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

Percentage Accurate: 65.5% → 99.9%

Time: 25.0s

Alternatives: 12

Speedup: 0.8×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 65.5% 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, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -11000:\\ \;\;\;\;x + \frac{\left(1 - x\right) - \frac{\left(1 - x\right) + \frac{x + -1}{y}}{y}}{y}\\ \mathbf{elif}\;y \leq 3100000:\\ \;\;\;\;1 + \left(1 - x\right) \cdot \frac{y}{-1 - y}\\ \mathbf{else}:\\ \;\;\;\;x + \left(\frac{1 - x}{y} + \frac{\frac{-1}{y}}{y}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -11000.0)
   (+ x (/ (- (- 1.0 x) (/ (+ (- 1.0 x) (/ (+ x -1.0) y)) y)) y))
   (if (<= y 3100000.0)
     (+ 1.0 (* (- 1.0 x) (/ y (- -1.0 y))))
     (+ x (+ (/ (- 1.0 x) y) (/ (/ -1.0 y) y))))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -11000.0) {
		tmp = x + (((1.0 - x) - (((1.0 - x) + ((x + -1.0) / y)) / y)) / y);
	} else if (y <= 3100000.0) {
		tmp = 1.0 + ((1.0 - x) * (y / (-1.0 - y)));
	} else {
		tmp = x + (((1.0 - x) / y) + ((-1.0 / y) / y));
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (y <= (-11000.0d0)) then
        tmp = x + (((1.0d0 - x) - (((1.0d0 - x) + ((x + (-1.0d0)) / y)) / y)) / y)
    else if (y <= 3100000.0d0) then
        tmp = 1.0d0 + ((1.0d0 - x) * (y / ((-1.0d0) - y)))
    else
        tmp = x + (((1.0d0 - x) / y) + (((-1.0d0) / y) / y))
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (y <= -11000.0) {
		tmp = x + (((1.0 - x) - (((1.0 - x) + ((x + -1.0) / y)) / y)) / y);
	} else if (y <= 3100000.0) {
		tmp = 1.0 + ((1.0 - x) * (y / (-1.0 - y)));
	} else {
		tmp = x + (((1.0 - x) / y) + ((-1.0 / y) / y));
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -11000.0:
		tmp = x + (((1.0 - x) - (((1.0 - x) + ((x + -1.0) / y)) / y)) / y)
	elif y <= 3100000.0:
		tmp = 1.0 + ((1.0 - x) * (y / (-1.0 - y)))
	else:
		tmp = x + (((1.0 - x) / y) + ((-1.0 / y) / y))
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -11000.0)
		tmp = Float64(x + Float64(Float64(Float64(1.0 - x) - Float64(Float64(Float64(1.0 - x) + Float64(Float64(x + -1.0) / y)) / y)) / y));
	elseif (y <= 3100000.0)
		tmp = Float64(1.0 + Float64(Float64(1.0 - x) * Float64(y / Float64(-1.0 - y))));
	else
		tmp = Float64(x + Float64(Float64(Float64(1.0 - x) / y) + Float64(Float64(-1.0 / y) / y)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -11000.0)
		tmp = x + (((1.0 - x) - (((1.0 - x) + ((x + -1.0) / y)) / y)) / y);
	elseif (y <= 3100000.0)
		tmp = 1.0 + ((1.0 - x) * (y / (-1.0 - y)));
	else
		tmp = x + (((1.0 - x) / y) + ((-1.0 / y) / y));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -11000.0], N[(x + N[(N[(N[(1.0 - x), $MachinePrecision] - N[(N[(N[(1.0 - x), $MachinePrecision] + N[(N[(x + -1.0), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3100000.0], N[(1.0 + N[(N[(1.0 - x), $MachinePrecision] * N[(y / N[(-1.0 - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(N[(1.0 - x), $MachinePrecision] / y), $MachinePrecision] + N[(N[(-1.0 / y), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -11000

   1. Initial program 31.2%

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

      1. associate-/l* 54.1%

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

      2. remove-double-neg 54.1%

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

      3. remove-double-neg 54.1%

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

      4. +-commutative 54.1%

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

   3. Simplified 54.1%

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

   5. Taylor expanded in y around -inf 99.9%

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

   7. Simplified 99.9%

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

   if -11000 < y < 3.1e6

   1. Initial program 99.9%

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

      1. associate-/l* 99.9%

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

      2. remove-double-neg 99.9%

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

      3. remove-double-neg 99.9%

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

      4. +-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 3.1e6 < y

   1. Initial program 30.3%

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

      1. associate-/l* 45.2%

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

      2. remove-double-neg 45.2%

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

      3. remove-double-neg 45.2%

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

      4. +-commutative 45.2%

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

   3. Simplified 45.2%

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

   5. Taylor expanded in y around inf 100.0%

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

      1. associate--l+ 100.0%

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

      2. neg-mul-1 100.0%

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

      3. sub-neg 100.0%

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

      4. associate--l+ 100.0%

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

      5. div-sub 100.0%

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

      6. sub-neg 100.0%

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

      7. +-commutative 100.0%

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

      8. neg-sub0 100.0%

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

      9. associate-+l- 100.0%

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

      10. neg-sub0 100.0%

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

      11. mul-1-neg 100.0%

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

      12. associate-*r/ 100.0%

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

      13. +-commutative 100.0%

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

   7. Simplified 100.0%

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

      1. *-un-lft-identity 100.0%

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

      2. unpow2 100.0%

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

      3. times-frac 100.0%

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

      4. +-commutative 100.0%

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

   9. Applied egg-rr 100.0%

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

       1. associate-*l/ 100.0%

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

       2. *-lft-identity 100.0%

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

   11. Simplified 100.0%

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

   12. Taylor expanded in x around 0 100.0%

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

4. Final simplification 99.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -11000:\\ \;\;\;\;x + \frac{\left(1 - x\right) - \frac{\left(1 - x\right) + \frac{x + -1}{y}}{y}}{y}\\ \mathbf{elif}\;y \leq 3100000:\\ \;\;\;\;1 + \left(1 - x\right) \cdot \frac{y}{-1 - y}\\ \mathbf{else}:\\ \;\;\;\;x + \left(\frac{1 - x}{y} + \frac{\frac{-1}{y}}{y}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 2: 99.6% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{y \cdot \left(1 - x\right)}{y + 1}\\ \mathbf{if}\;t\_0 \leq 0.9988 \lor \neg \left(t\_0 \leq 1.000002\right):\\ \;\;\;\;1 + \left(1 - x\right) \cdot \frac{y}{-1 - y}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{1 - x}{y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (/ (* y (- 1.0 x)) (+ y 1.0))))
   (if (or (<= t_0 0.9988) (not (<= t_0 1.000002)))
     (+ 1.0 (* (- 1.0 x) (/ y (- -1.0 y))))
     (+ x (/ (- 1.0 x) y)))))

C

double code(double x, double y) {
	double t_0 = (y * (1.0 - x)) / (y + 1.0);
	double tmp;
	if ((t_0 <= 0.9988) || !(t_0 <= 1.000002)) {
		tmp = 1.0 + ((1.0 - x) * (y / (-1.0 - y)));
	} 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 = (y * (1.0d0 - x)) / (y + 1.0d0)
    if ((t_0 <= 0.9988d0) .or. (.not. (t_0 <= 1.000002d0))) then
        tmp = 1.0d0 + ((1.0d0 - x) * (y / ((-1.0d0) - y)))
    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 = (y * (1.0 - x)) / (y + 1.0);
	double tmp;
	if ((t_0 <= 0.9988) || !(t_0 <= 1.000002)) {
		tmp = 1.0 + ((1.0 - x) * (y / (-1.0 - y)));
	} else {
		tmp = x + ((1.0 - x) / y);
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = (y * (1.0 - x)) / (y + 1.0)
	tmp = 0
	if (t_0 <= 0.9988) or not (t_0 <= 1.000002):
		tmp = 1.0 + ((1.0 - x) * (y / (-1.0 - y)))
	else:
		tmp = x + ((1.0 - x) / y)
	return tmp

Julia

function code(x, y)
	t_0 = Float64(Float64(y * Float64(1.0 - x)) / Float64(y + 1.0))
	tmp = 0.0
	if ((t_0 <= 0.9988) || !(t_0 <= 1.000002))
		tmp = Float64(1.0 + Float64(Float64(1.0 - x) * Float64(y / Float64(-1.0 - y))));
	else
		tmp = Float64(x + Float64(Float64(1.0 - x) / y));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = (y * (1.0 - x)) / (y + 1.0);
	tmp = 0.0;
	if ((t_0 <= 0.9988) || ~((t_0 <= 1.000002)))
		tmp = 1.0 + ((1.0 - x) * (y / (-1.0 - y)));
	else
		tmp = x + ((1.0 - x) / y);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(N[(y * N[(1.0 - x), $MachinePrecision]), $MachinePrecision] / N[(y + 1.0), $MachinePrecision]), $MachinePrecision]}, If[Or[LessEqual[t$95$0, 0.9988], N[Not[LessEqual[t$95$0, 1.000002]], $MachinePrecision]], N[(1.0 + N[(N[(1.0 - x), $MachinePrecision] * N[(y / N[(-1.0 - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(x + N[(N[(1.0 - 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))) < 0.998800000000000021 or 1.00000200000000006 < (/.f64 (*.f64 (-.f64 #s(literal 1 binary64) x) y) (+.f64 y #s(literal 1 binary64)))

   1. Initial program 84.3%

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

      1. associate-/l* 99.8%

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

      2. remove-double-neg 99.8%

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

      3. remove-double-neg 99.8%

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

      4. +-commutative 99.8%

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

   3. Simplified 99.8%

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

   if 0.998800000000000021 < (/.f64 (*.f64 (-.f64 #s(literal 1 binary64) x) y) (+.f64 y #s(literal 1 binary64))) < 1.00000200000000006

   1. Initial program 10.6%

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

      1. associate-/l* 10.6%

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

      2. remove-double-neg 10.6%

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

      3. remove-double-neg 10.6%

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

      4. +-commutative 10.6%

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

   3. Simplified 10.6%

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

   5. Taylor expanded in y around inf 98.4%

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

      1. associate--l+ 98.4%

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

      2. div-sub 98.4%

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

   7. Simplified 98.4%

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

4. Final simplification 99.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y \cdot \left(1 - x\right)}{y + 1} \leq 0.9988 \lor \neg \left(\frac{y \cdot \left(1 - x\right)}{y + 1} \leq 1.000002\right):\\ \;\;\;\;1 + \left(1 - x\right) \cdot \frac{y}{-1 - y}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{1 - x}{y}\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 85.2% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -6.1 \cdot 10^{+71}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -1:\\ \;\;\;\;\frac{1}{y}\\ \mathbf{elif}\;y \leq 16:\\ \;\;\;\;1 + y \cdot x\\ \mathbf{elif}\;y \leq 2.9 \cdot 10^{+32}:\\ \;\;\;\;\frac{1}{y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -6.1e+71)
   x
   (if (<= y -1.0)
     (/ 1.0 y)
     (if (<= y 16.0) (+ 1.0 (* y x)) (if (<= y 2.9e+32) (/ 1.0 y) x)))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -6.1e+71) {
		tmp = x;
	} else if (y <= -1.0) {
		tmp = 1.0 / y;
	} else if (y <= 16.0) {
		tmp = 1.0 + (y * x);
	} else if (y <= 2.9e+32) {
		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 <= (-6.1d+71)) then
        tmp = x
    else if (y <= (-1.0d0)) then
        tmp = 1.0d0 / y
    else if (y <= 16.0d0) then
        tmp = 1.0d0 + (y * x)
    else if (y <= 2.9d+32) 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 <= -6.1e+71) {
		tmp = x;
	} else if (y <= -1.0) {
		tmp = 1.0 / y;
	} else if (y <= 16.0) {
		tmp = 1.0 + (y * x);
	} else if (y <= 2.9e+32) {
		tmp = 1.0 / y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -6.1e+71:
		tmp = x
	elif y <= -1.0:
		tmp = 1.0 / y
	elif y <= 16.0:
		tmp = 1.0 + (y * x)
	elif y <= 2.9e+32:
		tmp = 1.0 / y
	else:
		tmp = x
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -6.1e+71)
		tmp = x;
	elseif (y <= -1.0)
		tmp = Float64(1.0 / y);
	elseif (y <= 16.0)
		tmp = Float64(1.0 + Float64(y * x));
	elseif (y <= 2.9e+32)
		tmp = Float64(1.0 / y);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -6.1e+71)
		tmp = x;
	elseif (y <= -1.0)
		tmp = 1.0 / y;
	elseif (y <= 16.0)
		tmp = 1.0 + (y * x);
	elseif (y <= 2.9e+32)
		tmp = 1.0 / y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -6.1e+71], x, If[LessEqual[y, -1.0], N[(1.0 / y), $MachinePrecision], If[LessEqual[y, 16.0], N[(1.0 + N[(y * x), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.9e+32], N[(1.0 / y), $MachinePrecision], x]]]]

Derivation

1. Split input into 3 regimes

2. if y < -6.1000000000000003e71 or 2.90000000000000003e32 < y

   1. Initial program 30.7%

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

      1. associate-/l* 52.8%

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

      2. remove-double-neg 52.8%

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

      3. remove-double-neg 52.8%

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

      4. +-commutative 52.8%

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

   3. Simplified 52.8%

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

   5. Taylor expanded in y around inf 78.9%

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

   if -6.1000000000000003e71 < y < -1 or 16 < y < 2.90000000000000003e32

   1. Initial program 33.2%

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

      1. associate-/l* 39.5%

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

      2. remove-double-neg 39.5%

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

      3. remove-double-neg 39.5%

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

      4. +-commutative 39.5%

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

   3. Simplified 39.5%

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

   5. Taylor expanded in x around 0 15.9%

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

      1. +-commutative 15.9%

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

   7. Simplified 15.9%

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

   8. Taylor expanded in y around inf 65.0%

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

   if -1 < y < 16

   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. remove-double-neg 100.0%

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

      3. remove-double-neg 100.0%

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

      4. +-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 98.8%

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

      1. mul-1-neg 98.8%

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

      2. distribute-neg-frac2 98.8%

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

      3. *-commutative 98.8%

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

      4. distribute-neg-in 98.8%

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

      5. metadata-eval 98.8%

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

      6. sub-neg 98.8%

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

   7. Simplified 98.8%

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

   8. Taylor expanded in y around 0 96.8%

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

      1. *-commutative 96.8%

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

   10. Simplified 96.8%

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

Alternative 4: 73.3% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5 \cdot 10^{+70}:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq -1:\\ \;\;\;\;\frac{1}{y}\\ \mathbf{elif}\;y \leq 7.8 \cdot 10^{-8}:\\ \;\;\;\;1 - y\\ \mathbf{elif}\;y \leq 1.55 \cdot 10^{+32}:\\ \;\;\;\;\frac{1}{y}\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -5e+70)
   x
   (if (<= y -1.0)
     (/ 1.0 y)
     (if (<= y 7.8e-8) (- 1.0 y) (if (<= y 1.55e+32) (/ 1.0 y) x)))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -5e+70) {
		tmp = x;
	} else if (y <= -1.0) {
		tmp = 1.0 / y;
	} else if (y <= 7.8e-8) {
		tmp = 1.0 - y;
	} else if (y <= 1.55e+32) {
		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 <= (-5d+70)) then
        tmp = x
    else if (y <= (-1.0d0)) then
        tmp = 1.0d0 / y
    else if (y <= 7.8d-8) then
        tmp = 1.0d0 - y
    else if (y <= 1.55d+32) 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 <= -5e+70) {
		tmp = x;
	} else if (y <= -1.0) {
		tmp = 1.0 / y;
	} else if (y <= 7.8e-8) {
		tmp = 1.0 - y;
	} else if (y <= 1.55e+32) {
		tmp = 1.0 / y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -5e+70:
		tmp = x
	elif y <= -1.0:
		tmp = 1.0 / y
	elif y <= 7.8e-8:
		tmp = 1.0 - y
	elif y <= 1.55e+32:
		tmp = 1.0 / y
	else:
		tmp = x
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -5e+70)
		tmp = x;
	elseif (y <= -1.0)
		tmp = Float64(1.0 / y);
	elseif (y <= 7.8e-8)
		tmp = Float64(1.0 - y);
	elseif (y <= 1.55e+32)
		tmp = Float64(1.0 / y);
	else
		tmp = x;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -5e+70)
		tmp = x;
	elseif (y <= -1.0)
		tmp = 1.0 / y;
	elseif (y <= 7.8e-8)
		tmp = 1.0 - y;
	elseif (y <= 1.55e+32)
		tmp = 1.0 / y;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -5e+70], x, If[LessEqual[y, -1.0], N[(1.0 / y), $MachinePrecision], If[LessEqual[y, 7.8e-8], N[(1.0 - y), $MachinePrecision], If[LessEqual[y, 1.55e+32], N[(1.0 / y), $MachinePrecision], x]]]]

Derivation

1. Split input into 3 regimes

2. if y < -5.0000000000000002e70 or 1.54999999999999997e32 < y

   1. Initial program 30.7%

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

      1. associate-/l* 52.8%

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

      2. remove-double-neg 52.8%

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

      3. remove-double-neg 52.8%

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

      4. +-commutative 52.8%

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

   3. Simplified 52.8%

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

   5. Taylor expanded in y around inf 78.9%

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

   if -5.0000000000000002e70 < y < -1 or 7.7999999999999997e-8 < y < 1.54999999999999997e32

   1. Initial program 39.4%

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

      1. associate-/l* 45.2%

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

      2. remove-double-neg 45.2%

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

      3. remove-double-neg 45.2%

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

      4. +-commutative 45.2%

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

   3. Simplified 45.2%

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

   5. Taylor expanded in x around 0 15.0%

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

      1. +-commutative 15.0%

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

   7. Simplified 15.0%

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

   8. Taylor expanded in y around inf 59.5%

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

   if -1 < y < 7.7999999999999997e-8

   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. remove-double-neg 100.0%

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

      3. remove-double-neg 100.0%

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

      4. +-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 98.7%

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

   6. Taylor expanded in x around 0 76.1%

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

Alternative 5: 99.9% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -330000 \lor \neg \left(y \leq 3700000\right):\\ \;\;\;\;x + \left(\frac{1 - x}{y} + \frac{\frac{-1}{y}}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;1 + \left(1 - x\right) \cdot \frac{y}{-1 - y}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= y -330000.0) (not (<= y 3700000.0)))
   (+ x (+ (/ (- 1.0 x) y) (/ (/ -1.0 y) y)))
   (+ 1.0 (* (- 1.0 x) (/ y (- -1.0 y))))))

C

double code(double x, double y) {
	double tmp;
	if ((y <= -330000.0) || !(y <= 3700000.0)) {
		tmp = x + (((1.0 - x) / y) + ((-1.0 / y) / y));
	} else {
		tmp = 1.0 + ((1.0 - x) * (y / (-1.0 - y)));
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if ((y <= (-330000.0d0)) .or. (.not. (y <= 3700000.0d0))) then
        tmp = x + (((1.0d0 - x) / y) + (((-1.0d0) / y) / y))
    else
        tmp = 1.0d0 + ((1.0d0 - x) * (y / ((-1.0d0) - y)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((y <= -330000.0) || !(y <= 3700000.0)) {
		tmp = x + (((1.0 - x) / y) + ((-1.0 / y) / y));
	} else {
		tmp = 1.0 + ((1.0 - x) * (y / (-1.0 - y)));
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (y <= -330000.0) or not (y <= 3700000.0):
		tmp = x + (((1.0 - x) / y) + ((-1.0 / y) / y))
	else:
		tmp = 1.0 + ((1.0 - x) * (y / (-1.0 - y)))
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((y <= -330000.0) || !(y <= 3700000.0))
		tmp = Float64(x + Float64(Float64(Float64(1.0 - x) / y) + Float64(Float64(-1.0 / y) / y)));
	else
		tmp = Float64(1.0 + Float64(Float64(1.0 - x) * Float64(y / Float64(-1.0 - y))));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((y <= -330000.0) || ~((y <= 3700000.0)))
		tmp = x + (((1.0 - x) / y) + ((-1.0 / y) / y));
	else
		tmp = 1.0 + ((1.0 - x) * (y / (-1.0 - y)));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[y, -330000.0], N[Not[LessEqual[y, 3700000.0]], $MachinePrecision]], N[(x + N[(N[(N[(1.0 - x), $MachinePrecision] / y), $MachinePrecision] + N[(N[(-1.0 / y), $MachinePrecision] / y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(1.0 + N[(N[(1.0 - x), $MachinePrecision] * N[(y / N[(-1.0 - y), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -3.3e5 or 3.7e6 < y

   1. Initial program 30.8%

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

      1. associate-/l* 49.8%

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

      2. remove-double-neg 49.8%

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

      3. remove-double-neg 49.8%

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

      4. +-commutative 49.8%

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

   3. Simplified 49.8%

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

   5. Taylor expanded in y around inf 99.8%

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

      1. associate--l+ 99.8%

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

      2. neg-mul-1 99.8%

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

      3. sub-neg 99.8%

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

      4. associate--l+ 99.8%

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

      5. div-sub 99.8%

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

      6. sub-neg 99.8%

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

      7. +-commutative 99.8%

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

      8. neg-sub0 99.8%

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

      9. associate-+l- 99.8%

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

      10. neg-sub0 99.8%

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

      11. mul-1-neg 99.8%

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

      12. associate-*r/ 99.8%

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

      13. +-commutative 99.8%

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

   7. Simplified 99.8%

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

      1. *-un-lft-identity 99.8%

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

      2. unpow2 99.8%

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

      3. times-frac 99.8%

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

      4. +-commutative 99.8%

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

   9. Applied egg-rr 99.8%

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

       1. associate-*l/ 99.8%

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

       2. *-lft-identity 99.8%

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

   11. Simplified 99.8%

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

   12. Taylor expanded in x around 0 99.8%

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

   if -3.3e5 < y < 3.7e6

   1. Initial program 99.9%

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

      1. associate-/l* 99.9%

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

      2. remove-double-neg 99.9%

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

      3. remove-double-neg 99.9%

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

      4. +-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
3. Recombined 2 regimes into one program.

4. Final simplification 99.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -330000 \lor \neg \left(y \leq 3700000\right):\\ \;\;\;\;x + \left(\frac{1 - x}{y} + \frac{\frac{-1}{y}}{y}\right)\\ \mathbf{else}:\\ \;\;\;\;1 + \left(1 - x\right) \cdot \frac{y}{-1 - y}\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 98.6% accurate, 0.6× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -11500 \lor \neg \left(y \leq 600\right):\\ \;\;\;\;x + \frac{1}{y}\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{y \cdot x}{y + 1}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= y -11500.0) (not (<= y 600.0)))
   (+ x (/ 1.0 y))
   (+ 1.0 (/ (* y x) (+ y 1.0)))))

C

double code(double x, double y) {
	double tmp;
	if ((y <= -11500.0) || !(y <= 600.0)) {
		tmp = x + (1.0 / y);
	} else {
		tmp = 1.0 + ((y * x) / (y + 1.0));
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if ((y <= (-11500.0d0)) .or. (.not. (y <= 600.0d0))) then
        tmp = x + (1.0d0 / y)
    else
        tmp = 1.0d0 + ((y * x) / (y + 1.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((y <= -11500.0) || !(y <= 600.0)) {
		tmp = x + (1.0 / y);
	} else {
		tmp = 1.0 + ((y * x) / (y + 1.0));
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (y <= -11500.0) or not (y <= 600.0):
		tmp = x + (1.0 / y)
	else:
		tmp = 1.0 + ((y * x) / (y + 1.0))
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((y <= -11500.0) || !(y <= 600.0))
		tmp = Float64(x + Float64(1.0 / y));
	else
		tmp = Float64(1.0 + Float64(Float64(y * x) / Float64(y + 1.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((y <= -11500.0) || ~((y <= 600.0)))
		tmp = x + (1.0 / y);
	else
		tmp = 1.0 + ((y * x) / (y + 1.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[y, -11500.0], N[Not[LessEqual[y, 600.0]], $MachinePrecision]], N[(x + N[(1.0 / y), $MachinePrecision]), $MachinePrecision], N[(1.0 + N[(N[(y * x), $MachinePrecision] / N[(y + 1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -11500 or 600 < y

   1. Initial program 31.2%

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

      1. associate-/l* 50.1%

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

      2. remove-double-neg 50.1%

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

      3. remove-double-neg 50.1%

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

      4. +-commutative 50.1%

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

   3. Simplified 50.1%

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

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

   8. Taylor expanded in x around 0 98.3%

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

   if -11500 < y < 600

   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. remove-double-neg 100.0%

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

      3. remove-double-neg 100.0%

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

      4. +-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 98.8%

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

      1. mul-1-neg 98.8%

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

      2. distribute-neg-frac2 98.8%

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

      3. *-commutative 98.8%

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

      4. distribute-neg-in 98.8%

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

      5. metadata-eval 98.8%

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

      6. sub-neg 98.8%

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

   7. Simplified 98.8%

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

4. Final simplification 98.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -11500 \lor \neg \left(y \leq 600\right):\\ \;\;\;\;x + \frac{1}{y}\\ \mathbf{else}:\\ \;\;\;\;1 + \frac{y \cdot x}{y + 1}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 98.1% accurate, 0.6× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

2. if y < -1 or 0.80000000000000004 < y

   1. Initial program 31.2%

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

      1. associate-/l* 50.1%

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

      2. remove-double-neg 50.1%

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

      3. remove-double-neg 50.1%

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

      4. +-commutative 50.1%

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

   3. Simplified 50.1%

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

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

   8. Taylor expanded in x around 0 98.3%

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

   if -1 < y < 0.80000000000000004

   1. Initial program 100.0%

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

      1. associate-/l* 100.0%

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

      2. remove-double-neg 100.0%

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

      3. remove-double-neg 100.0%

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

      4. +-commutative 100.0%

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

   3. Simplified 100.0%

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

   5. Taylor expanded in y around 0 97.4%

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

4. Final simplification 97.9%

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

Alternative 8: 97.9% accurate, 0.7× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

2. if y < -1 or 1 < y

   1. Initial program 31.2%

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

      1. associate-/l* 50.1%

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

      2. remove-double-neg 50.1%

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

      3. remove-double-neg 50.1%

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

      4. +-commutative 50.1%

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

   3. Simplified 50.1%

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

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

   8. Taylor expanded in x around 0 98.3%

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

   if -1 < y < 1

   1. Initial program 100.0%

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

      1. associate-/l* 100.0%

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

      2. remove-double-neg 100.0%

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

      3. remove-double-neg 100.0%

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

      4. +-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 98.8%

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

      1. mul-1-neg 98.8%

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

      2. distribute-neg-frac2 98.8%

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

      3. *-commutative 98.8%

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

      4. distribute-neg-in 98.8%

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

      5. metadata-eval 98.8%

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

      6. sub-neg 98.8%

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

   7. Simplified 98.8%

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

   8. Taylor expanded in y around 0 96.8%

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

      1. *-commutative 96.8%

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

   10. Simplified 96.8%

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

4. Final simplification 97.6%

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

Alternative 9: 74.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 7.8 \cdot 10^{-8}:\\ \;\;\;\;1 - y\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -1.0) x (if (<= y 7.8e-8) (- 1.0 y) x)))

C

double code(double x, double y) {
	double tmp;
	if (y <= -1.0) {
		tmp = x;
	} else if (y <= 7.8e-8) {
		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 <= 7.8d-8) 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 <= 7.8e-8) {
		tmp = 1.0 - y;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -1.0:
		tmp = x
	elif y <= 7.8e-8:
		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 <= 7.8e-8)
		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 <= 7.8e-8)
		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, 7.8e-8], N[(1.0 - y), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if y < -1 or 7.7999999999999997e-8 < y

   1. Initial program 32.6%

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

      1. associate-/l* 51.1%

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

      2. remove-double-neg 51.1%

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

      3. remove-double-neg 51.1%

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

      4. +-commutative 51.1%

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

   3. Simplified 51.1%

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

   5. Taylor expanded in y around inf 67.5%

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

   if -1 < y < 7.7999999999999997e-8

   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. remove-double-neg 100.0%

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

      3. remove-double-neg 100.0%

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

      4. +-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 98.7%

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

   6. Taylor expanded in x around 0 76.1%

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

Alternative 10: 62.3% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 4.4 \cdot 10^{+21}:\\ \;\;\;\;x + 1\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -1.0) x (if (<= y 4.4e+21) (+ x 1.0) x)))

C

double code(double x, double y) {
	double tmp;
	if (y <= -1.0) {
		tmp = x;
	} else if (y <= 4.4e+21) {
		tmp = x + 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 <= 4.4d+21) then
        tmp = x + 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 <= 4.4e+21) {
		tmp = x + 1.0;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -1.0:
		tmp = x
	elif y <= 4.4e+21:
		tmp = x + 1.0
	else:
		tmp = x
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -1.0)
		tmp = x;
	elseif (y <= 4.4e+21)
		tmp = Float64(x + 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 <= 4.4e+21)
		tmp = x + 1.0;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -1.0], x, If[LessEqual[y, 4.4e+21], N[(x + 1.0), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if y < -1 or 4.4e21 < y

   1. Initial program 30.9%

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

      1. associate-/l* 50.5%

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

      2. remove-double-neg 50.5%

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

      3. remove-double-neg 50.5%

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

      4. +-commutative 50.5%

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

   3. Simplified 50.5%

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

   5. Taylor expanded in y around inf 71.0%

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

   if -1 < y < 4.4e21

   1. Initial program 97.4%

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

      1. associate-/l* 97.4%

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

      2. remove-double-neg 97.4%

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

      3. remove-double-neg 97.4%

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

      4. +-commutative 97.4%

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

   3. Simplified 97.4%

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

   5. Taylor expanded in x around inf 95.1%

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

      1. mul-1-neg 95.1%

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

      2. distribute-neg-frac2 95.1%

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

      3. *-commutative 95.1%

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

      4. distribute-neg-in 95.1%

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

      5. metadata-eval 95.1%

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

      6. sub-neg 95.1%

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

   7. Simplified 95.1%

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

   8. Taylor expanded in y around inf 52.6%

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

      1. sub-neg 52.6%

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

      2. neg-mul-1 52.6%

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

      3. remove-double-neg 52.6%

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

   10. Simplified 52.6%

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

4. Final simplification 62.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 4.4 \cdot 10^{+21}:\\ \;\;\;\;x + 1\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 50.1% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1:\\ \;\;\;\;x\\ \mathbf{elif}\;y \leq 8 \cdot 10^{+20}:\\ \;\;\;\;y \cdot x\\ \mathbf{else}:\\ \;\;\;\;x\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -1.0) x (if (<= y 8e+20) (* y x) x)))

C

double code(double x, double y) {
	double tmp;
	if (y <= -1.0) {
		tmp = x;
	} else if (y <= 8e+20) {
		tmp = 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 <= 8d+20) then
        tmp = 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 <= 8e+20) {
		tmp = y * x;
	} else {
		tmp = x;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -1.0:
		tmp = x
	elif y <= 8e+20:
		tmp = y * x
	else:
		tmp = x
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -1.0)
		tmp = x;
	elseif (y <= 8e+20)
		tmp = 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 <= 8e+20)
		tmp = y * x;
	else
		tmp = x;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -1.0], x, If[LessEqual[y, 8e+20], N[(y * x), $MachinePrecision], x]]

Derivation

1. Split input into 2 regimes

2. if y < -1 or 8e20 < y

   1. Initial program 30.9%

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

      1. associate-/l* 50.5%

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

      2. remove-double-neg 50.5%

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

      3. remove-double-neg 50.5%

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

      4. +-commutative 50.5%

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

   3. Simplified 50.5%

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

   5. Taylor expanded in y around inf 71.0%

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

   if -1 < y < 8e20

   1. Initial program 97.4%

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

      1. sub-neg 97.4%

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

      2. +-commutative 97.4%

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

      3. *-commutative 97.4%

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

      4. associate-/l* 97.4%

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

      5. distribute-rgt-neg-in 97.4%

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

      6. fma-define 97.4%

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

      7. distribute-frac-neg2 97.4%

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

      8. +-commutative 97.4%

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

      9. distribute-neg-in 97.4%

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

      10. metadata-eval 97.4%

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

      11. unsub-neg 97.4%

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

   3. Simplified 97.4%

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

   5. Taylor expanded in x around inf 24.7%

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

      1. associate-/l* 24.7%

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

      2. +-commutative 24.7%

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

   7. Simplified 24.7%

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

   8. Taylor expanded in y around 0 23.1%

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

      1. *-commutative 23.1%

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

   10. Simplified 23.1%

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

Alternative 12: 39.7% accurate, 11.0× speedup

Math

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

FPCore

(FPCore (x y) :precision binary64 x)

C

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

Fortran

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

Java

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

Python

def code(x, y):
	return x

Julia

function code(x, y)
	return x
end

MATLAB

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

Wolfram

code[x_, y_] := x

Derivation

1. Initial program 61.3%

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

   1. associate-/l* 71.9%

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

   2. remove-double-neg 71.9%

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

   3. remove-double-neg 71.9%

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

   4. +-commutative 71.9%

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

3. Simplified 71.9%

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

5. Taylor expanded in y around inf 40.4%

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

Developer Target 1: 99.7% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2024143 
(FPCore (x y)
  :name "Diagrams.Trail:splitAtParam  from diagrams-lib-1.3.0.3, D"
  :precision binary64

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

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