1 * (x + (-1.0d0)))
    else if (t_0 <= 1.0d0) then
        tmp = x + ((1.0d0 - x) / y)
    else
        tmp = x * (t_1 + ((1.0d0 - t_1) / x))
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double t_0 = ((1.0 - x) * y) / (1.0 + y);
	double t_1 = y / (1.0 + y);
	double tmp;
	if (t_0 <= 0.9995) {
		tmp = 1.0 + (t_1 * (x + -1.0));
	} else if (t_0 <= 1.0) {
		tmp = x + ((1.0 - x) / y);
	} else {
		tmp = x * (t_1 + ((1.0 - t_1) / x));
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = ((1.0 - x) * y) / (1.0 + y)
	t_1 = y / (1.0 + y)
	tmp = 0
	if t_0 <= 0.9995:
		tmp = 1.0 + (t_1 * (x + -1.0))
	elif t_0 <= 1.0:
		tmp = x + ((1.0 - x) / y)
	else:
		tmp = x * (t_1 + ((1.0 - t_1) / x))
	return tmp

Julia

function code(x, y)
	t_0 = Float64(Float64(Float64(1.0 - x) * y) / Float64(1.0 + y))
	t_1 = Float64(y / Float64(1.0 + y))
	tmp = 0.0
	if (t_0 <= 0.9995)
		tmp = Float64(1.0 + Float64(t_1 * Float64(x + -1.0)));
	elseif (t_0 <= 1.0)
		tmp = Float64(x + Float64(Float64(1.0 - x) / y));
	else
		tmp = Float64(x * Float64(t_1 + Float64(Float64(1.0 - t_1) / x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = ((1.0 - x) * y) / (1.0 + y);
	t_1 = y / (1.0 + y);
	tmp = 0.0;
	if (t_0 <= 0.9995)
		tmp = 1.0 + (t_1 * (x + -1.0));
	elseif (t_0 <= 1.0)
		tmp = x + ((1.0 - x) / y);
	else
		tmp = x * (t_1 + ((1.0 - t_1) / x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(N[(N[(1.0 - x), $MachinePrecision] * y), $MachinePrecision] / N[(1.0 + y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(y / N[(1.0 + y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[t$95$0, 0.9995], N[(1.0 + N[(t$95$1 * N[(x + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[t$95$0, 1.0], N[(x + N[(N[(1.0 - x), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], N[(x * N[(t$95$1 + N[(N[(1.0 - t$95$1), $MachinePrecision] / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if (/.f64 (*.f64 (-.f64 #s(literal 1 binary64) x) y) (+.f64 y #s(literal 1 binary64))) < 0.99950000000000006

   1. Initial program 91.9%

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

      1. associate-/l* 99.9%

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

      2. +-commutative 99.9%

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

   3. Simplified 99.9%

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

   if 0.99950000000000006 < (/.f64 (*.f64 (-.f64 #s(literal 1 binary64) x) y) (+.f64 y #s(literal 1 binary64))) < 1

   1. Initial program 5.0%

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

      1. associate-/l* 5.0%

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

      2. +-commutative 5.0%

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

   3. Simplified 5.0%

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

   5. Taylor expanded in y around inf 100.0%

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

      1. associate--l+ 100.0%

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

      2. div-sub 100.0%

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

   7. Simplified 100.0%

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

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

   1. Initial program 70.0%

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

      1. associate-/l* 96.6%

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

      2. +-commutative 96.6%

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

   3. Simplified 96.6%

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

   5. Taylor expanded in x around inf 97.6%

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

      1. associate--r+ 97.6%

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

      2. cancel-sign-sub-inv 97.6%

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

      3. metadata-eval 97.6%

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

      4. *-lft-identity 97.6%

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

      5. +-commutative 97.6%

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

      6. associate-/l/ 99.9%

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

      7. associate-+r- 99.9%

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

      8. div-sub 99.9%

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

      9. sub-neg 99.9%

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

      10. distribute-neg-frac2 99.9%

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

      11. distribute-neg-in 99.9%

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

      12. metadata-eval 99.9%

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

      13. sub-neg 99.9%

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

   7. Simplified 99.9%

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

4. Final simplification 99.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(1 - x\right) \cdot y}{1 + y} \leq 0.9995:\\ \;\;\;\;1 + \frac{y}{1 + y} \cdot \left(x + -1\right)\\ \mathbf{elif}\;\frac{\left(1 - x\right) \cdot y}{1 + y} \leq 1:\\ \;\;\;\;x + \frac{1 - x}{y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\frac{y}{1 + y} + \frac{1 - \frac{y}{1 + y}}{x}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 99.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{\left(1 - x\right) \cdot y}{1 + y}\\ \mathbf{if}\;t\_0 \leq 0.9995 \lor \neg \left(t\_0 \leq 1.05\right):\\ \;\;\;\;1 + \frac{y}{1 + y} \cdot \left(x + -1\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{1 - x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (/ (* (- 1.0 x) y) (+ 1.0 y))))
   (if (or (<= t_0 0.9995) (not (<= t_0 1.05)))
     (+ 1.0 (* (/ y (+ 1.0 y)) (+ x -1.0)))
     (+ x (/ (- 1.0 x) y)))))

C

double code(double x, double y) {
	double t_0 = ((1.0 - x) * y) / (1.0 + y);
	double tmp;
	if ((t_0 <= 0.9995) || !(t_0 <= 1.05)) {
		tmp = 1.0 + ((y / (1.0 + y)) * (x + -1.0));
	} else {
		tmp = x + ((1.0 - x) / y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: t_0
    real(8) :: tmp
    t_0 = ((1.0d0 - x) * y) / (1.0d0 + y)
    if ((t_0 <= 0.9995d0) .or. (.not. (t_0 <= 1.05d0))) then
        tmp = 1.0d0 + ((y / (1.0d0 + y)) * (x + (-1.0d0)))
    else
        tmp = x + ((1.0d0 - x) / y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double t_0 = ((1.0 - x) * y) / (1.0 + y);
	double tmp;
	if ((t_0 <= 0.9995) || !(t_0 <= 1.05)) {
		tmp = 1.0 + ((y / (1.0 + y)) * (x + -1.0));
	} else {
		tmp = x + ((1.0 - x) / y);
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = ((1.0 - x) * y) / (1.0 + y)
	tmp = 0
	if (t_0 <= 0.9995) or not (t_0 <= 1.05):
		tmp = 1.0 + ((y / (1.0 + y)) * (x + -1.0))
	else:
		tmp = x + ((1.0 - x) / y)
	return tmp

Julia

function code(x, y)
	t_0 = Float64(Float64(Float64(1.0 - x) * y) / Float64(1.0 + y))
	tmp = 0.0
	if ((t_0 <= 0.9995) || !(t_0 <= 1.05))
		tmp = Float64(1.0 + Float64(Float64(y / Float64(1.0 + y)) * Float64(x + -1.0)));
	else
		tmp = Float64(x + Float64(Float64(1.0 - x) / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = ((1.0 - x) * y) / (1.0 + y);
	tmp = 0.0;
	if ((t_0 <= 0.9995) || ~((t_0 <= 1.05)))
		tmp = 1.0 + ((y / (1.0 + y)) * (x + -1.0));
	else
		tmp = x + ((1.0 - x) / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(N[(N[(1.0 - x), $MachinePrecision] * y), $MachinePrecision] / N[(1.0 + y), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$0, 0.9995], N[Not[LessEqual[t$95$0, 1.05]], $MachinePrecision]], N[(1.0 + N[(N[(y / N[(1.0 + y), $MachinePrecision]), $MachinePrecision] * N[(x + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(1.0 - x), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 2 regimes

2. if (/.f64 (*.f64 (-.f64 #s(literal 1 binary64) x) y) (+.f64 y #s(literal 1 binary64))) < 0.99950000000000006 or 1.05000000000000004 < (/.f64 (*.f64 (-.f64 #s(literal 1 binary64) x) y) (+.f64 y #s(literal 1 binary64)))

   1. Initial program 87.1%

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

      1. associate-/l* 99.9%

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

      2. +-commutative 99.9%

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

   3. Simplified 99.9%

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

   if 0.99950000000000006 < (/.f64 (*.f64 (-.f64 #s(literal 1 binary64) x) y) (+.f64 y #s(literal 1 binary64))) < 1.05000000000000004

   1. Initial program 6.8%

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

      1. associate-/l* 6.9%

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

      2. +-commutative 6.9%

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

   3. Simplified 6.9%

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

   5. Taylor expanded in y around inf 100.0%

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

      1. associate--l+ 100.0%

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

      2. div-sub 100.0%

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

   7. Simplified 100.0%

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

4. Final simplification 99.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(1 - x\right) \cdot y}{1 + y} \leq 0.9995 \lor \neg \left(\frac{\left(1 - x\right) \cdot y}{1 + y} \leq 1.05\right):\\ \;\;\;\;1 + \frac{y}{1 + y} \cdot \left(x + -1\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{1 - x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 98.7% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -17 \lor \neg \left(y \leq 58\right):\\ \;\;\;\;x + \frac{1 - x}{y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\frac{y}{1 + y} + \frac{1}{x}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= y -17.0) (not (<= y 58.0)))
   (+ x (/ (- 1.0 x) y))
   (* x (+ (/ y (+ 1.0 y)) (/ 1.0 x)))))

C

double code(double x, double y) {
	double tmp;
	if ((y <= -17.0) || !(y <= 58.0)) {
		tmp = x + ((1.0 - x) / y);
	} else {
		tmp = x * ((y / (1.0 + y)) + (1.0 / 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 <= (-17.0d0)) .or. (.not. (y <= 58.0d0))) then
        tmp = x + ((1.0d0 - x) / y)
    else
        tmp = x * ((y / (1.0d0 + y)) + (1.0d0 / x))
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((y <= -17.0) || !(y <= 58.0)) {
		tmp = x + ((1.0 - x) / y);
	} else {
		tmp = x * ((y / (1.0 + y)) + (1.0 / x));
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (y <= -17.0) or not (y <= 58.0):
		tmp = x + ((1.0 - x) / y)
	else:
		tmp = x * ((y / (1.0 + y)) + (1.0 / x))
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((y <= -17.0) || !(y <= 58.0))
		tmp = Float64(x + Float64(Float64(1.0 - x) / y));
	else
		tmp = Float64(x * Float64(Float64(y / Float64(1.0 + y)) + Float64(1.0 / x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((y <= -17.0) || ~((y <= 58.0)))
		tmp = x + ((1.0 - x) / y);
	else
		tmp = x * ((y / (1.0 + y)) + (1.0 / x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[y, -17.0], N[Not[LessEqual[y, 58.0]], $MachinePrecision]], N[(x + N[(N[(1.0 - x), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], N[(x * N[(N[(y / N[(1.0 + y), $MachinePrecision]), $MachinePrecision] + N[(1.0 / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -17 or 58 < y

   1. Initial program 30.2%

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

      1. associate-/l* 48.2%

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

      2. +-commutative 48.2%

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

   3. Simplified 48.2%

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

   5. Taylor expanded in y around inf 98.3%

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

      1. associate--l+ 98.3%

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

      2. div-sub 98.3%

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

   7. Simplified 98.3%

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

   if -17 < y < 58

   1. Initial program 100.0%

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

      1. associate-/l* 100.0%

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

      2. +-commutative 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in x around inf 99.8%

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

      1. associate--r+ 99.8%

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

      2. cancel-sign-sub-inv 99.8%

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

      3. metadata-eval 99.8%

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

      4. *-lft-identity 99.8%

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

      5. +-commutative 99.8%

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

      6. associate-/l/ 99.8%

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

      7. associate-+r- 99.8%

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

      8. div-sub 99.8%

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

      9. sub-neg 99.8%

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

      10. distribute-neg-frac2 99.8%

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

      11. distribute-neg-in 99.8%

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

      12. metadata-eval 99.8%

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

      13. sub-neg 99.8%

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

   7. Simplified 99.8%

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

   8. Taylor expanded in y around 0 98.6%

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

4. Final simplification 98.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -17 \lor \neg \left(y \leq 58\right):\\ \;\;\;\;x + \frac{1 - x}{y}\\ \mathbf{else}:\\ \;\;\;\;x \cdot \left(\frac{y}{1 + y} + \frac{1}{x}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 98.4% accurate, 0.6× speedup

Math

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

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 30.7%

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

      1. associate-/l* 48.6%

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

      2. +-commutative 48.6%

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

   3. Simplified 48.6%

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

   5. Taylor expanded in y around inf 97.7%

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

      1. associate--l+ 97.7%

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

      2. div-sub 97.7%

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

   7. Simplified 97.7%

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

   if -1 < y < 1

   1. Initial program 100.0%

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

      1. associate-/l* 100.0%

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

      2. +-commutative 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in y around 0 98.6%

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

4. Final simplification 98.2%

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

Alternative 6: 98.2% accurate, 0.6× speedup

Math

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

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= y -1.0) (not (<= y 1.2))) (+ x (/ (- 1.0 x) y)) (+ 1.0 (* x y))))

C

double code(double x, double y) {
	double tmp;
	if ((y <= -1.0) || !(y <= 1.2)) {
		tmp = x + ((1.0 - x) / y);
	} else {
		tmp = 1.0 + (x * y);
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if ((y <= (-1.0d0)) .or. (.not. (y <= 1.2d0))) then
        tmp = x + ((1.0d0 - x) / y)
    else
        tmp = 1.0d0 + (x * y)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((y <= -1.0) || !(y <= 1.2)) {
		tmp = x + ((1.0 - x) / y);
	} else {
		tmp = 1.0 + (x * y);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (y <= -1.0) or not (y <= 1.2):
		tmp = x + ((1.0 - x) / y)
	else:
		tmp = 1.0 + (x * y)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((y <= -1.0) || !(y <= 1.2))
		tmp = Float64(x + Float64(Float64(1.0 - x) / y));
	else
		tmp = Float64(1.0 + Float64(x * y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((y <= -1.0) || ~((y <= 1.2)))
		tmp = x + ((1.0 - x) / y);
	else
		tmp = 1.0 + (x * y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[y, -1.0], N[Not[LessEqual[y, 1.2]], $MachinePrecision]], N[(x + N[(N[(1.0 - x), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], N[(1.0 + N[(x * y), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1 or 1.19999999999999996 < y

   1. Initial program 30.7%

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

      1. associate-/l* 48.6%

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

      2. +-commutative 48.6%

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

   3. Simplified 48.6%

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

   5. Taylor expanded in y around inf 97.7%

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

      1. associate--l+ 97.7%

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

      2. div-sub 97.7%

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

   7. Simplified 97.7%

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

   if -1 < y < 1.19999999999999996

   1. Initial program 100.0%

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

      1. associate-/l* 100.0%

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

      2. +-commutative 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in x around inf 99.8%

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

      1. associate--r+ 99.8%

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

      2. cancel-sign-sub-inv 99.8%

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

      3. metadata-eval 99.8%

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

      4. *-lft-identity 99.8%

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

      5. +-commutative 99.8%

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

      6. associate-/l/ 99.8%

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

      7. associate-+r- 99.8%

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

      8. div-sub 99.8%

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

      9. sub-neg 99.8%

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

      10. distribute-neg-frac2 99.8%

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

      11. distribute-neg-in 99.8%

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

      12. metadata-eval 99.8%

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

      13. sub-neg 99.8%

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

   7. Simplified 99.8%

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

   8. Taylor expanded in y around 0 98.6%

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

   9. Taylor expanded in y around 0 98.4%

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

4. Final simplification 98.1%

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

Alternative 7: 85.5% accurate, 0.7× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 3 \cdot 10^{+20}:\\ \;\;\;\;1 + x \cdot y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -1.0) x (if (<= y 3e+20) (+ 1.0 (* x y)) x)))

C

double code(double x, double y) {
	double tmp;
	if (y <= -1.0) {
		tmp = x;
	} else if (y <= 3e+20) {
		tmp = 1.0 + (x * 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 <= 3d+20) then
        tmp = 1.0d0 + (x * 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 <= 3e+20) {
		tmp = 1.0 + (x * y);
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -1.0:
		tmp = x
	elif y <= 3e+20:
		tmp = 1.0 + (x * y)
	else:
		tmp = x
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -1.0)
		tmp = x;
	elseif (y <= 3e+20)
		tmp = Float64(1.0 + Float64(x * 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 <= 3e+20)
		tmp = 1.0 + (x * y);
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -1.0], x, If[LessEqual[y, 3e+20], N[(1.0 + N[(x * y), $MachinePrecision]), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if y < -1 or 3e20 < y

   1. Initial program 29.7%

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

      1. associate-/l* 48.3%

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

      2. +-commutative 48.3%

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

   3. Simplified 48.3%

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

   5. Taylor expanded in y around inf 76.2%

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

   if -1 < y < 3e20

   1. Initial program 98.3%

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

      1. associate-/l* 98.3%

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

      2. +-commutative 98.3%

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

   3. Simplified 98.3%

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

   5. Taylor expanded in x around inf 98.1%

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

      1. associate--r+ 98.1%

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

      2. cancel-sign-sub-inv 98.1%

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

      3. metadata-eval 98.1%

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

      4. *-lft-identity 98.1%

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

      5. +-commutative 98.1%

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

      6. associate-/l/ 98.1%

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

      7. associate-+r- 98.1%

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

      8. div-sub 98.1%

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

      9. sub-neg 98.1%

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

      10. distribute-neg-frac2 98.1%

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

      11. distribute-neg-in 98.1%

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

      12. metadata-eval 98.1%

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

      13. sub-neg 98.1%

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

   7. Simplified 98.1%

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

   8. Taylor expanded in y around 0 96.0%

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

   9. Taylor expanded in y around 0 95.1%

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

Alternative 8: 74.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 0.9:\\ \;\;\;\;1 - y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -1.0) x (if (<= y 0.9) (- 1.0 y) x)))

C

double code(double x, double y) {
	double tmp;
	if (y <= -1.0) {
		tmp = x;
	} else if (y <= 0.9) {
		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 <= 0.9d0) 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 <= 0.9) {
		tmp = 1.0 - y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -1.0:
		tmp = x
	elif y <= 0.9:
		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 <= 0.9)
		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 <= 0.9)
		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, 0.9], N[(1.0 - y), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if y < -1 or 0.900000000000000022 < y

   1. Initial program 30.7%

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

      1. associate-/l* 48.6%

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

      2. +-commutative 48.6%

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

   3. Simplified 48.6%

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

   5. Taylor expanded in y around inf 73.6%

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

   if -1 < y < 0.900000000000000022

   1. Initial program 100.0%

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

      1. associate-/l* 100.0%

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

      2. +-commutative 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in x around 0 75.0%

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

   6. Taylor expanded in y around 0 74.0%

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

Alternative 9: 73.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 3 \cdot 10^{+20}:\\ \;\;\;\;1\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (if (<= y -1.0) x (if (<= y 3e+20) 1.0 x)))

C

double code(double x, double y) {
	double tmp;
	if (y <= -1.0) {
		tmp = x;
	} else if (y <= 3e+20) {
		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 <= 3d+20) 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 <= 3e+20) {
		tmp = 1.0;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -1.0:
		tmp = x
	elif y <= 3e+20:
		tmp = 1.0
	else:
		tmp = x
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -1.0)
		tmp = x;
	elseif (y <= 3e+20)
		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 <= 3e+20)
		tmp = 1.0;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -1.0], x, If[LessEqual[y, 3e+20], 1.0, x]]

Derivation

1. Split input into 2 regimes

2. if y < -1 or 3e20 < y

   1. Initial program 29.7%

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

      1. associate-/l* 48.3%

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

      2. +-commutative 48.3%

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

   3. Simplified 48.3%

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

   5. Taylor expanded in y around inf 76.2%

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

   if -1 < y < 3e20

   1. Initial program 98.3%

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

      1. associate-/l* 98.3%

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

      2. +-commutative 98.3%

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

   3. Simplified 98.3%

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

   5. Taylor expanded in y around 0 71.4%

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

Alternative 10: 38.8% 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 64.6%

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

   1. associate-/l* 73.7%

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

   2. +-commutative 73.7%

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

3. Simplified 73.7%

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

5. Taylor expanded in y around 0 38.0%

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

Developer target: 99.6% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024088 
(FPCore (x y)
  :name "Diagrams.Trail:splitAtParam  from diagrams-lib-1.3.0.3, D"
  :precision binary64

  :alt
  (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))))