Numeric.SpecFunctions:incompleteGamma from math-functions-0.1.5.2, B

Percentage Accurate: 99.4% → 99.4%

Time: 10.9s

Alternatives: 13

Speedup: 1.0×

Specification

Math

\[\begin{array}{l} \\ \left(3 \cdot \sqrt{x}\right) \cdot \left(\left(y + \frac{1}{x \cdot 9}\right) - 1\right) \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (* (* 3.0 (sqrt x)) (- (+ y (/ 1.0 (* x 9.0))) 1.0)))

C

double code(double x, double y) {
	return (3.0 * sqrt(x)) * ((y + (1.0 / (x * 9.0))) - 1.0);
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = (3.0d0 * sqrt(x)) * ((y + (1.0d0 / (x * 9.0d0))) - 1.0d0)
end function

Java

public static double code(double x, double y) {
	return (3.0 * Math.sqrt(x)) * ((y + (1.0 / (x * 9.0))) - 1.0);
}

Python

def code(x, y):
	return (3.0 * math.sqrt(x)) * ((y + (1.0 / (x * 9.0))) - 1.0)

Julia

function code(x, y)
	return Float64(Float64(3.0 * sqrt(x)) * Float64(Float64(y + Float64(1.0 / Float64(x * 9.0))) - 1.0))
end

MATLAB

function tmp = code(x, y)
	tmp = (3.0 * sqrt(x)) * ((y + (1.0 / (x * 9.0))) - 1.0);
end

Wolfram

code[x_, y_] := N[(N[(3.0 * N[Sqrt[x], $MachinePrecision]), $MachinePrecision] * N[(N[(y + N[(1.0 / N[(x * 9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - 1.0), $MachinePrecision]), $MachinePrecision]

Initial Program: 99.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \left(3 \cdot \sqrt{x}\right) \cdot \left(\left(y + \frac{1}{x \cdot 9}\right) - 1\right) \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (* (* 3.0 (sqrt x)) (- (+ y (/ 1.0 (* x 9.0))) 1.0)))

C

double code(double x, double y) {
	return (3.0 * sqrt(x)) * ((y + (1.0 / (x * 9.0))) - 1.0);
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = (3.0d0 * sqrt(x)) * ((y + (1.0d0 / (x * 9.0d0))) - 1.0d0)
end function

Java

public static double code(double x, double y) {
	return (3.0 * Math.sqrt(x)) * ((y + (1.0 / (x * 9.0))) - 1.0);
}

Python

def code(x, y):
	return (3.0 * math.sqrt(x)) * ((y + (1.0 / (x * 9.0))) - 1.0)

Julia

function code(x, y)
	return Float64(Float64(3.0 * sqrt(x)) * Float64(Float64(y + Float64(1.0 / Float64(x * 9.0))) - 1.0))
end

MATLAB

function tmp = code(x, y)
	tmp = (3.0 * sqrt(x)) * ((y + (1.0 / (x * 9.0))) - 1.0);
end

Wolfram

code[x_, y_] := N[(N[(3.0 * N[Sqrt[x], $MachinePrecision]), $MachinePrecision] * N[(N[(y + N[(1.0 / N[(x * 9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] - 1.0), $MachinePrecision]), $MachinePrecision]

Alternative 1: 99.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{3 \cdot y + \left(-3 + \frac{0.3333333333333333}{x}\right)}{{x}^{-0.5}} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (/ (+ (* 3.0 y) (+ -3.0 (/ 0.3333333333333333 x))) (pow x -0.5)))

C

double code(double x, double y) {
	return ((3.0 * y) + (-3.0 + (0.3333333333333333 / x))) / pow(x, -0.5);
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = ((3.0d0 * y) + ((-3.0d0) + (0.3333333333333333d0 / x))) / (x ** (-0.5d0))
end function

Java

public static double code(double x, double y) {
	return ((3.0 * y) + (-3.0 + (0.3333333333333333 / x))) / Math.pow(x, -0.5);
}

Python

def code(x, y):
	return ((3.0 * y) + (-3.0 + (0.3333333333333333 / x))) / math.pow(x, -0.5)

Julia

function code(x, y)
	return Float64(Float64(Float64(3.0 * y) + Float64(-3.0 + Float64(0.3333333333333333 / x))) / (x ^ -0.5))
end

MATLAB

function tmp = code(x, y)
	tmp = ((3.0 * y) + (-3.0 + (0.3333333333333333 / x))) / (x ^ -0.5);
end

Wolfram

code[x_, y_] := N[(N[(N[(3.0 * y), $MachinePrecision] + N[(-3.0 + N[(0.3333333333333333 / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] / N[Power[x, -0.5], $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 99.4%

   \[\left(3 \cdot \sqrt{x}\right) \cdot \left(\left(y + \frac{1}{x \cdot 9}\right) - 1\right) \]
2. Step-by-step derivation

   1. *-commutative N/A

      \[\leadsto \left(\sqrt{x} \cdot 3\right) \cdot \left(\color{blue}{\left(y + \frac{1}{x \cdot 9}\right)} - 1\right) \]

   2. associate-*l* N/A

      \[\leadsto \sqrt{x} \cdot \color{blue}{\left(3 \cdot \left(\left(y + \frac{1}{x \cdot 9}\right) - 1\right)\right)} \]

   3. *-lowering-*.f64 N/A

      \[\leadsto \mathsf{*.f64}\left(\left(\sqrt{x}\right), \color{blue}{\left(3 \cdot \left(\left(y + \frac{1}{x \cdot 9}\right) - 1\right)\right)}\right) \]

   4. sqrt-lowering-sqrt.f64 N/A

      \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \left(\color{blue}{3} \cdot \left(\left(y + \frac{1}{x \cdot 9}\right) - 1\right)\right)\right) \]

   5. associate--l+ N/A

      \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \left(3 \cdot \left(y + \color{blue}{\left(\frac{1}{x \cdot 9} - 1\right)}\right)\right)\right) \]

   6. distribute-lft-in N/A

      \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \left(3 \cdot y + \color{blue}{3 \cdot \left(\frac{1}{x \cdot 9} - 1\right)}\right)\right) \]

   7. *-commutative N/A

      \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \left(3 \cdot y + \left(\frac{1}{x \cdot 9} - 1\right) \cdot \color{blue}{3}\right)\right) \]

   8. +-lowering-+.f64 N/A

      \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{+.f64}\left(\left(3 \cdot y\right), \color{blue}{\left(\left(\frac{1}{x \cdot 9} - 1\right) \cdot 3\right)}\right)\right) \]

   9. *-lowering-*.f64 N/A

      \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(3, y\right), \left(\color{blue}{\left(\frac{1}{x \cdot 9} - 1\right)} \cdot 3\right)\right)\right) \]

   10. *-commutative N/A

       \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(3, y\right), \left(3 \cdot \color{blue}{\left(\frac{1}{x \cdot 9} - 1\right)}\right)\right)\right) \]

   11. sub-neg N/A

       \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(3, y\right), \left(3 \cdot \left(\frac{1}{x \cdot 9} + \color{blue}{\left(\mathsf{neg}\left(1\right)\right)}\right)\right)\right)\right) \]

   12. +-commutative N/A

       \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(3, y\right), \left(3 \cdot \left(\left(\mathsf{neg}\left(1\right)\right) + \color{blue}{\frac{1}{x \cdot 9}}\right)\right)\right)\right) \]

   13. distribute-lft-in N/A

       \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(3, y\right), \left(3 \cdot \left(\mathsf{neg}\left(1\right)\right) + \color{blue}{3 \cdot \frac{1}{x \cdot 9}}\right)\right)\right) \]

   14. *-commutative N/A

       \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(3, y\right), \left(3 \cdot \left(\mathsf{neg}\left(1\right)\right) + \frac{1}{x \cdot 9} \cdot \color{blue}{3}\right)\right)\right) \]

   15. +-lowering-+.f64 N/A

       \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(3, y\right), \mathsf{+.f64}\left(\left(3 \cdot \left(\mathsf{neg}\left(1\right)\right)\right), \color{blue}{\left(\frac{1}{x \cdot 9} \cdot 3\right)}\right)\right)\right) \]

   16. metadata-eval N/A

       \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(3, y\right), \mathsf{+.f64}\left(\left(3 \cdot -1\right), \left(\frac{1}{\color{blue}{x \cdot 9}} \cdot 3\right)\right)\right)\right) \]

   17. metadata-eval N/A

       \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(3, y\right), \mathsf{+.f64}\left(-3, \left(\color{blue}{\frac{1}{x \cdot 9}} \cdot 3\right)\right)\right)\right) \]

   18. *-commutative N/A

       \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(3, y\right), \mathsf{+.f64}\left(-3, \left(3 \cdot \color{blue}{\frac{1}{x \cdot 9}}\right)\right)\right)\right) \]

   19. *-commutative N/A

       \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(3, y\right), \mathsf{+.f64}\left(-3, \left(3 \cdot \frac{1}{9 \cdot \color{blue}{x}}\right)\right)\right)\right) \]

   20. associate-/r* N/A

       \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(3, y\right), \mathsf{+.f64}\left(-3, \left(3 \cdot \frac{\frac{1}{9}}{\color{blue}{x}}\right)\right)\right)\right) \]

   21. associate-*r/ N/A

       \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(3, y\right), \mathsf{+.f64}\left(-3, \left(\frac{3 \cdot \frac{1}{9}}{\color{blue}{x}}\right)\right)\right)\right) \]

   22. /-lowering-/.f64 N/A

       \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(3, y\right), \mathsf{+.f64}\left(-3, \mathsf{/.f64}\left(\left(3 \cdot \frac{1}{9}\right), \color{blue}{x}\right)\right)\right)\right) \]

3. Simplified 99.4%

   \[\leadsto \color{blue}{\sqrt{x} \cdot \left(3 \cdot y + \left(-3 + \frac{0.3333333333333333}{x}\right)\right)} \]
4. Add Preprocessing

6. Applied egg-rr 99.4%

   \[\leadsto \color{blue}{\frac{3 \cdot y + \left(-3 + \frac{0.3333333333333333}{x}\right)}{{x}^{-0.5}}} \]
7. Add Preprocessing

Alternative 2: 61.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \frac{-3}{{x}^{-0.5}}\\ \mathbf{if}\;x \leq 0.00044:\\ \;\;\;\;\frac{{x}^{-0.5}}{3}\\ \mathbf{elif}\;x \leq 5.2 \cdot 10^{+91}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 7.6 \cdot 10^{+113}:\\ \;\;\;\;\frac{3 \cdot y}{{x}^{-0.5}}\\ \mathbf{elif}\;x \leq 4.2 \cdot 10^{+259}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;3 \cdot \left(y \cdot \sqrt{x}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (/ -3.0 (pow x -0.5))))
   (if (<= x 0.00044)
     (/ (pow x -0.5) 3.0)
     (if (<= x 5.2e+91)
       t_0
       (if (<= x 7.6e+113)
         (/ (* 3.0 y) (pow x -0.5))
         (if (<= x 4.2e+259) t_0 (* 3.0 (* y (sqrt x)))))))))

C

double code(double x, double y) {
	double t_0 = -3.0 / pow(x, -0.5);
	double tmp;
	if (x <= 0.00044) {
		tmp = pow(x, -0.5) / 3.0;
	} else if (x <= 5.2e+91) {
		tmp = t_0;
	} else if (x <= 7.6e+113) {
		tmp = (3.0 * y) / pow(x, -0.5);
	} else if (x <= 4.2e+259) {
		tmp = t_0;
	} else {
		tmp = 3.0 * (y * sqrt(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) :: tmp
    t_0 = (-3.0d0) / (x ** (-0.5d0))
    if (x <= 0.00044d0) then
        tmp = (x ** (-0.5d0)) / 3.0d0
    else if (x <= 5.2d+91) then
        tmp = t_0
    else if (x <= 7.6d+113) then
        tmp = (3.0d0 * y) / (x ** (-0.5d0))
    else if (x <= 4.2d+259) then
        tmp = t_0
    else
        tmp = 3.0d0 * (y * sqrt(x))
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double t_0 = -3.0 / Math.pow(x, -0.5);
	double tmp;
	if (x <= 0.00044) {
		tmp = Math.pow(x, -0.5) / 3.0;
	} else if (x <= 5.2e+91) {
		tmp = t_0;
	} else if (x <= 7.6e+113) {
		tmp = (3.0 * y) / Math.pow(x, -0.5);
	} else if (x <= 4.2e+259) {
		tmp = t_0;
	} else {
		tmp = 3.0 * (y * Math.sqrt(x));
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = -3.0 / math.pow(x, -0.5)
	tmp = 0
	if x <= 0.00044:
		tmp = math.pow(x, -0.5) / 3.0
	elif x <= 5.2e+91:
		tmp = t_0
	elif x <= 7.6e+113:
		tmp = (3.0 * y) / math.pow(x, -0.5)
	elif x <= 4.2e+259:
		tmp = t_0
	else:
		tmp = 3.0 * (y * math.sqrt(x))
	return tmp

Julia

function code(x, y)
	t_0 = Float64(-3.0 / (x ^ -0.5))
	tmp = 0.0
	if (x <= 0.00044)
		tmp = Float64((x ^ -0.5) / 3.0);
	elseif (x <= 5.2e+91)
		tmp = t_0;
	elseif (x <= 7.6e+113)
		tmp = Float64(Float64(3.0 * y) / (x ^ -0.5));
	elseif (x <= 4.2e+259)
		tmp = t_0;
	else
		tmp = Float64(3.0 * Float64(y * sqrt(x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = -3.0 / (x ^ -0.5);
	tmp = 0.0;
	if (x <= 0.00044)
		tmp = (x ^ -0.5) / 3.0;
	elseif (x <= 5.2e+91)
		tmp = t_0;
	elseif (x <= 7.6e+113)
		tmp = (3.0 * y) / (x ^ -0.5);
	elseif (x <= 4.2e+259)
		tmp = t_0;
	else
		tmp = 3.0 * (y * sqrt(x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(-3.0 / N[Power[x, -0.5], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, 0.00044], N[(N[Power[x, -0.5], $MachinePrecision] / 3.0), $MachinePrecision], If[LessEqual[x, 5.2e+91], t$95$0, If[LessEqual[x, 7.6e+113], N[(N[(3.0 * y), $MachinePrecision] / N[Power[x, -0.5], $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 4.2e+259], t$95$0, N[(3.0 * N[(y * N[Sqrt[x], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if x < 4.40000000000000016e-4

   1. Initial program 99.2%

      \[\left(3 \cdot \sqrt{x}\right) \cdot \left(\left(y + \frac{1}{x \cdot 9}\right) - 1\right) \]
   2. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \left(\sqrt{x} \cdot 3\right) \cdot \left(\color{blue}{\left(y + \frac{1}{x \cdot 9}\right)} - 1\right) \]

      2. associate-*l* N/A

         \[\leadsto \sqrt{x} \cdot \color{blue}{\left(3 \cdot \left(\left(y + \frac{1}{x \cdot 9}\right) - 1\right)\right)} \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(\sqrt{x}\right), \color{blue}{\left(3 \cdot \left(\left(y + \frac{1}{x \cdot 9}\right) - 1\right)\right)}\right) \]

      4. sqrt-lowering-sqrt.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \left(\color{blue}{3} \cdot \left(\left(y + \frac{1}{x \cdot 9}\right) - 1\right)\right)\right) \]

      5. associate--l+ N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \left(3 \cdot \left(y + \color{blue}{\left(\frac{1}{x \cdot 9} - 1\right)}\right)\right)\right) \]

      6. distribute-lft-in N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \left(3 \cdot y + \color{blue}{3 \cdot \left(\frac{1}{x \cdot 9} - 1\right)}\right)\right) \]

      7. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \left(3 \cdot y + \left(\frac{1}{x \cdot 9} - 1\right) \cdot \color{blue}{3}\right)\right) \]

      8. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{+.f64}\left(\left(3 \cdot y\right), \color{blue}{\left(\left(\frac{1}{x \cdot 9} - 1\right) \cdot 3\right)}\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(3, y\right), \left(\color{blue}{\left(\frac{1}{x \cdot 9} - 1\right)} \cdot 3\right)\right)\right) \]

      10. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(3, y\right), \left(3 \cdot \color{blue}{\left(\frac{1}{x \cdot 9} - 1\right)}\right)\right)\right) \]

      11. sub-neg N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(3, y\right), \left(3 \cdot \left(\frac{1}{x \cdot 9} + \color{blue}{\left(\mathsf{neg}\left(1\right)\right)}\right)\right)\right)\right) \]

      12. +-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(3, y\right), \left(3 \cdot \left(\left(\mathsf{neg}\left(1\right)\right) + \color{blue}{\frac{1}{x \cdot 9}}\right)\right)\right)\right) \]

      13. distribute-lft-in N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(3, y\right), \left(3 \cdot \left(\mathsf{neg}\left(1\right)\right) + \color{blue}{3 \cdot \frac{1}{x \cdot 9}}\right)\right)\right) \]

      14. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(3, y\right), \left(3 \cdot \left(\mathsf{neg}\left(1\right)\right) + \frac{1}{x \cdot 9} \cdot \color{blue}{3}\right)\right)\right) \]

      15. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(3, y\right), \mathsf{+.f64}\left(\left(3 \cdot \left(\mathsf{neg}\left(1\right)\right)\right), \color{blue}{\left(\frac{1}{x \cdot 9} \cdot 3\right)}\right)\right)\right) \]

      16. metadata-eval N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(3, y\right), \mathsf{+.f64}\left(\left(3 \cdot -1\right), \left(\frac{1}{\color{blue}{x \cdot 9}} \cdot 3\right)\right)\right)\right) \]

      17. metadata-eval N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(3, y\right), \mathsf{+.f64}\left(-3, \left(\color{blue}{\frac{1}{x \cdot 9}} \cdot 3\right)\right)\right)\right) \]

      18. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(3, y\right), \mathsf{+.f64}\left(-3, \left(3 \cdot \color{blue}{\frac{1}{x \cdot 9}}\right)\right)\right)\right) \]

      19. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(3, y\right), \mathsf{+.f64}\left(-3, \left(3 \cdot \frac{1}{9 \cdot \color{blue}{x}}\right)\right)\right)\right) \]

      20. associate-/r* N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(3, y\right), \mathsf{+.f64}\left(-3, \left(3 \cdot \frac{\frac{1}{9}}{\color{blue}{x}}\right)\right)\right)\right) \]

      21. associate-*r/ N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(3, y\right), \mathsf{+.f64}\left(-3, \left(\frac{3 \cdot \frac{1}{9}}{\color{blue}{x}}\right)\right)\right)\right) \]

      22. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(3, y\right), \mathsf{+.f64}\left(-3, \mathsf{/.f64}\left(\left(3 \cdot \frac{1}{9}\right), \color{blue}{x}\right)\right)\right)\right) \]

   3. Simplified 99.3%

      \[\leadsto \color{blue}{\sqrt{x} \cdot \left(3 \cdot y + \left(-3 + \frac{0.3333333333333333}{x}\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in x around 0

      \[\leadsto \color{blue}{\frac{1}{3} \cdot \sqrt{\frac{1}{x}}} \]
   6. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\frac{1}{3}, \color{blue}{\left(\sqrt{\frac{1}{x}}\right)}\right) \]

      2. sqrt-lowering-sqrt.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\frac{1}{3}, \mathsf{sqrt.f64}\left(\left(\frac{1}{x}\right)\right)\right) \]

      3. /-lowering-/.f64 77.2%

         \[\leadsto \mathsf{*.f64}\left(\frac{1}{3}, \mathsf{sqrt.f64}\left(\mathsf{/.f64}\left(1, x\right)\right)\right) \]

   7. Simplified 77.2%

      \[\leadsto \color{blue}{0.3333333333333333 \cdot \sqrt{\frac{1}{x}}} \]
   8. Step-by-step derivation

      1. sqrt-div N/A

         \[\leadsto \frac{1}{3} \cdot \frac{\sqrt{1}}{\color{blue}{\sqrt{x}}} \]

      2. metadata-eval N/A

         \[\leadsto \frac{1}{3} \cdot \frac{1}{\sqrt{\color{blue}{x}}} \]

      3. un-div-inv N/A

         \[\leadsto \frac{\frac{1}{3}}{\color{blue}{\sqrt{x}}} \]

      4. metadata-eval N/A

         \[\leadsto \frac{1 \cdot \frac{1}{3}}{\sqrt{\color{blue}{x}}} \]

      5. pow1/2 N/A

         \[\leadsto \frac{1 \cdot \frac{1}{3}}{{x}^{\color{blue}{\frac{1}{2}}}} \]

      6. metadata-eval N/A

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

      7. pow-plus N/A

         \[\leadsto \frac{1 \cdot \frac{1}{3}}{{x}^{\frac{-1}{2}} \cdot \color{blue}{x}} \]

      8. frac-times N/A

         \[\leadsto \frac{1}{{x}^{\frac{-1}{2}}} \cdot \color{blue}{\frac{\frac{1}{3}}{x}} \]

      9. pow-flip N/A

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

      10. metadata-eval N/A

          \[\leadsto {x}^{\frac{1}{2}} \cdot \frac{\frac{1}{3}}{x} \]

      11. metadata-eval N/A

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

      12. pow-plus N/A

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

      13. associate-*l* N/A

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

      14. remove-double-div N/A

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

      15. clear-num N/A

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

      16. frac-times N/A

          \[\leadsto {x}^{\frac{-1}{2}} \cdot \frac{1 \cdot 1}{\color{blue}{\frac{1}{x} \cdot \frac{x}{\frac{1}{3}}}} \]

      17. metadata-eval N/A

          \[\leadsto {x}^{\frac{-1}{2}} \cdot \frac{1}{\color{blue}{\frac{1}{x}} \cdot \frac{x}{\frac{1}{3}}} \]

      18. un-div-inv N/A

          \[\leadsto \frac{{x}^{\frac{-1}{2}}}{\color{blue}{\frac{1}{x} \cdot \frac{x}{\frac{1}{3}}}} \]

      19. inv-pow N/A

          \[\leadsto \frac{{x}^{\frac{-1}{2}}}{{x}^{-1} \cdot \frac{\color{blue}{x}}{\frac{1}{3}}} \]

      20. clear-num N/A

          \[\leadsto \frac{{x}^{\frac{-1}{2}}}{{x}^{-1} \cdot \frac{1}{\color{blue}{\frac{\frac{1}{3}}{x}}}} \]

      21. inv-pow N/A

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

      22. pow-prod-down N/A

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

      23. *-commutative N/A

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

      24. div-inv N/A

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

      25. associate-*l* N/A

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

      26. lft-mult-inverse N/A

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

      27. metadata-eval N/A

          \[\leadsto \frac{{x}^{\frac{-1}{2}}}{{\frac{1}{3}}^{-1}} \]

   9. Applied egg-rr 77.3%

      \[\leadsto \color{blue}{\frac{{x}^{-0.5}}{3}} \]

   if 4.40000000000000016e-4 < x < 5.2000000000000001e91 or 7.6000000000000007e113 < x < 4.20000000000000011e259

   1. Initial program 99.5%

      \[\left(3 \cdot \sqrt{x}\right) \cdot \left(\left(y + \frac{1}{x \cdot 9}\right) - 1\right) \]
   2. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \left(\sqrt{x} \cdot 3\right) \cdot \left(\color{blue}{\left(y + \frac{1}{x \cdot 9}\right)} - 1\right) \]

      2. associate-*l* N/A

         \[\leadsto \sqrt{x} \cdot \color{blue}{\left(3 \cdot \left(\left(y + \frac{1}{x \cdot 9}\right) - 1\right)\right)} \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(\sqrt{x}\right), \color{blue}{\left(3 \cdot \left(\left(y + \frac{1}{x \cdot 9}\right) - 1\right)\right)}\right) \]

      4. sqrt-lowering-sqrt.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \left(\color{blue}{3} \cdot \left(\left(y + \frac{1}{x \cdot 9}\right) - 1\right)\right)\right) \]

      5. associate--l+ N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \left(3 \cdot \left(y + \color{blue}{\left(\frac{1}{x \cdot 9} - 1\right)}\right)\right)\right) \]

      6. distribute-lft-in N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \left(3 \cdot y + \color{blue}{3 \cdot \left(\frac{1}{x \cdot 9} - 1\right)}\right)\right) \]

      7. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \left(3 \cdot y + \left(\frac{1}{x \cdot 9} - 1\right) \cdot \color{blue}{3}\right)\right) \]

      8. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{+.f64}\left(\left(3 \cdot y\right), \color{blue}{\left(\left(\frac{1}{x \cdot 9} - 1\right) \cdot 3\right)}\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(3, y\right), \left(\color{blue}{\left(\frac{1}{x \cdot 9} - 1\right)} \cdot 3\right)\right)\right) \]

      10. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(3, y\right), \left(3 \cdot \color{blue}{\left(\frac{1}{x \cdot 9} - 1\right)}\right)\right)\right) \]

      11. sub-neg N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(3, y\right), \left(3 \cdot \left(\frac{1}{x \cdot 9} + \color{blue}{\left(\mathsf{neg}\left(1\right)\right)}\right)\right)\right)\right) \]

      12. +-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(3, y\right), \left(3 \cdot \left(\left(\mathsf{neg}\left(1\right)\right) + \color{blue}{\frac{1}{x \cdot 9}}\right)\right)\right)\right) \]

      13. distribute-lft-in N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(3, y\right), \left(3 \cdot \left(\mathsf{neg}\left(1\right)\right) + \color{blue}{3 \cdot \frac{1}{x \cdot 9}}\right)\right)\right) \]

      14. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(3, y\right), \left(3 \cdot \left(\mathsf{neg}\left(1\right)\right) + \frac{1}{x \cdot 9} \cdot \color{blue}{3}\right)\right)\right) \]

      15. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(3, y\right), \mathsf{+.f64}\left(\left(3 \cdot \left(\mathsf{neg}\left(1\right)\right)\right), \color{blue}{\left(\frac{1}{x \cdot 9} \cdot 3\right)}\right)\right)\right) \]

      16. metadata-eval N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(3, y\right), \mathsf{+.f64}\left(\left(3 \cdot -1\right), \left(\frac{1}{\color{blue}{x \cdot 9}} \cdot 3\right)\right)\right)\right) \]

      17. metadata-eval N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(3, y\right), \mathsf{+.f64}\left(-3, \left(\color{blue}{\frac{1}{x \cdot 9}} \cdot 3\right)\right)\right)\right) \]

      18. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(3, y\right), \mathsf{+.f64}\left(-3, \left(3 \cdot \color{blue}{\frac{1}{x \cdot 9}}\right)\right)\right)\right) \]

      19. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(3, y\right), \mathsf{+.f64}\left(-3, \left(3 \cdot \frac{1}{9 \cdot \color{blue}{x}}\right)\right)\right)\right) \]

      20. associate-/r* N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(3, y\right), \mathsf{+.f64}\left(-3, \left(3 \cdot \frac{\frac{1}{9}}{\color{blue}{x}}\right)\right)\right)\right) \]

      21. associate-*r/ N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(3, y\right), \mathsf{+.f64}\left(-3, \left(\frac{3 \cdot \frac{1}{9}}{\color{blue}{x}}\right)\right)\right)\right) \]

      22. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(3, y\right), \mathsf{+.f64}\left(-3, \mathsf{/.f64}\left(\left(3 \cdot \frac{1}{9}\right), \color{blue}{x}\right)\right)\right)\right) \]

   3. Simplified 99.5%

      \[\leadsto \color{blue}{\sqrt{x} \cdot \left(3 \cdot y + \left(-3 + \frac{0.3333333333333333}{x}\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf

      \[\leadsto \color{blue}{\sqrt{x} \cdot \left(3 \cdot y - 3\right)} \]
   6. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(\sqrt{x}\right), \color{blue}{\left(3 \cdot y - 3\right)}\right) \]

      2. sqrt-lowering-sqrt.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \left(\color{blue}{3 \cdot y} - 3\right)\right) \]

      3. sub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \left(3 \cdot y + \color{blue}{\left(\mathsf{neg}\left(3\right)\right)}\right)\right) \]

      4. metadata-eval N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \left(3 \cdot y + -3\right)\right) \]

      5. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{+.f64}\left(\left(3 \cdot y\right), \color{blue}{-3}\right)\right) \]

      6. *-lowering-*.f64 98.3%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(3, y\right), -3\right)\right) \]

   7. Simplified 98.3%

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

   8. Taylor expanded in y around 0

      \[\leadsto \color{blue}{-3 \cdot \sqrt{x}} \]
   9. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \sqrt{x} \cdot \color{blue}{-3} \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(\sqrt{x}\right), \color{blue}{-3}\right) \]

      3. sqrt-lowering-sqrt.f64 58.9%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), -3\right) \]

   10. Simplified 58.9%

       \[\leadsto \color{blue}{\sqrt{x} \cdot -3} \]
   11. Step-by-step derivation

       1. *-commutative N/A

          \[\leadsto -3 \cdot \color{blue}{\sqrt{x}} \]

       2. pow1/2 N/A

          \[\leadsto -3 \cdot {x}^{\color{blue}{\frac{1}{2}}} \]

       3. metadata-eval N/A

          \[\leadsto -3 \cdot {x}^{\left(\mathsf{neg}\left(\frac{-1}{2}\right)\right)} \]

       4. pow-flip N/A

          \[\leadsto -3 \cdot \frac{1}{\color{blue}{{x}^{\frac{-1}{2}}}} \]

       5. un-div-inv N/A

          \[\leadsto \frac{-3}{\color{blue}{{x}^{\frac{-1}{2}}}} \]

       6. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(-3, \color{blue}{\left({x}^{\frac{-1}{2}}\right)}\right) \]

       7. pow-lowering-pow.f64 59.0%

          \[\leadsto \mathsf{/.f64}\left(-3, \mathsf{pow.f64}\left(x, \color{blue}{\frac{-1}{2}}\right)\right) \]

   12. Applied egg-rr 59.0%

       \[\leadsto \color{blue}{\frac{-3}{{x}^{-0.5}}} \]

   if 5.2000000000000001e91 < x < 7.6000000000000007e113

   1. Initial program 99.5%

      \[\left(3 \cdot \sqrt{x}\right) \cdot \left(\left(y + \frac{1}{x \cdot 9}\right) - 1\right) \]
   2. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \left(\sqrt{x} \cdot 3\right) \cdot \left(\color{blue}{\left(y + \frac{1}{x \cdot 9}\right)} - 1\right) \]

      2. associate-*l* N/A

         \[\leadsto \sqrt{x} \cdot \color{blue}{\left(3 \cdot \left(\left(y + \frac{1}{x \cdot 9}\right) - 1\right)\right)} \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(\sqrt{x}\right), \color{blue}{\left(3 \cdot \left(\left(y + \frac{1}{x \cdot 9}\right) - 1\right)\right)}\right) \]

      4. sqrt-lowering-sqrt.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \left(\color{blue}{3} \cdot \left(\left(y + \frac{1}{x \cdot 9}\right) - 1\right)\right)\right) \]

      5. associate--l+ N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \left(3 \cdot \left(y + \color{blue}{\left(\frac{1}{x \cdot 9} - 1\right)}\right)\right)\right) \]

      6. distribute-lft-in N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \left(3 \cdot y + \color{blue}{3 \cdot \left(\frac{1}{x \cdot 9} - 1\right)}\right)\right) \]

      7. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \left(3 \cdot y + \left(\frac{1}{x \cdot 9} - 1\right) \cdot \color{blue}{3}\right)\right) \]

      8. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{+.f64}\left(\left(3 \cdot y\right), \color{blue}{\left(\left(\frac{1}{x \cdot 9} - 1\right) \cdot 3\right)}\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(3, y\right), \left(\color{blue}{\left(\frac{1}{x \cdot 9} - 1\right)} \cdot 3\right)\right)\right) \]

      10. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(3, y\right), \left(3 \cdot \color{blue}{\left(\frac{1}{x \cdot 9} - 1\right)}\right)\right)\right) \]

      11. sub-neg N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(3, y\right), \left(3 \cdot \left(\frac{1}{x \cdot 9} + \color{blue}{\left(\mathsf{neg}\left(1\right)\right)}\right)\right)\right)\right) \]

      12. +-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(3, y\right), \left(3 \cdot \left(\left(\mathsf{neg}\left(1\right)\right) + \color{blue}{\frac{1}{x \cdot 9}}\right)\right)\right)\right) \]

      13. distribute-lft-in N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(3, y\right), \left(3 \cdot \left(\mathsf{neg}\left(1\right)\right) + \color{blue}{3 \cdot \frac{1}{x \cdot 9}}\right)\right)\right) \]

      14. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(3, y\right), \left(3 \cdot \left(\mathsf{neg}\left(1\right)\right) + \frac{1}{x \cdot 9} \cdot \color{blue}{3}\right)\right)\right) \]

      15. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(3, y\right), \mathsf{+.f64}\left(\left(3 \cdot \left(\mathsf{neg}\left(1\right)\right)\right), \color{blue}{\left(\frac{1}{x \cdot 9} \cdot 3\right)}\right)\right)\right) \]

      16. metadata-eval N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(3, y\right), \mathsf{+.f64}\left(\left(3 \cdot -1\right), \left(\frac{1}{\color{blue}{x \cdot 9}} \cdot 3\right)\right)\right)\right) \]

      17. metadata-eval N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(3, y\right), \mathsf{+.f64}\left(-3, \left(\color{blue}{\frac{1}{x \cdot 9}} \cdot 3\right)\right)\right)\right) \]

      18. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(3, y\right), \mathsf{+.f64}\left(-3, \left(3 \cdot \color{blue}{\frac{1}{x \cdot 9}}\right)\right)\right)\right) \]

      19. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(3, y\right), \mathsf{+.f64}\left(-3, \left(3 \cdot \frac{1}{9 \cdot \color{blue}{x}}\right)\right)\right)\right) \]

      20. associate-/r* N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(3, y\right), \mathsf{+.f64}\left(-3, \left(3 \cdot \frac{\frac{1}{9}}{\color{blue}{x}}\right)\right)\right)\right) \]

      21. associate-*r/ N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(3, y\right), \mathsf{+.f64}\left(-3, \left(\frac{3 \cdot \frac{1}{9}}{\color{blue}{x}}\right)\right)\right)\right) \]

      22. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(3, y\right), \mathsf{+.f64}\left(-3, \mathsf{/.f64}\left(\left(3 \cdot \frac{1}{9}\right), \color{blue}{x}\right)\right)\right)\right) \]

   3. Simplified 99.7%

      \[\leadsto \color{blue}{\sqrt{x} \cdot \left(3 \cdot y + \left(-3 + \frac{0.3333333333333333}{x}\right)\right)} \]
   4. Add Preprocessing

   6. Applied egg-rr 99.9%

      \[\leadsto \color{blue}{\frac{3 \cdot y + \left(-3 + \frac{0.3333333333333333}{x}\right)}{{x}^{-0.5}}} \]

   7. Taylor expanded in y around inf

      \[\leadsto \mathsf{/.f64}\left(\color{blue}{\left(3 \cdot y\right)}, \mathsf{pow.f64}\left(x, \frac{-1}{2}\right)\right) \]
   8. Step-by-step derivation

      1. *-lowering-*.f64 80.7%

         \[\leadsto \mathsf{/.f64}\left(\mathsf{*.f64}\left(3, y\right), \mathsf{pow.f64}\left(\color{blue}{x}, \frac{-1}{2}\right)\right) \]

   9. Simplified 80.7%

      \[\leadsto \frac{\color{blue}{3 \cdot y}}{{x}^{-0.5}} \]

   if 4.20000000000000011e259 < x

   1. Initial program 99.8%

      \[\left(3 \cdot \sqrt{x}\right) \cdot \left(\left(y + \frac{1}{x \cdot 9}\right) - 1\right) \]
   2. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \left(\sqrt{x} \cdot 3\right) \cdot \left(\color{blue}{\left(y + \frac{1}{x \cdot 9}\right)} - 1\right) \]

      2. associate-*l* N/A

         \[\leadsto \sqrt{x} \cdot \color{blue}{\left(3 \cdot \left(\left(y + \frac{1}{x \cdot 9}\right) - 1\right)\right)} \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(\sqrt{x}\right), \color{blue}{\left(3 \cdot \left(\left(y + \frac{1}{x \cdot 9}\right) - 1\right)\right)}\right) \]

      4. sqrt-lowering-sqrt.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \left(\color{blue}{3} \cdot \left(\left(y + \frac{1}{x \cdot 9}\right) - 1\right)\right)\right) \]

      5. associate--l+ N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \left(3 \cdot \left(y + \color{blue}{\left(\frac{1}{x \cdot 9} - 1\right)}\right)\right)\right) \]

      6. distribute-lft-in N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \left(3 \cdot y + \color{blue}{3 \cdot \left(\frac{1}{x \cdot 9} - 1\right)}\right)\right) \]

      7. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \left(3 \cdot y + \left(\frac{1}{x \cdot 9} - 1\right) \cdot \color{blue}{3}\right)\right) \]

      8. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{+.f64}\left(\left(3 \cdot y\right), \color{blue}{\left(\left(\frac{1}{x \cdot 9} - 1\right) \cdot 3\right)}\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(3, y\right), \left(\color{blue}{\left(\frac{1}{x \cdot 9} - 1\right)} \cdot 3\right)\right)\right) \]

      10. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(3, y\right), \left(3 \cdot \color{blue}{\left(\frac{1}{x \cdot 9} - 1\right)}\right)\right)\right) \]

      11. sub-neg N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(3, y\right), \left(3 \cdot \left(\frac{1}{x \cdot 9} + \color{blue}{\left(\mathsf{neg}\left(1\right)\right)}\right)\right)\right)\right) \]

      12. +-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(3, y\right), \left(3 \cdot \left(\left(\mathsf{neg}\left(1\right)\right) + \color{blue}{\frac{1}{x \cdot 9}}\right)\right)\right)\right) \]

      13. distribute-lft-in N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(3, y\right), \left(3 \cdot \left(\mathsf{neg}\left(1\right)\right) + \color{blue}{3 \cdot \frac{1}{x \cdot 9}}\right)\right)\right) \]

      14. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(3, y\right), \left(3 \cdot \left(\mathsf{neg}\left(1\right)\right) + \frac{1}{x \cdot 9} \cdot \color{blue}{3}\right)\right)\right) \]

      15. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(3, y\right), \mathsf{+.f64}\left(\left(3 \cdot \left(\mathsf{neg}\left(1\right)\right)\right), \color{blue}{\left(\frac{1}{x \cdot 9} \cdot 3\right)}\right)\right)\right) \]

      16. metadata-eval N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(3, y\right), \mathsf{+.f64}\left(\left(3 \cdot -1\right), \left(\frac{1}{\color{blue}{x \cdot 9}} \cdot 3\right)\right)\right)\right) \]

      17. metadata-eval N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(3, y\right), \mathsf{+.f64}\left(-3, \left(\color{blue}{\frac{1}{x \cdot 9}} \cdot 3\right)\right)\right)\right) \]

      18. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(3, y\right), \mathsf{+.f64}\left(-3, \left(3 \cdot \color{blue}{\frac{1}{x \cdot 9}}\right)\right)\right)\right) \]

      19. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(3, y\right), \mathsf{+.f64}\left(-3, \left(3 \cdot \frac{1}{9 \cdot \color{blue}{x}}\right)\right)\right)\right) \]

      20. associate-/r* N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(3, y\right), \mathsf{+.f64}\left(-3, \left(3 \cdot \frac{\frac{1}{9}}{\color{blue}{x}}\right)\right)\right)\right) \]

      21. associate-*r/ N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(3, y\right), \mathsf{+.f64}\left(-3, \left(\frac{3 \cdot \frac{1}{9}}{\color{blue}{x}}\right)\right)\right)\right) \]

      22. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(3, y\right), \mathsf{+.f64}\left(-3, \mathsf{/.f64}\left(\left(3 \cdot \frac{1}{9}\right), \color{blue}{x}\right)\right)\right)\right) \]

   3. Simplified 99.8%

      \[\leadsto \color{blue}{\sqrt{x} \cdot \left(3 \cdot y + \left(-3 + \frac{0.3333333333333333}{x}\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around inf

      \[\leadsto \color{blue}{3 \cdot \left(\sqrt{x} \cdot y\right)} \]
   6. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(3, \color{blue}{\left(\sqrt{x} \cdot y\right)}\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(3, \mathsf{*.f64}\left(\left(\sqrt{x}\right), \color{blue}{y}\right)\right) \]

      3. sqrt-lowering-sqrt.f64 66.0%

         \[\leadsto \mathsf{*.f64}\left(3, \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), y\right)\right) \]

   7. Simplified 66.0%

      \[\leadsto \color{blue}{3 \cdot \left(\sqrt{x} \cdot y\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 69.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 0.00044:\\ \;\;\;\;\frac{{x}^{-0.5}}{3}\\ \mathbf{elif}\;x \leq 5.2 \cdot 10^{+91}:\\ \;\;\;\;\frac{-3}{{x}^{-0.5}}\\ \mathbf{elif}\;x \leq 7.6 \cdot 10^{+113}:\\ \;\;\;\;\frac{3 \cdot y}{{x}^{-0.5}}\\ \mathbf{elif}\;x \leq 4.2 \cdot 10^{+259}:\\ \;\;\;\;\frac{-3}{{x}^{-0.5}}\\ \mathbf{else}:\\ \;\;\;\;3 \cdot \left(y \cdot \sqrt{x}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 61.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 3 \cdot \left(y \cdot \sqrt{x}\right)\\ t_1 := \frac{-3}{{x}^{-0.5}}\\ \mathbf{if}\;x \leq 0.00044:\\ \;\;\;\;\frac{{x}^{-0.5}}{3}\\ \mathbf{elif}\;x \leq 4.1 \cdot 10^{+91}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 4.9 \cdot 10^{+117}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 3.1 \cdot 10^{+262}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (* 3.0 (* y (sqrt x)))) (t_1 (/ -3.0 (pow x -0.5))))
   (if (<= x 0.00044)
     (/ (pow x -0.5) 3.0)
     (if (<= x 4.1e+91)
       t_1
       (if (<= x 4.9e+117) t_0 (if (<= x 3.1e+262) t_1 t_0))))))

C

double code(double x, double y) {
	double t_0 = 3.0 * (y * sqrt(x));
	double t_1 = -3.0 / pow(x, -0.5);
	double tmp;
	if (x <= 0.00044) {
		tmp = pow(x, -0.5) / 3.0;
	} else if (x <= 4.1e+91) {
		tmp = t_1;
	} else if (x <= 4.9e+117) {
		tmp = t_0;
	} else if (x <= 3.1e+262) {
		tmp = t_1;
	} 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) :: t_1
    real(8) :: tmp
    t_0 = 3.0d0 * (y * sqrt(x))
    t_1 = (-3.0d0) / (x ** (-0.5d0))
    if (x <= 0.00044d0) then
        tmp = (x ** (-0.5d0)) / 3.0d0
    else if (x <= 4.1d+91) then
        tmp = t_1
    else if (x <= 4.9d+117) then
        tmp = t_0
    else if (x <= 3.1d+262) then
        tmp = t_1
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double t_0 = 3.0 * (y * Math.sqrt(x));
	double t_1 = -3.0 / Math.pow(x, -0.5);
	double tmp;
	if (x <= 0.00044) {
		tmp = Math.pow(x, -0.5) / 3.0;
	} else if (x <= 4.1e+91) {
		tmp = t_1;
	} else if (x <= 4.9e+117) {
		tmp = t_0;
	} else if (x <= 3.1e+262) {
		tmp = t_1;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = 3.0 * (y * math.sqrt(x))
	t_1 = -3.0 / math.pow(x, -0.5)
	tmp = 0
	if x <= 0.00044:
		tmp = math.pow(x, -0.5) / 3.0
	elif x <= 4.1e+91:
		tmp = t_1
	elif x <= 4.9e+117:
		tmp = t_0
	elif x <= 3.1e+262:
		tmp = t_1
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y)
	t_0 = Float64(3.0 * Float64(y * sqrt(x)))
	t_1 = Float64(-3.0 / (x ^ -0.5))
	tmp = 0.0
	if (x <= 0.00044)
		tmp = Float64((x ^ -0.5) / 3.0);
	elseif (x <= 4.1e+91)
		tmp = t_1;
	elseif (x <= 4.9e+117)
		tmp = t_0;
	elseif (x <= 3.1e+262)
		tmp = t_1;
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = 3.0 * (y * sqrt(x));
	t_1 = -3.0 / (x ^ -0.5);
	tmp = 0.0;
	if (x <= 0.00044)
		tmp = (x ^ -0.5) / 3.0;
	elseif (x <= 4.1e+91)
		tmp = t_1;
	elseif (x <= 4.9e+117)
		tmp = t_0;
	elseif (x <= 3.1e+262)
		tmp = t_1;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(3.0 * N[(y * N[Sqrt[x], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(-3.0 / N[Power[x, -0.5], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, 0.00044], N[(N[Power[x, -0.5], $MachinePrecision] / 3.0), $MachinePrecision], If[LessEqual[x, 4.1e+91], t$95$1, If[LessEqual[x, 4.9e+117], t$95$0, If[LessEqual[x, 3.1e+262], t$95$1, t$95$0]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < 4.40000000000000016e-4

   1. Initial program 99.2%

      \[\left(3 \cdot \sqrt{x}\right) \cdot \left(\left(y + \frac{1}{x \cdot 9}\right) - 1\right) \]
   2. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \left(\sqrt{x} \cdot 3\right) \cdot \left(\color{blue}{\left(y + \frac{1}{x \cdot 9}\right)} - 1\right) \]

      2. associate-*l* N/A

         \[\leadsto \sqrt{x} \cdot \color{blue}{\left(3 \cdot \left(\left(y + \frac{1}{x \cdot 9}\right) - 1\right)\right)} \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(\sqrt{x}\right), \color{blue}{\left(3 \cdot \left(\left(y + \frac{1}{x \cdot 9}\right) - 1\right)\right)}\right) \]

      4. sqrt-lowering-sqrt.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \left(\color{blue}{3} \cdot \left(\left(y + \frac{1}{x \cdot 9}\right) - 1\right)\right)\right) \]

      5. associate--l+ N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \left(3 \cdot \left(y + \color{blue}{\left(\frac{1}{x \cdot 9} - 1\right)}\right)\right)\right) \]

      6. distribute-lft-in N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \left(3 \cdot y + \color{blue}{3 \cdot \left(\frac{1}{x \cdot 9} - 1\right)}\right)\right) \]

      7. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \left(3 \cdot y + \left(\frac{1}{x \cdot 9} - 1\right) \cdot \color{blue}{3}\right)\right) \]

      8. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{+.f64}\left(\left(3 \cdot y\right), \color{blue}{\left(\left(\frac{1}{x \cdot 9} - 1\right) \cdot 3\right)}\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(3, y\right), \left(\color{blue}{\left(\frac{1}{x \cdot 9} - 1\right)} \cdot 3\right)\right)\right) \]

      10. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(3, y\right), \left(3 \cdot \color{blue}{\left(\frac{1}{x \cdot 9} - 1\right)}\right)\right)\right) \]

      11. sub-neg N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(3, y\right), \left(3 \cdot \left(\frac{1}{x \cdot 9} + \color{blue}{\left(\mathsf{neg}\left(1\right)\right)}\right)\right)\right)\right) \]

      12. +-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(3, y\right), \left(3 \cdot \left(\left(\mathsf{neg}\left(1\right)\right) + \color{blue}{\frac{1}{x \cdot 9}}\right)\right)\right)\right) \]

      13. distribute-lft-in N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(3, y\right), \left(3 \cdot \left(\mathsf{neg}\left(1\right)\right) + \color{blue}{3 \cdot \frac{1}{x \cdot 9}}\right)\right)\right) \]

      14. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(3, y\right), \left(3 \cdot \left(\mathsf{neg}\left(1\right)\right) + \frac{1}{x \cdot 9} \cdot \color{blue}{3}\right)\right)\right) \]

      15. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(3, y\right), \mathsf{+.f64}\left(\left(3 \cdot \left(\mathsf{neg}\left(1\right)\right)\right), \color{blue}{\left(\frac{1}{x \cdot 9} \cdot 3\right)}\right)\right)\right) \]

      16. metadata-eval N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(3, y\right), \mathsf{+.f64}\left(\left(3 \cdot -1\right), \left(\frac{1}{\color{blue}{x \cdot 9}} \cdot 3\right)\right)\right)\right) \]

      17. metadata-eval N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(3, y\right), \mathsf{+.f64}\left(-3, \left(\color{blue}{\frac{1}{x \cdot 9}} \cdot 3\right)\right)\right)\right) \]

      18. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(3, y\right), \mathsf{+.f64}\left(-3, \left(3 \cdot \color{blue}{\frac{1}{x \cdot 9}}\right)\right)\right)\right) \]

      19. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(3, y\right), \mathsf{+.f64}\left(-3, \left(3 \cdot \frac{1}{9 \cdot \color{blue}{x}}\right)\right)\right)\right) \]

      20. associate-/r* N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(3, y\right), \mathsf{+.f64}\left(-3, \left(3 \cdot \frac{\frac{1}{9}}{\color{blue}{x}}\right)\right)\right)\right) \]

      21. associate-*r/ N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(3, y\right), \mathsf{+.f64}\left(-3, \left(\frac{3 \cdot \frac{1}{9}}{\color{blue}{x}}\right)\right)\right)\right) \]

      22. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(3, y\right), \mathsf{+.f64}\left(-3, \mathsf{/.f64}\left(\left(3 \cdot \frac{1}{9}\right), \color{blue}{x}\right)\right)\right)\right) \]

   3. Simplified 99.3%

      \[\leadsto \color{blue}{\sqrt{x} \cdot \left(3 \cdot y + \left(-3 + \frac{0.3333333333333333}{x}\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in x around 0

      \[\leadsto \color{blue}{\frac{1}{3} \cdot \sqrt{\frac{1}{x}}} \]
   6. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\frac{1}{3}, \color{blue}{\left(\sqrt{\frac{1}{x}}\right)}\right) \]

      2. sqrt-lowering-sqrt.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\frac{1}{3}, \mathsf{sqrt.f64}\left(\left(\frac{1}{x}\right)\right)\right) \]

      3. /-lowering-/.f64 77.2%

         \[\leadsto \mathsf{*.f64}\left(\frac{1}{3}, \mathsf{sqrt.f64}\left(\mathsf{/.f64}\left(1, x\right)\right)\right) \]

   7. Simplified 77.2%

      \[\leadsto \color{blue}{0.3333333333333333 \cdot \sqrt{\frac{1}{x}}} \]
   8. Step-by-step derivation

      1. sqrt-div N/A

         \[\leadsto \frac{1}{3} \cdot \frac{\sqrt{1}}{\color{blue}{\sqrt{x}}} \]

      2. metadata-eval N/A

         \[\leadsto \frac{1}{3} \cdot \frac{1}{\sqrt{\color{blue}{x}}} \]

      3. un-div-inv N/A

         \[\leadsto \frac{\frac{1}{3}}{\color{blue}{\sqrt{x}}} \]

      4. metadata-eval N/A

         \[\leadsto \frac{1 \cdot \frac{1}{3}}{\sqrt{\color{blue}{x}}} \]

      5. pow1/2 N/A

         \[\leadsto \frac{1 \cdot \frac{1}{3}}{{x}^{\color{blue}{\frac{1}{2}}}} \]

      6. metadata-eval N/A

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

      7. pow-plus N/A

         \[\leadsto \frac{1 \cdot \frac{1}{3}}{{x}^{\frac{-1}{2}} \cdot \color{blue}{x}} \]

      8. frac-times N/A

         \[\leadsto \frac{1}{{x}^{\frac{-1}{2}}} \cdot \color{blue}{\frac{\frac{1}{3}}{x}} \]

      9. pow-flip N/A

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

      10. metadata-eval N/A

          \[\leadsto {x}^{\frac{1}{2}} \cdot \frac{\frac{1}{3}}{x} \]

      11. metadata-eval N/A

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

      12. pow-plus N/A

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

      13. associate-*l* N/A

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

      14. remove-double-div N/A

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

      15. clear-num N/A

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

      16. frac-times N/A

          \[\leadsto {x}^{\frac{-1}{2}} \cdot \frac{1 \cdot 1}{\color{blue}{\frac{1}{x} \cdot \frac{x}{\frac{1}{3}}}} \]

      17. metadata-eval N/A

          \[\leadsto {x}^{\frac{-1}{2}} \cdot \frac{1}{\color{blue}{\frac{1}{x}} \cdot \frac{x}{\frac{1}{3}}} \]

      18. un-div-inv N/A

          \[\leadsto \frac{{x}^{\frac{-1}{2}}}{\color{blue}{\frac{1}{x} \cdot \frac{x}{\frac{1}{3}}}} \]

      19. inv-pow N/A

          \[\leadsto \frac{{x}^{\frac{-1}{2}}}{{x}^{-1} \cdot \frac{\color{blue}{x}}{\frac{1}{3}}} \]

      20. clear-num N/A

          \[\leadsto \frac{{x}^{\frac{-1}{2}}}{{x}^{-1} \cdot \frac{1}{\color{blue}{\frac{\frac{1}{3}}{x}}}} \]

      21. inv-pow N/A

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

      22. pow-prod-down N/A

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

      23. *-commutative N/A

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

      24. div-inv N/A

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

      25. associate-*l* N/A

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

      26. lft-mult-inverse N/A

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

      27. metadata-eval N/A

          \[\leadsto \frac{{x}^{\frac{-1}{2}}}{{\frac{1}{3}}^{-1}} \]

   9. Applied egg-rr 77.3%

      \[\leadsto \color{blue}{\frac{{x}^{-0.5}}{3}} \]

   if 4.40000000000000016e-4 < x < 4.1000000000000002e91 or 4.9000000000000001e117 < x < 3.09999999999999991e262

   1. Initial program 99.5%

      \[\left(3 \cdot \sqrt{x}\right) \cdot \left(\left(y + \frac{1}{x \cdot 9}\right) - 1\right) \]
   2. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \left(\sqrt{x} \cdot 3\right) \cdot \left(\color{blue}{\left(y + \frac{1}{x \cdot 9}\right)} - 1\right) \]

      2. associate-*l* N/A

         \[\leadsto \sqrt{x} \cdot \color{blue}{\left(3 \cdot \left(\left(y + \frac{1}{x \cdot 9}\right) - 1\right)\right)} \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(\sqrt{x}\right), \color{blue}{\left(3 \cdot \left(\left(y + \frac{1}{x \cdot 9}\right) - 1\right)\right)}\right) \]

      4. sqrt-lowering-sqrt.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \left(\color{blue}{3} \cdot \left(\left(y + \frac{1}{x \cdot 9}\right) - 1\right)\right)\right) \]

      5. associate--l+ N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \left(3 \cdot \left(y + \color{blue}{\left(\frac{1}{x \cdot 9} - 1\right)}\right)\right)\right) \]

      6. distribute-lft-in N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \left(3 \cdot y + \color{blue}{3 \cdot \left(\frac{1}{x \cdot 9} - 1\right)}\right)\right) \]

      7. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \left(3 \cdot y + \left(\frac{1}{x \cdot 9} - 1\right) \cdot \color{blue}{3}\right)\right) \]

      8. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{+.f64}\left(\left(3 \cdot y\right), \color{blue}{\left(\left(\frac{1}{x \cdot 9} - 1\right) \cdot 3\right)}\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(3, y\right), \left(\color{blue}{\left(\frac{1}{x \cdot 9} - 1\right)} \cdot 3\right)\right)\right) \]

      10. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(3, y\right), \left(3 \cdot \color{blue}{\left(\frac{1}{x \cdot 9} - 1\right)}\right)\right)\right) \]

      11. sub-neg N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(3, y\right), \left(3 \cdot \left(\frac{1}{x \cdot 9} + \color{blue}{\left(\mathsf{neg}\left(1\right)\right)}\right)\right)\right)\right) \]

      12. +-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(3, y\right), \left(3 \cdot \left(\left(\mathsf{neg}\left(1\right)\right) + \color{blue}{\frac{1}{x \cdot 9}}\right)\right)\right)\right) \]

      13. distribute-lft-in N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(3, y\right), \left(3 \cdot \left(\mathsf{neg}\left(1\right)\right) + \color{blue}{3 \cdot \frac{1}{x \cdot 9}}\right)\right)\right) \]

      14. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(3, y\right), \left(3 \cdot \left(\mathsf{neg}\left(1\right)\right) + \frac{1}{x \cdot 9} \cdot \color{blue}{3}\right)\right)\right) \]

      15. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(3, y\right), \mathsf{+.f64}\left(\left(3 \cdot \left(\mathsf{neg}\left(1\right)\right)\right), \color{blue}{\left(\frac{1}{x \cdot 9} \cdot 3\right)}\right)\right)\right) \]

      16. metadata-eval N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(3, y\right), \mathsf{+.f64}\left(\left(3 \cdot -1\right), \left(\frac{1}{\color{blue}{x \cdot 9}} \cdot 3\right)\right)\right)\right) \]

      17. metadata-eval N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(3, y\right), \mathsf{+.f64}\left(-3, \left(\color{blue}{\frac{1}{x \cdot 9}} \cdot 3\right)\right)\right)\right) \]

      18. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(3, y\right), \mathsf{+.f64}\left(-3, \left(3 \cdot \color{blue}{\frac{1}{x \cdot 9}}\right)\right)\right)\right) \]

      19. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(3, y\right), \mathsf{+.f64}\left(-3, \left(3 \cdot \frac{1}{9 \cdot \color{blue}{x}}\right)\right)\right)\right) \]

      20. associate-/r* N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(3, y\right), \mathsf{+.f64}\left(-3, \left(3 \cdot \frac{\frac{1}{9}}{\color{blue}{x}}\right)\right)\right)\right) \]

      21. associate-*r/ N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(3, y\right), \mathsf{+.f64}\left(-3, \left(\frac{3 \cdot \frac{1}{9}}{\color{blue}{x}}\right)\right)\right)\right) \]

      22. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(3, y\right), \mathsf{+.f64}\left(-3, \mathsf{/.f64}\left(\left(3 \cdot \frac{1}{9}\right), \color{blue}{x}\right)\right)\right)\right) \]

   3. Simplified 99.5%

      \[\leadsto \color{blue}{\sqrt{x} \cdot \left(3 \cdot y + \left(-3 + \frac{0.3333333333333333}{x}\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf

      \[\leadsto \color{blue}{\sqrt{x} \cdot \left(3 \cdot y - 3\right)} \]
   6. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(\sqrt{x}\right), \color{blue}{\left(3 \cdot y - 3\right)}\right) \]

      2. sqrt-lowering-sqrt.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \left(\color{blue}{3 \cdot y} - 3\right)\right) \]

      3. sub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \left(3 \cdot y + \color{blue}{\left(\mathsf{neg}\left(3\right)\right)}\right)\right) \]

      4. metadata-eval N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \left(3 \cdot y + -3\right)\right) \]

      5. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{+.f64}\left(\left(3 \cdot y\right), \color{blue}{-3}\right)\right) \]

      6. *-lowering-*.f64 98.3%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(3, y\right), -3\right)\right) \]

   7. Simplified 98.3%

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

   8. Taylor expanded in y around 0

      \[\leadsto \color{blue}{-3 \cdot \sqrt{x}} \]
   9. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \sqrt{x} \cdot \color{blue}{-3} \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(\sqrt{x}\right), \color{blue}{-3}\right) \]

      3. sqrt-lowering-sqrt.f64 58.9%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), -3\right) \]

   10. Simplified 58.9%

       \[\leadsto \color{blue}{\sqrt{x} \cdot -3} \]
   11. Step-by-step derivation

       1. *-commutative N/A

          \[\leadsto -3 \cdot \color{blue}{\sqrt{x}} \]

       2. pow1/2 N/A

          \[\leadsto -3 \cdot {x}^{\color{blue}{\frac{1}{2}}} \]

       3. metadata-eval N/A

          \[\leadsto -3 \cdot {x}^{\left(\mathsf{neg}\left(\frac{-1}{2}\right)\right)} \]

       4. pow-flip N/A

          \[\leadsto -3 \cdot \frac{1}{\color{blue}{{x}^{\frac{-1}{2}}}} \]

       5. un-div-inv N/A

          \[\leadsto \frac{-3}{\color{blue}{{x}^{\frac{-1}{2}}}} \]

       6. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(-3, \color{blue}{\left({x}^{\frac{-1}{2}}\right)}\right) \]

       7. pow-lowering-pow.f64 59.0%

          \[\leadsto \mathsf{/.f64}\left(-3, \mathsf{pow.f64}\left(x, \color{blue}{\frac{-1}{2}}\right)\right) \]

   12. Applied egg-rr 59.0%

       \[\leadsto \color{blue}{\frac{-3}{{x}^{-0.5}}} \]

   if 4.1000000000000002e91 < x < 4.9000000000000001e117 or 3.09999999999999991e262 < x

   1. Initial program 99.7%

      \[\left(3 \cdot \sqrt{x}\right) \cdot \left(\left(y + \frac{1}{x \cdot 9}\right) - 1\right) \]
   2. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \left(\sqrt{x} \cdot 3\right) \cdot \left(\color{blue}{\left(y + \frac{1}{x \cdot 9}\right)} - 1\right) \]

      2. associate-*l* N/A

         \[\leadsto \sqrt{x} \cdot \color{blue}{\left(3 \cdot \left(\left(y + \frac{1}{x \cdot 9}\right) - 1\right)\right)} \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(\sqrt{x}\right), \color{blue}{\left(3 \cdot \left(\left(y + \frac{1}{x \cdot 9}\right) - 1\right)\right)}\right) \]

      4. sqrt-lowering-sqrt.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \left(\color{blue}{3} \cdot \left(\left(y + \frac{1}{x \cdot 9}\right) - 1\right)\right)\right) \]

      5. associate--l+ N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \left(3 \cdot \left(y + \color{blue}{\left(\frac{1}{x \cdot 9} - 1\right)}\right)\right)\right) \]

      6. distribute-lft-in N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \left(3 \cdot y + \color{blue}{3 \cdot \left(\frac{1}{x \cdot 9} - 1\right)}\right)\right) \]

      7. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \left(3 \cdot y + \left(\frac{1}{x \cdot 9} - 1\right) \cdot \color{blue}{3}\right)\right) \]

      8. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{+.f64}\left(\left(3 \cdot y\right), \color{blue}{\left(\left(\frac{1}{x \cdot 9} - 1\right) \cdot 3\right)}\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(3, y\right), \left(\color{blue}{\left(\frac{1}{x \cdot 9} - 1\right)} \cdot 3\right)\right)\right) \]

      10. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(3, y\right), \left(3 \cdot \color{blue}{\left(\frac{1}{x \cdot 9} - 1\right)}\right)\right)\right) \]

      11. sub-neg N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(3, y\right), \left(3 \cdot \left(\frac{1}{x \cdot 9} + \color{blue}{\left(\mathsf{neg}\left(1\right)\right)}\right)\right)\right)\right) \]

      12. +-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(3, y\right), \left(3 \cdot \left(\left(\mathsf{neg}\left(1\right)\right) + \color{blue}{\frac{1}{x \cdot 9}}\right)\right)\right)\right) \]

      13. distribute-lft-in N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(3, y\right), \left(3 \cdot \left(\mathsf{neg}\left(1\right)\right) + \color{blue}{3 \cdot \frac{1}{x \cdot 9}}\right)\right)\right) \]

      14. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(3, y\right), \left(3 \cdot \left(\mathsf{neg}\left(1\right)\right) + \frac{1}{x \cdot 9} \cdot \color{blue}{3}\right)\right)\right) \]

      15. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(3, y\right), \mathsf{+.f64}\left(\left(3 \cdot \left(\mathsf{neg}\left(1\right)\right)\right), \color{blue}{\left(\frac{1}{x \cdot 9} \cdot 3\right)}\right)\right)\right) \]

      16. metadata-eval N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(3, y\right), \mathsf{+.f64}\left(\left(3 \cdot -1\right), \left(\frac{1}{\color{blue}{x \cdot 9}} \cdot 3\right)\right)\right)\right) \]

      17. metadata-eval N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(3, y\right), \mathsf{+.f64}\left(-3, \left(\color{blue}{\frac{1}{x \cdot 9}} \cdot 3\right)\right)\right)\right) \]

      18. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(3, y\right), \mathsf{+.f64}\left(-3, \left(3 \cdot \color{blue}{\frac{1}{x \cdot 9}}\right)\right)\right)\right) \]

      19. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(3, y\right), \mathsf{+.f64}\left(-3, \left(3 \cdot \frac{1}{9 \cdot \color{blue}{x}}\right)\right)\right)\right) \]

      20. associate-/r* N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(3, y\right), \mathsf{+.f64}\left(-3, \left(3 \cdot \frac{\frac{1}{9}}{\color{blue}{x}}\right)\right)\right)\right) \]

      21. associate-*r/ N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(3, y\right), \mathsf{+.f64}\left(-3, \left(\frac{3 \cdot \frac{1}{9}}{\color{blue}{x}}\right)\right)\right)\right) \]

      22. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(3, y\right), \mathsf{+.f64}\left(-3, \mathsf{/.f64}\left(\left(3 \cdot \frac{1}{9}\right), \color{blue}{x}\right)\right)\right)\right) \]

   3. Simplified 99.8%

      \[\leadsto \color{blue}{\sqrt{x} \cdot \left(3 \cdot y + \left(-3 + \frac{0.3333333333333333}{x}\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around inf

      \[\leadsto \color{blue}{3 \cdot \left(\sqrt{x} \cdot y\right)} \]
   6. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(3, \color{blue}{\left(\sqrt{x} \cdot y\right)}\right) \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(3, \mathsf{*.f64}\left(\left(\sqrt{x}\right), \color{blue}{y}\right)\right) \]

      3. sqrt-lowering-sqrt.f64 72.9%

         \[\leadsto \mathsf{*.f64}\left(3, \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), y\right)\right) \]

   7. Simplified 72.9%

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

4. Final simplification 69.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 0.00044:\\ \;\;\;\;\frac{{x}^{-0.5}}{3}\\ \mathbf{elif}\;x \leq 4.1 \cdot 10^{+91}:\\ \;\;\;\;\frac{-3}{{x}^{-0.5}}\\ \mathbf{elif}\;x \leq 4.9 \cdot 10^{+117}:\\ \;\;\;\;3 \cdot \left(y \cdot \sqrt{x}\right)\\ \mathbf{elif}\;x \leq 3.1 \cdot 10^{+262}:\\ \;\;\;\;\frac{-3}{{x}^{-0.5}}\\ \mathbf{else}:\\ \;\;\;\;3 \cdot \left(y \cdot \sqrt{x}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 98.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 0.00135:\\ \;\;\;\;\frac{0.3333333333333333 + \left(3 \cdot y\right) \cdot x}{\sqrt{x}}\\ \mathbf{else}:\\ \;\;\;\;\sqrt{x} \cdot \left(3 \cdot y + -3\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x 0.00135)
   (/ (+ 0.3333333333333333 (* (* 3.0 y) x)) (sqrt x))
   (* (sqrt x) (+ (* 3.0 y) -3.0))))

C

double code(double x, double y) {
	double tmp;
	if (x <= 0.00135) {
		tmp = (0.3333333333333333 + ((3.0 * y) * x)) / sqrt(x);
	} else {
		tmp = sqrt(x) * ((3.0 * y) + -3.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (x <= 0.00135d0) then
        tmp = (0.3333333333333333d0 + ((3.0d0 * y) * x)) / sqrt(x)
    else
        tmp = sqrt(x) * ((3.0d0 * y) + (-3.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= 0.00135) {
		tmp = (0.3333333333333333 + ((3.0 * y) * x)) / Math.sqrt(x);
	} else {
		tmp = Math.sqrt(x) * ((3.0 * y) + -3.0);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= 0.00135:
		tmp = (0.3333333333333333 + ((3.0 * y) * x)) / math.sqrt(x)
	else:
		tmp = math.sqrt(x) * ((3.0 * y) + -3.0)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= 0.00135)
		tmp = Float64(Float64(0.3333333333333333 + Float64(Float64(3.0 * y) * x)) / sqrt(x));
	else
		tmp = Float64(sqrt(x) * Float64(Float64(3.0 * y) + -3.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= 0.00135)
		tmp = (0.3333333333333333 + ((3.0 * y) * x)) / sqrt(x);
	else
		tmp = sqrt(x) * ((3.0 * y) + -3.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, 0.00135], N[(N[(0.3333333333333333 + N[(N[(3.0 * y), $MachinePrecision] * x), $MachinePrecision]), $MachinePrecision] / N[Sqrt[x], $MachinePrecision]), $MachinePrecision], N[(N[Sqrt[x], $MachinePrecision] * N[(N[(3.0 * y), $MachinePrecision] + -3.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < 0.0013500000000000001

   1. Initial program 99.2%

      \[\left(3 \cdot \sqrt{x}\right) \cdot \left(\left(y + \frac{1}{x \cdot 9}\right) - 1\right) \]
   2. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \left(\sqrt{x} \cdot 3\right) \cdot \left(\color{blue}{\left(y + \frac{1}{x \cdot 9}\right)} - 1\right) \]

      2. associate-*l* N/A

         \[\leadsto \sqrt{x} \cdot \color{blue}{\left(3 \cdot \left(\left(y + \frac{1}{x \cdot 9}\right) - 1\right)\right)} \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(\sqrt{x}\right), \color{blue}{\left(3 \cdot \left(\left(y + \frac{1}{x \cdot 9}\right) - 1\right)\right)}\right) \]

      4. sqrt-lowering-sqrt.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \left(\color{blue}{3} \cdot \left(\left(y + \frac{1}{x \cdot 9}\right) - 1\right)\right)\right) \]

      5. associate--l+ N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \left(3 \cdot \left(y + \color{blue}{\left(\frac{1}{x \cdot 9} - 1\right)}\right)\right)\right) \]

      6. distribute-lft-in N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \left(3 \cdot y + \color{blue}{3 \cdot \left(\frac{1}{x \cdot 9} - 1\right)}\right)\right) \]

      7. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \left(3 \cdot y + \left(\frac{1}{x \cdot 9} - 1\right) \cdot \color{blue}{3}\right)\right) \]

      8. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{+.f64}\left(\left(3 \cdot y\right), \color{blue}{\left(\left(\frac{1}{x \cdot 9} - 1\right) \cdot 3\right)}\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(3, y\right), \left(\color{blue}{\left(\frac{1}{x \cdot 9} - 1\right)} \cdot 3\right)\right)\right) \]

      10. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(3, y\right), \left(3 \cdot \color{blue}{\left(\frac{1}{x \cdot 9} - 1\right)}\right)\right)\right) \]

      11. sub-neg N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(3, y\right), \left(3 \cdot \left(\frac{1}{x \cdot 9} + \color{blue}{\left(\mathsf{neg}\left(1\right)\right)}\right)\right)\right)\right) \]

      12. +-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(3, y\right), \left(3 \cdot \left(\left(\mathsf{neg}\left(1\right)\right) + \color{blue}{\frac{1}{x \cdot 9}}\right)\right)\right)\right) \]

      13. distribute-lft-in N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(3, y\right), \left(3 \cdot \left(\mathsf{neg}\left(1\right)\right) + \color{blue}{3 \cdot \frac{1}{x \cdot 9}}\right)\right)\right) \]

      14. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(3, y\right), \left(3 \cdot \left(\mathsf{neg}\left(1\right)\right) + \frac{1}{x \cdot 9} \cdot \color{blue}{3}\right)\right)\right) \]

      15. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(3, y\right), \mathsf{+.f64}\left(\left(3 \cdot \left(\mathsf{neg}\left(1\right)\right)\right), \color{blue}{\left(\frac{1}{x \cdot 9} \cdot 3\right)}\right)\right)\right) \]

      16. metadata-eval N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(3, y\right), \mathsf{+.f64}\left(\left(3 \cdot -1\right), \left(\frac{1}{\color{blue}{x \cdot 9}} \cdot 3\right)\right)\right)\right) \]

      17. metadata-eval N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(3, y\right), \mathsf{+.f64}\left(-3, \left(\color{blue}{\frac{1}{x \cdot 9}} \cdot 3\right)\right)\right)\right) \]

      18. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(3, y\right), \mathsf{+.f64}\left(-3, \left(3 \cdot \color{blue}{\frac{1}{x \cdot 9}}\right)\right)\right)\right) \]

      19. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(3, y\right), \mathsf{+.f64}\left(-3, \left(3 \cdot \frac{1}{9 \cdot \color{blue}{x}}\right)\right)\right)\right) \]

      20. associate-/r* N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(3, y\right), \mathsf{+.f64}\left(-3, \left(3 \cdot \frac{\frac{1}{9}}{\color{blue}{x}}\right)\right)\right)\right) \]

      21. associate-*r/ N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(3, y\right), \mathsf{+.f64}\left(-3, \left(\frac{3 \cdot \frac{1}{9}}{\color{blue}{x}}\right)\right)\right)\right) \]

      22. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(3, y\right), \mathsf{+.f64}\left(-3, \mathsf{/.f64}\left(\left(3 \cdot \frac{1}{9}\right), \color{blue}{x}\right)\right)\right)\right) \]

   3. Simplified 99.3%

      \[\leadsto \color{blue}{\sqrt{x} \cdot \left(3 \cdot y + \left(-3 + \frac{0.3333333333333333}{x}\right)\right)} \]
   4. Add Preprocessing

   6. Applied egg-rr 99.3%

      \[\leadsto \color{blue}{\frac{3 \cdot y + \left(-3 + \frac{0.3333333333333333}{x}\right)}{{x}^{-0.5}}} \]
   7. Step-by-step derivation

      1. metadata-eval N/A

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

      2. pow-prod-up N/A

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

      3. pow1/2 N/A

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

      4. inv-pow N/A

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

      5. div-inv N/A

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

      6. un-div-inv N/A

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

      7. clear-num N/A

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

      8. associate-*r/ N/A

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

      9. *-commutative N/A

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

      10. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\left(x \cdot \left(3 \cdot y + \left(-3 + \frac{\frac{1}{3}}{x}\right)\right)\right), \color{blue}{\left(\sqrt{x}\right)}\right) \]

   8. Applied egg-rr 99.4%

      \[\leadsto \color{blue}{\frac{0.3333333333333333 + x \cdot \left(3 \cdot y + -3\right)}{\sqrt{x}}} \]

   9. Taylor expanded in y around inf

      \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\frac{1}{3}, \color{blue}{\left(3 \cdot \left(x \cdot y\right)\right)}\right), \mathsf{sqrt.f64}\left(x\right)\right) \]
   10. Step-by-step derivation

       1. *-commutative N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\frac{1}{3}, \left(\left(x \cdot y\right) \cdot 3\right)\right), \mathsf{sqrt.f64}\left(x\right)\right) \]

       2. associate-*l* N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\frac{1}{3}, \left(x \cdot \left(y \cdot 3\right)\right)\right), \mathsf{sqrt.f64}\left(x\right)\right) \]

       3. *-commutative N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\frac{1}{3}, \left(x \cdot \left(3 \cdot y\right)\right)\right), \mathsf{sqrt.f64}\left(x\right)\right) \]

       4. *-lowering-*.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\frac{1}{3}, \mathsf{*.f64}\left(x, \left(3 \cdot y\right)\right)\right), \mathsf{sqrt.f64}\left(x\right)\right) \]

       5. *-lowering-*.f64 98.7%

          \[\leadsto \mathsf{/.f64}\left(\mathsf{+.f64}\left(\frac{1}{3}, \mathsf{*.f64}\left(x, \mathsf{*.f64}\left(3, y\right)\right)\right), \mathsf{sqrt.f64}\left(x\right)\right) \]

   11. Simplified 98.7%

       \[\leadsto \frac{0.3333333333333333 + \color{blue}{x \cdot \left(3 \cdot y\right)}}{\sqrt{x}} \]

   if 0.0013500000000000001 < x

   1. Initial program 99.6%

      \[\left(3 \cdot \sqrt{x}\right) \cdot \left(\left(y + \frac{1}{x \cdot 9}\right) - 1\right) \]
   2. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \left(\sqrt{x} \cdot 3\right) \cdot \left(\color{blue}{\left(y + \frac{1}{x \cdot 9}\right)} - 1\right) \]

      2. associate-*l* N/A

         \[\leadsto \sqrt{x} \cdot \color{blue}{\left(3 \cdot \left(\left(y + \frac{1}{x \cdot 9}\right) - 1\right)\right)} \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(\sqrt{x}\right), \color{blue}{\left(3 \cdot \left(\left(y + \frac{1}{x \cdot 9}\right) - 1\right)\right)}\right) \]

      4. sqrt-lowering-sqrt.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \left(\color{blue}{3} \cdot \left(\left(y + \frac{1}{x \cdot 9}\right) - 1\right)\right)\right) \]

      5. associate--l+ N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \left(3 \cdot \left(y + \color{blue}{\left(\frac{1}{x \cdot 9} - 1\right)}\right)\right)\right) \]

      6. distribute-lft-in N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \left(3 \cdot y + \color{blue}{3 \cdot \left(\frac{1}{x \cdot 9} - 1\right)}\right)\right) \]

      7. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \left(3 \cdot y + \left(\frac{1}{x \cdot 9} - 1\right) \cdot \color{blue}{3}\right)\right) \]

      8. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{+.f64}\left(\left(3 \cdot y\right), \color{blue}{\left(\left(\frac{1}{x \cdot 9} - 1\right) \cdot 3\right)}\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(3, y\right), \left(\color{blue}{\left(\frac{1}{x \cdot 9} - 1\right)} \cdot 3\right)\right)\right) \]

      10. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(3, y\right), \left(3 \cdot \color{blue}{\left(\frac{1}{x \cdot 9} - 1\right)}\right)\right)\right) \]

      11. sub-neg N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(3, y\right), \left(3 \cdot \left(\frac{1}{x \cdot 9} + \color{blue}{\left(\mathsf{neg}\left(1\right)\right)}\right)\right)\right)\right) \]

      12. +-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(3, y\right), \left(3 \cdot \left(\left(\mathsf{neg}\left(1\right)\right) + \color{blue}{\frac{1}{x \cdot 9}}\right)\right)\right)\right) \]

      13. distribute-lft-in N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(3, y\right), \left(3 \cdot \left(\mathsf{neg}\left(1\right)\right) + \color{blue}{3 \cdot \frac{1}{x \cdot 9}}\right)\right)\right) \]

      14. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(3, y\right), \left(3 \cdot \left(\mathsf{neg}\left(1\right)\right) + \frac{1}{x \cdot 9} \cdot \color{blue}{3}\right)\right)\right) \]

      15. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(3, y\right), \mathsf{+.f64}\left(\left(3 \cdot \left(\mathsf{neg}\left(1\right)\right)\right), \color{blue}{\left(\frac{1}{x \cdot 9} \cdot 3\right)}\right)\right)\right) \]

      16. metadata-eval N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(3, y\right), \mathsf{+.f64}\left(\left(3 \cdot -1\right), \left(\frac{1}{\color{blue}{x \cdot 9}} \cdot 3\right)\right)\right)\right) \]

      17. metadata-eval N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(3, y\right), \mathsf{+.f64}\left(-3, \left(\color{blue}{\frac{1}{x \cdot 9}} \cdot 3\right)\right)\right)\right) \]

      18. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(3, y\right), \mathsf{+.f64}\left(-3, \left(3 \cdot \color{blue}{\frac{1}{x \cdot 9}}\right)\right)\right)\right) \]

      19. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(3, y\right), \mathsf{+.f64}\left(-3, \left(3 \cdot \frac{1}{9 \cdot \color{blue}{x}}\right)\right)\right)\right) \]

      20. associate-/r* N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(3, y\right), \mathsf{+.f64}\left(-3, \left(3 \cdot \frac{\frac{1}{9}}{\color{blue}{x}}\right)\right)\right)\right) \]

      21. associate-*r/ N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(3, y\right), \mathsf{+.f64}\left(-3, \left(\frac{3 \cdot \frac{1}{9}}{\color{blue}{x}}\right)\right)\right)\right) \]

      22. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(3, y\right), \mathsf{+.f64}\left(-3, \mathsf{/.f64}\left(\left(3 \cdot \frac{1}{9}\right), \color{blue}{x}\right)\right)\right)\right) \]

   3. Simplified 99.6%

      \[\leadsto \color{blue}{\sqrt{x} \cdot \left(3 \cdot y + \left(-3 + \frac{0.3333333333333333}{x}\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf

      \[\leadsto \color{blue}{\sqrt{x} \cdot \left(3 \cdot y - 3\right)} \]
   6. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(\sqrt{x}\right), \color{blue}{\left(3 \cdot y - 3\right)}\right) \]

      2. sqrt-lowering-sqrt.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \left(\color{blue}{3 \cdot y} - 3\right)\right) \]

      3. sub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \left(3 \cdot y + \color{blue}{\left(\mathsf{neg}\left(3\right)\right)}\right)\right) \]

      4. metadata-eval N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \left(3 \cdot y + -3\right)\right) \]

      5. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{+.f64}\left(\left(3 \cdot y\right), \color{blue}{-3}\right)\right) \]

      6. *-lowering-*.f64 98.6%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(3, y\right), -3\right)\right) \]

   7. Simplified 98.6%

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

4. Final simplification 98.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 0.00135:\\ \;\;\;\;\frac{0.3333333333333333 + \left(3 \cdot y\right) \cdot x}{\sqrt{x}}\\ \mathbf{else}:\\ \;\;\;\;\sqrt{x} \cdot \left(3 \cdot y + -3\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 86.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 3.2 \cdot 10^{-8}:\\ \;\;\;\;3 \cdot \frac{0.1111111111111111 - x}{\sqrt{x}}\\ \mathbf{else}:\\ \;\;\;\;\sqrt{x} \cdot \left(3 \cdot y + -3\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x 3.2e-8)
   (* 3.0 (/ (- 0.1111111111111111 x) (sqrt x)))
   (* (sqrt x) (+ (* 3.0 y) -3.0))))

C

double code(double x, double y) {
	double tmp;
	if (x <= 3.2e-8) {
		tmp = 3.0 * ((0.1111111111111111 - x) / sqrt(x));
	} else {
		tmp = sqrt(x) * ((3.0 * y) + -3.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (x <= 3.2d-8) then
        tmp = 3.0d0 * ((0.1111111111111111d0 - x) / sqrt(x))
    else
        tmp = sqrt(x) * ((3.0d0 * y) + (-3.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= 3.2e-8) {
		tmp = 3.0 * ((0.1111111111111111 - x) / Math.sqrt(x));
	} else {
		tmp = Math.sqrt(x) * ((3.0 * y) + -3.0);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= 3.2e-8:
		tmp = 3.0 * ((0.1111111111111111 - x) / math.sqrt(x))
	else:
		tmp = math.sqrt(x) * ((3.0 * y) + -3.0)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= 3.2e-8)
		tmp = Float64(3.0 * Float64(Float64(0.1111111111111111 - x) / sqrt(x)));
	else
		tmp = Float64(sqrt(x) * Float64(Float64(3.0 * y) + -3.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= 3.2e-8)
		tmp = 3.0 * ((0.1111111111111111 - x) / sqrt(x));
	else
		tmp = sqrt(x) * ((3.0 * y) + -3.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, 3.2e-8], N[(3.0 * N[(N[(0.1111111111111111 - x), $MachinePrecision] / N[Sqrt[x], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[Sqrt[x], $MachinePrecision] * N[(N[(3.0 * y), $MachinePrecision] + -3.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < 3.2000000000000002e-8

   1. Initial program 99.2%

      \[\left(3 \cdot \sqrt{x}\right) \cdot \left(\left(y + \frac{1}{x \cdot 9}\right) - 1\right) \]
   2. Add Preprocessing

   3. Taylor expanded in y around 0

      \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(3, \mathsf{sqrt.f64}\left(x\right)\right), \mathsf{\_.f64}\left(\color{blue}{\left(\frac{\frac{1}{9}}{x}\right)}, 1\right)\right) \]
   4. Step-by-step derivation

      1. /-lowering-/.f64 77.7%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(3, \mathsf{sqrt.f64}\left(x\right)\right), \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\frac{1}{9}, x\right), 1\right)\right) \]

   5. Simplified 77.7%

      \[\leadsto \left(3 \cdot \sqrt{x}\right) \cdot \left(\color{blue}{\frac{0.1111111111111111}{x}} - 1\right) \]
   6. Step-by-step derivation

      1. associate-*l* N/A

         \[\leadsto 3 \cdot \color{blue}{\left(\sqrt{x} \cdot \left(\frac{\frac{1}{9}}{x} - 1\right)\right)} \]

      2. *-commutative N/A

         \[\leadsto \left(\sqrt{x} \cdot \left(\frac{\frac{1}{9}}{x} - 1\right)\right) \cdot \color{blue}{3} \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(\sqrt{x} \cdot \left(\frac{\frac{1}{9}}{x} - 1\right)\right), \color{blue}{3}\right) \]

   7. Applied egg-rr 77.9%

      \[\leadsto \color{blue}{\frac{0.1111111111111111 - x}{\sqrt{x}} \cdot 3} \]

   if 3.2000000000000002e-8 < x

   1. Initial program 99.6%

      \[\left(3 \cdot \sqrt{x}\right) \cdot \left(\left(y + \frac{1}{x \cdot 9}\right) - 1\right) \]
   2. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \left(\sqrt{x} \cdot 3\right) \cdot \left(\color{blue}{\left(y + \frac{1}{x \cdot 9}\right)} - 1\right) \]

      2. associate-*l* N/A

         \[\leadsto \sqrt{x} \cdot \color{blue}{\left(3 \cdot \left(\left(y + \frac{1}{x \cdot 9}\right) - 1\right)\right)} \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(\sqrt{x}\right), \color{blue}{\left(3 \cdot \left(\left(y + \frac{1}{x \cdot 9}\right) - 1\right)\right)}\right) \]

      4. sqrt-lowering-sqrt.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \left(\color{blue}{3} \cdot \left(\left(y + \frac{1}{x \cdot 9}\right) - 1\right)\right)\right) \]

      5. associate--l+ N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \left(3 \cdot \left(y + \color{blue}{\left(\frac{1}{x \cdot 9} - 1\right)}\right)\right)\right) \]

      6. distribute-lft-in N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \left(3 \cdot y + \color{blue}{3 \cdot \left(\frac{1}{x \cdot 9} - 1\right)}\right)\right) \]

      7. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \left(3 \cdot y + \left(\frac{1}{x \cdot 9} - 1\right) \cdot \color{blue}{3}\right)\right) \]

      8. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{+.f64}\left(\left(3 \cdot y\right), \color{blue}{\left(\left(\frac{1}{x \cdot 9} - 1\right) \cdot 3\right)}\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(3, y\right), \left(\color{blue}{\left(\frac{1}{x \cdot 9} - 1\right)} \cdot 3\right)\right)\right) \]

      10. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(3, y\right), \left(3 \cdot \color{blue}{\left(\frac{1}{x \cdot 9} - 1\right)}\right)\right)\right) \]

      11. sub-neg N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(3, y\right), \left(3 \cdot \left(\frac{1}{x \cdot 9} + \color{blue}{\left(\mathsf{neg}\left(1\right)\right)}\right)\right)\right)\right) \]

      12. +-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(3, y\right), \left(3 \cdot \left(\left(\mathsf{neg}\left(1\right)\right) + \color{blue}{\frac{1}{x \cdot 9}}\right)\right)\right)\right) \]

      13. distribute-lft-in N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(3, y\right), \left(3 \cdot \left(\mathsf{neg}\left(1\right)\right) + \color{blue}{3 \cdot \frac{1}{x \cdot 9}}\right)\right)\right) \]

      14. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(3, y\right), \left(3 \cdot \left(\mathsf{neg}\left(1\right)\right) + \frac{1}{x \cdot 9} \cdot \color{blue}{3}\right)\right)\right) \]

      15. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(3, y\right), \mathsf{+.f64}\left(\left(3 \cdot \left(\mathsf{neg}\left(1\right)\right)\right), \color{blue}{\left(\frac{1}{x \cdot 9} \cdot 3\right)}\right)\right)\right) \]

      16. metadata-eval N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(3, y\right), \mathsf{+.f64}\left(\left(3 \cdot -1\right), \left(\frac{1}{\color{blue}{x \cdot 9}} \cdot 3\right)\right)\right)\right) \]

      17. metadata-eval N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(3, y\right), \mathsf{+.f64}\left(-3, \left(\color{blue}{\frac{1}{x \cdot 9}} \cdot 3\right)\right)\right)\right) \]

      18. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(3, y\right), \mathsf{+.f64}\left(-3, \left(3 \cdot \color{blue}{\frac{1}{x \cdot 9}}\right)\right)\right)\right) \]

      19. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(3, y\right), \mathsf{+.f64}\left(-3, \left(3 \cdot \frac{1}{9 \cdot \color{blue}{x}}\right)\right)\right)\right) \]

      20. associate-/r* N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(3, y\right), \mathsf{+.f64}\left(-3, \left(3 \cdot \frac{\frac{1}{9}}{\color{blue}{x}}\right)\right)\right)\right) \]

      21. associate-*r/ N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(3, y\right), \mathsf{+.f64}\left(-3, \left(\frac{3 \cdot \frac{1}{9}}{\color{blue}{x}}\right)\right)\right)\right) \]

      22. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(3, y\right), \mathsf{+.f64}\left(-3, \mathsf{/.f64}\left(\left(3 \cdot \frac{1}{9}\right), \color{blue}{x}\right)\right)\right)\right) \]

   3. Simplified 99.6%

      \[\leadsto \color{blue}{\sqrt{x} \cdot \left(3 \cdot y + \left(-3 + \frac{0.3333333333333333}{x}\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf

      \[\leadsto \color{blue}{\sqrt{x} \cdot \left(3 \cdot y - 3\right)} \]
   6. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(\sqrt{x}\right), \color{blue}{\left(3 \cdot y - 3\right)}\right) \]

      2. sqrt-lowering-sqrt.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \left(\color{blue}{3 \cdot y} - 3\right)\right) \]

      3. sub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \left(3 \cdot y + \color{blue}{\left(\mathsf{neg}\left(3\right)\right)}\right)\right) \]

      4. metadata-eval N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \left(3 \cdot y + -3\right)\right) \]

      5. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{+.f64}\left(\left(3 \cdot y\right), \color{blue}{-3}\right)\right) \]

      6. *-lowering-*.f64 98.6%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(3, y\right), -3\right)\right) \]

   7. Simplified 98.6%

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

4. Final simplification 88.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 3.2 \cdot 10^{-8}:\\ \;\;\;\;3 \cdot \frac{0.1111111111111111 - x}{\sqrt{x}}\\ \mathbf{else}:\\ \;\;\;\;\sqrt{x} \cdot \left(3 \cdot y + -3\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 86.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 0.00016:\\ \;\;\;\;\sqrt{x} \cdot \left(-3 + \frac{0.3333333333333333}{x}\right)\\ \mathbf{else}:\\ \;\;\;\;\sqrt{x} \cdot \left(3 \cdot y + -3\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x 0.00016)
   (* (sqrt x) (+ -3.0 (/ 0.3333333333333333 x)))
   (* (sqrt x) (+ (* 3.0 y) -3.0))))

C

double code(double x, double y) {
	double tmp;
	if (x <= 0.00016) {
		tmp = sqrt(x) * (-3.0 + (0.3333333333333333 / x));
	} else {
		tmp = sqrt(x) * ((3.0 * y) + -3.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (x <= 0.00016d0) then
        tmp = sqrt(x) * ((-3.0d0) + (0.3333333333333333d0 / x))
    else
        tmp = sqrt(x) * ((3.0d0 * y) + (-3.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= 0.00016) {
		tmp = Math.sqrt(x) * (-3.0 + (0.3333333333333333 / x));
	} else {
		tmp = Math.sqrt(x) * ((3.0 * y) + -3.0);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= 0.00016:
		tmp = math.sqrt(x) * (-3.0 + (0.3333333333333333 / x))
	else:
		tmp = math.sqrt(x) * ((3.0 * y) + -3.0)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= 0.00016)
		tmp = Float64(sqrt(x) * Float64(-3.0 + Float64(0.3333333333333333 / x)));
	else
		tmp = Float64(sqrt(x) * Float64(Float64(3.0 * y) + -3.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= 0.00016)
		tmp = sqrt(x) * (-3.0 + (0.3333333333333333 / x));
	else
		tmp = sqrt(x) * ((3.0 * y) + -3.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, 0.00016], N[(N[Sqrt[x], $MachinePrecision] * N[(-3.0 + N[(0.3333333333333333 / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[Sqrt[x], $MachinePrecision] * N[(N[(3.0 * y), $MachinePrecision] + -3.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < 1.60000000000000013e-4

   1. Initial program 99.2%

      \[\left(3 \cdot \sqrt{x}\right) \cdot \left(\left(y + \frac{1}{x \cdot 9}\right) - 1\right) \]
   2. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \left(\sqrt{x} \cdot 3\right) \cdot \left(\color{blue}{\left(y + \frac{1}{x \cdot 9}\right)} - 1\right) \]

      2. associate-*l* N/A

         \[\leadsto \sqrt{x} \cdot \color{blue}{\left(3 \cdot \left(\left(y + \frac{1}{x \cdot 9}\right) - 1\right)\right)} \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(\sqrt{x}\right), \color{blue}{\left(3 \cdot \left(\left(y + \frac{1}{x \cdot 9}\right) - 1\right)\right)}\right) \]

      4. sqrt-lowering-sqrt.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \left(\color{blue}{3} \cdot \left(\left(y + \frac{1}{x \cdot 9}\right) - 1\right)\right)\right) \]

      5. associate--l+ N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \left(3 \cdot \left(y + \color{blue}{\left(\frac{1}{x \cdot 9} - 1\right)}\right)\right)\right) \]

      6. distribute-lft-in N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \left(3 \cdot y + \color{blue}{3 \cdot \left(\frac{1}{x \cdot 9} - 1\right)}\right)\right) \]

      7. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \left(3 \cdot y + \left(\frac{1}{x \cdot 9} - 1\right) \cdot \color{blue}{3}\right)\right) \]

      8. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{+.f64}\left(\left(3 \cdot y\right), \color{blue}{\left(\left(\frac{1}{x \cdot 9} - 1\right) \cdot 3\right)}\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(3, y\right), \left(\color{blue}{\left(\frac{1}{x \cdot 9} - 1\right)} \cdot 3\right)\right)\right) \]

      10. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(3, y\right), \left(3 \cdot \color{blue}{\left(\frac{1}{x \cdot 9} - 1\right)}\right)\right)\right) \]

      11. sub-neg N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(3, y\right), \left(3 \cdot \left(\frac{1}{x \cdot 9} + \color{blue}{\left(\mathsf{neg}\left(1\right)\right)}\right)\right)\right)\right) \]

      12. +-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(3, y\right), \left(3 \cdot \left(\left(\mathsf{neg}\left(1\right)\right) + \color{blue}{\frac{1}{x \cdot 9}}\right)\right)\right)\right) \]

      13. distribute-lft-in N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(3, y\right), \left(3 \cdot \left(\mathsf{neg}\left(1\right)\right) + \color{blue}{3 \cdot \frac{1}{x \cdot 9}}\right)\right)\right) \]

      14. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(3, y\right), \left(3 \cdot \left(\mathsf{neg}\left(1\right)\right) + \frac{1}{x \cdot 9} \cdot \color{blue}{3}\right)\right)\right) \]

      15. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(3, y\right), \mathsf{+.f64}\left(\left(3 \cdot \left(\mathsf{neg}\left(1\right)\right)\right), \color{blue}{\left(\frac{1}{x \cdot 9} \cdot 3\right)}\right)\right)\right) \]

      16. metadata-eval N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(3, y\right), \mathsf{+.f64}\left(\left(3 \cdot -1\right), \left(\frac{1}{\color{blue}{x \cdot 9}} \cdot 3\right)\right)\right)\right) \]

      17. metadata-eval N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(3, y\right), \mathsf{+.f64}\left(-3, \left(\color{blue}{\frac{1}{x \cdot 9}} \cdot 3\right)\right)\right)\right) \]

      18. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(3, y\right), \mathsf{+.f64}\left(-3, \left(3 \cdot \color{blue}{\frac{1}{x \cdot 9}}\right)\right)\right)\right) \]

      19. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(3, y\right), \mathsf{+.f64}\left(-3, \left(3 \cdot \frac{1}{9 \cdot \color{blue}{x}}\right)\right)\right)\right) \]

      20. associate-/r* N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(3, y\right), \mathsf{+.f64}\left(-3, \left(3 \cdot \frac{\frac{1}{9}}{\color{blue}{x}}\right)\right)\right)\right) \]

      21. associate-*r/ N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(3, y\right), \mathsf{+.f64}\left(-3, \left(\frac{3 \cdot \frac{1}{9}}{\color{blue}{x}}\right)\right)\right)\right) \]

      22. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(3, y\right), \mathsf{+.f64}\left(-3, \mathsf{/.f64}\left(\left(3 \cdot \frac{1}{9}\right), \color{blue}{x}\right)\right)\right)\right) \]

   3. Simplified 99.3%

      \[\leadsto \color{blue}{\sqrt{x} \cdot \left(3 \cdot y + \left(-3 + \frac{0.3333333333333333}{x}\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in y around 0

      \[\leadsto \color{blue}{\sqrt{x} \cdot \left(\frac{1}{3} \cdot \frac{1}{x} - 3\right)} \]
   6. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(\sqrt{x}\right), \color{blue}{\left(\frac{1}{3} \cdot \frac{1}{x} - 3\right)}\right) \]

      2. sqrt-lowering-sqrt.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \left(\color{blue}{\frac{1}{3} \cdot \frac{1}{x}} - 3\right)\right) \]

      3. sub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \left(\frac{1}{3} \cdot \frac{1}{x} + \color{blue}{\left(\mathsf{neg}\left(3\right)\right)}\right)\right) \]

      4. metadata-eval N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \left(\frac{1}{3} \cdot \frac{1}{x} + -3\right)\right) \]

      5. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{+.f64}\left(\left(\frac{1}{3} \cdot \frac{1}{x}\right), \color{blue}{-3}\right)\right) \]

      6. associate-*r/ N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{+.f64}\left(\left(\frac{\frac{1}{3} \cdot 1}{x}\right), -3\right)\right) \]

      7. metadata-eval N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{+.f64}\left(\left(\frac{\frac{1}{3}}{x}\right), -3\right)\right) \]

      8. /-lowering-/.f64 77.7%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{+.f64}\left(\mathsf{/.f64}\left(\frac{1}{3}, x\right), -3\right)\right) \]

   7. Simplified 77.7%

      \[\leadsto \color{blue}{\sqrt{x} \cdot \left(\frac{0.3333333333333333}{x} + -3\right)} \]

   if 1.60000000000000013e-4 < x

   1. Initial program 99.6%

      \[\left(3 \cdot \sqrt{x}\right) \cdot \left(\left(y + \frac{1}{x \cdot 9}\right) - 1\right) \]
   2. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \left(\sqrt{x} \cdot 3\right) \cdot \left(\color{blue}{\left(y + \frac{1}{x \cdot 9}\right)} - 1\right) \]

      2. associate-*l* N/A

         \[\leadsto \sqrt{x} \cdot \color{blue}{\left(3 \cdot \left(\left(y + \frac{1}{x \cdot 9}\right) - 1\right)\right)} \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(\sqrt{x}\right), \color{blue}{\left(3 \cdot \left(\left(y + \frac{1}{x \cdot 9}\right) - 1\right)\right)}\right) \]

      4. sqrt-lowering-sqrt.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \left(\color{blue}{3} \cdot \left(\left(y + \frac{1}{x \cdot 9}\right) - 1\right)\right)\right) \]

      5. associate--l+ N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \left(3 \cdot \left(y + \color{blue}{\left(\frac{1}{x \cdot 9} - 1\right)}\right)\right)\right) \]

      6. distribute-lft-in N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \left(3 \cdot y + \color{blue}{3 \cdot \left(\frac{1}{x \cdot 9} - 1\right)}\right)\right) \]

      7. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \left(3 \cdot y + \left(\frac{1}{x \cdot 9} - 1\right) \cdot \color{blue}{3}\right)\right) \]

      8. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{+.f64}\left(\left(3 \cdot y\right), \color{blue}{\left(\left(\frac{1}{x \cdot 9} - 1\right) \cdot 3\right)}\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(3, y\right), \left(\color{blue}{\left(\frac{1}{x \cdot 9} - 1\right)} \cdot 3\right)\right)\right) \]

      10. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(3, y\right), \left(3 \cdot \color{blue}{\left(\frac{1}{x \cdot 9} - 1\right)}\right)\right)\right) \]

      11. sub-neg N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(3, y\right), \left(3 \cdot \left(\frac{1}{x \cdot 9} + \color{blue}{\left(\mathsf{neg}\left(1\right)\right)}\right)\right)\right)\right) \]

      12. +-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(3, y\right), \left(3 \cdot \left(\left(\mathsf{neg}\left(1\right)\right) + \color{blue}{\frac{1}{x \cdot 9}}\right)\right)\right)\right) \]

      13. distribute-lft-in N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(3, y\right), \left(3 \cdot \left(\mathsf{neg}\left(1\right)\right) + \color{blue}{3 \cdot \frac{1}{x \cdot 9}}\right)\right)\right) \]

      14. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(3, y\right), \left(3 \cdot \left(\mathsf{neg}\left(1\right)\right) + \frac{1}{x \cdot 9} \cdot \color{blue}{3}\right)\right)\right) \]

      15. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(3, y\right), \mathsf{+.f64}\left(\left(3 \cdot \left(\mathsf{neg}\left(1\right)\right)\right), \color{blue}{\left(\frac{1}{x \cdot 9} \cdot 3\right)}\right)\right)\right) \]

      16. metadata-eval N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(3, y\right), \mathsf{+.f64}\left(\left(3 \cdot -1\right), \left(\frac{1}{\color{blue}{x \cdot 9}} \cdot 3\right)\right)\right)\right) \]

      17. metadata-eval N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(3, y\right), \mathsf{+.f64}\left(-3, \left(\color{blue}{\frac{1}{x \cdot 9}} \cdot 3\right)\right)\right)\right) \]

      18. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(3, y\right), \mathsf{+.f64}\left(-3, \left(3 \cdot \color{blue}{\frac{1}{x \cdot 9}}\right)\right)\right)\right) \]

      19. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(3, y\right), \mathsf{+.f64}\left(-3, \left(3 \cdot \frac{1}{9 \cdot \color{blue}{x}}\right)\right)\right)\right) \]

      20. associate-/r* N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(3, y\right), \mathsf{+.f64}\left(-3, \left(3 \cdot \frac{\frac{1}{9}}{\color{blue}{x}}\right)\right)\right)\right) \]

      21. associate-*r/ N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(3, y\right), \mathsf{+.f64}\left(-3, \left(\frac{3 \cdot \frac{1}{9}}{\color{blue}{x}}\right)\right)\right)\right) \]

      22. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(3, y\right), \mathsf{+.f64}\left(-3, \mathsf{/.f64}\left(\left(3 \cdot \frac{1}{9}\right), \color{blue}{x}\right)\right)\right)\right) \]

   3. Simplified 99.6%

      \[\leadsto \color{blue}{\sqrt{x} \cdot \left(3 \cdot y + \left(-3 + \frac{0.3333333333333333}{x}\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf

      \[\leadsto \color{blue}{\sqrt{x} \cdot \left(3 \cdot y - 3\right)} \]
   6. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(\sqrt{x}\right), \color{blue}{\left(3 \cdot y - 3\right)}\right) \]

      2. sqrt-lowering-sqrt.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \left(\color{blue}{3 \cdot y} - 3\right)\right) \]

      3. sub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \left(3 \cdot y + \color{blue}{\left(\mathsf{neg}\left(3\right)\right)}\right)\right) \]

      4. metadata-eval N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \left(3 \cdot y + -3\right)\right) \]

      5. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{+.f64}\left(\left(3 \cdot y\right), \color{blue}{-3}\right)\right) \]

      6. *-lowering-*.f64 98.6%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(3, y\right), -3\right)\right) \]

   7. Simplified 98.6%

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

4. Final simplification 88.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 0.00016:\\ \;\;\;\;\sqrt{x} \cdot \left(-3 + \frac{0.3333333333333333}{x}\right)\\ \mathbf{else}:\\ \;\;\;\;\sqrt{x} \cdot \left(3 \cdot y + -3\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 86.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 10^{-8}:\\ \;\;\;\;\frac{{x}^{-0.5}}{3}\\ \mathbf{else}:\\ \;\;\;\;\sqrt{x} \cdot \left(3 \cdot y + -3\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x 1e-8) (/ (pow x -0.5) 3.0) (* (sqrt x) (+ (* 3.0 y) -3.0))))

C

double code(double x, double y) {
	double tmp;
	if (x <= 1e-8) {
		tmp = pow(x, -0.5) / 3.0;
	} else {
		tmp = sqrt(x) * ((3.0 * y) + -3.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (x <= 1d-8) then
        tmp = (x ** (-0.5d0)) / 3.0d0
    else
        tmp = sqrt(x) * ((3.0d0 * y) + (-3.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= 1e-8) {
		tmp = Math.pow(x, -0.5) / 3.0;
	} else {
		tmp = Math.sqrt(x) * ((3.0 * y) + -3.0);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= 1e-8:
		tmp = math.pow(x, -0.5) / 3.0
	else:
		tmp = math.sqrt(x) * ((3.0 * y) + -3.0)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= 1e-8)
		tmp = Float64((x ^ -0.5) / 3.0);
	else
		tmp = Float64(sqrt(x) * Float64(Float64(3.0 * y) + -3.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= 1e-8)
		tmp = (x ^ -0.5) / 3.0;
	else
		tmp = sqrt(x) * ((3.0 * y) + -3.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, 1e-8], N[(N[Power[x, -0.5], $MachinePrecision] / 3.0), $MachinePrecision], N[(N[Sqrt[x], $MachinePrecision] * N[(N[(3.0 * y), $MachinePrecision] + -3.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < 1e-8

   1. Initial program 99.2%

      \[\left(3 \cdot \sqrt{x}\right) \cdot \left(\left(y + \frac{1}{x \cdot 9}\right) - 1\right) \]
   2. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \left(\sqrt{x} \cdot 3\right) \cdot \left(\color{blue}{\left(y + \frac{1}{x \cdot 9}\right)} - 1\right) \]

      2. associate-*l* N/A

         \[\leadsto \sqrt{x} \cdot \color{blue}{\left(3 \cdot \left(\left(y + \frac{1}{x \cdot 9}\right) - 1\right)\right)} \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(\sqrt{x}\right), \color{blue}{\left(3 \cdot \left(\left(y + \frac{1}{x \cdot 9}\right) - 1\right)\right)}\right) \]

      4. sqrt-lowering-sqrt.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \left(\color{blue}{3} \cdot \left(\left(y + \frac{1}{x \cdot 9}\right) - 1\right)\right)\right) \]

      5. associate--l+ N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \left(3 \cdot \left(y + \color{blue}{\left(\frac{1}{x \cdot 9} - 1\right)}\right)\right)\right) \]

      6. distribute-lft-in N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \left(3 \cdot y + \color{blue}{3 \cdot \left(\frac{1}{x \cdot 9} - 1\right)}\right)\right) \]

      7. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \left(3 \cdot y + \left(\frac{1}{x \cdot 9} - 1\right) \cdot \color{blue}{3}\right)\right) \]

      8. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{+.f64}\left(\left(3 \cdot y\right), \color{blue}{\left(\left(\frac{1}{x \cdot 9} - 1\right) \cdot 3\right)}\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(3, y\right), \left(\color{blue}{\left(\frac{1}{x \cdot 9} - 1\right)} \cdot 3\right)\right)\right) \]

      10. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(3, y\right), \left(3 \cdot \color{blue}{\left(\frac{1}{x \cdot 9} - 1\right)}\right)\right)\right) \]

      11. sub-neg N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(3, y\right), \left(3 \cdot \left(\frac{1}{x \cdot 9} + \color{blue}{\left(\mathsf{neg}\left(1\right)\right)}\right)\right)\right)\right) \]

      12. +-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(3, y\right), \left(3 \cdot \left(\left(\mathsf{neg}\left(1\right)\right) + \color{blue}{\frac{1}{x \cdot 9}}\right)\right)\right)\right) \]

      13. distribute-lft-in N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(3, y\right), \left(3 \cdot \left(\mathsf{neg}\left(1\right)\right) + \color{blue}{3 \cdot \frac{1}{x \cdot 9}}\right)\right)\right) \]

      14. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(3, y\right), \left(3 \cdot \left(\mathsf{neg}\left(1\right)\right) + \frac{1}{x \cdot 9} \cdot \color{blue}{3}\right)\right)\right) \]

      15. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(3, y\right), \mathsf{+.f64}\left(\left(3 \cdot \left(\mathsf{neg}\left(1\right)\right)\right), \color{blue}{\left(\frac{1}{x \cdot 9} \cdot 3\right)}\right)\right)\right) \]

      16. metadata-eval N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(3, y\right), \mathsf{+.f64}\left(\left(3 \cdot -1\right), \left(\frac{1}{\color{blue}{x \cdot 9}} \cdot 3\right)\right)\right)\right) \]

      17. metadata-eval N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(3, y\right), \mathsf{+.f64}\left(-3, \left(\color{blue}{\frac{1}{x \cdot 9}} \cdot 3\right)\right)\right)\right) \]

      18. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(3, y\right), \mathsf{+.f64}\left(-3, \left(3 \cdot \color{blue}{\frac{1}{x \cdot 9}}\right)\right)\right)\right) \]

      19. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(3, y\right), \mathsf{+.f64}\left(-3, \left(3 \cdot \frac{1}{9 \cdot \color{blue}{x}}\right)\right)\right)\right) \]

      20. associate-/r* N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(3, y\right), \mathsf{+.f64}\left(-3, \left(3 \cdot \frac{\frac{1}{9}}{\color{blue}{x}}\right)\right)\right)\right) \]

      21. associate-*r/ N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(3, y\right), \mathsf{+.f64}\left(-3, \left(\frac{3 \cdot \frac{1}{9}}{\color{blue}{x}}\right)\right)\right)\right) \]

      22. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(3, y\right), \mathsf{+.f64}\left(-3, \mathsf{/.f64}\left(\left(3 \cdot \frac{1}{9}\right), \color{blue}{x}\right)\right)\right)\right) \]

   3. Simplified 99.3%

      \[\leadsto \color{blue}{\sqrt{x} \cdot \left(3 \cdot y + \left(-3 + \frac{0.3333333333333333}{x}\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in x around 0

      \[\leadsto \color{blue}{\frac{1}{3} \cdot \sqrt{\frac{1}{x}}} \]
   6. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\frac{1}{3}, \color{blue}{\left(\sqrt{\frac{1}{x}}\right)}\right) \]

      2. sqrt-lowering-sqrt.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\frac{1}{3}, \mathsf{sqrt.f64}\left(\left(\frac{1}{x}\right)\right)\right) \]

      3. /-lowering-/.f64 77.2%

         \[\leadsto \mathsf{*.f64}\left(\frac{1}{3}, \mathsf{sqrt.f64}\left(\mathsf{/.f64}\left(1, x\right)\right)\right) \]

   7. Simplified 77.2%

      \[\leadsto \color{blue}{0.3333333333333333 \cdot \sqrt{\frac{1}{x}}} \]
   8. Step-by-step derivation

      1. sqrt-div N/A

         \[\leadsto \frac{1}{3} \cdot \frac{\sqrt{1}}{\color{blue}{\sqrt{x}}} \]

      2. metadata-eval N/A

         \[\leadsto \frac{1}{3} \cdot \frac{1}{\sqrt{\color{blue}{x}}} \]

      3. un-div-inv N/A

         \[\leadsto \frac{\frac{1}{3}}{\color{blue}{\sqrt{x}}} \]

      4. metadata-eval N/A

         \[\leadsto \frac{1 \cdot \frac{1}{3}}{\sqrt{\color{blue}{x}}} \]

      5. pow1/2 N/A

         \[\leadsto \frac{1 \cdot \frac{1}{3}}{{x}^{\color{blue}{\frac{1}{2}}}} \]

      6. metadata-eval N/A

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

      7. pow-plus N/A

         \[\leadsto \frac{1 \cdot \frac{1}{3}}{{x}^{\frac{-1}{2}} \cdot \color{blue}{x}} \]

      8. frac-times N/A

         \[\leadsto \frac{1}{{x}^{\frac{-1}{2}}} \cdot \color{blue}{\frac{\frac{1}{3}}{x}} \]

      9. pow-flip N/A

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

      10. metadata-eval N/A

          \[\leadsto {x}^{\frac{1}{2}} \cdot \frac{\frac{1}{3}}{x} \]

      11. metadata-eval N/A

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

      12. pow-plus N/A

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

      13. associate-*l* N/A

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

      14. remove-double-div N/A

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

      15. clear-num N/A

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

      16. frac-times N/A

          \[\leadsto {x}^{\frac{-1}{2}} \cdot \frac{1 \cdot 1}{\color{blue}{\frac{1}{x} \cdot \frac{x}{\frac{1}{3}}}} \]

      17. metadata-eval N/A

          \[\leadsto {x}^{\frac{-1}{2}} \cdot \frac{1}{\color{blue}{\frac{1}{x}} \cdot \frac{x}{\frac{1}{3}}} \]

      18. un-div-inv N/A

          \[\leadsto \frac{{x}^{\frac{-1}{2}}}{\color{blue}{\frac{1}{x} \cdot \frac{x}{\frac{1}{3}}}} \]

      19. inv-pow N/A

          \[\leadsto \frac{{x}^{\frac{-1}{2}}}{{x}^{-1} \cdot \frac{\color{blue}{x}}{\frac{1}{3}}} \]

      20. clear-num N/A

          \[\leadsto \frac{{x}^{\frac{-1}{2}}}{{x}^{-1} \cdot \frac{1}{\color{blue}{\frac{\frac{1}{3}}{x}}}} \]

      21. inv-pow N/A

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

      22. pow-prod-down N/A

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

      23. *-commutative N/A

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

      24. div-inv N/A

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

      25. associate-*l* N/A

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

      26. lft-mult-inverse N/A

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

      27. metadata-eval N/A

          \[\leadsto \frac{{x}^{\frac{-1}{2}}}{{\frac{1}{3}}^{-1}} \]

   9. Applied egg-rr 77.3%

      \[\leadsto \color{blue}{\frac{{x}^{-0.5}}{3}} \]

   if 1e-8 < x

   1. Initial program 99.6%

      \[\left(3 \cdot \sqrt{x}\right) \cdot \left(\left(y + \frac{1}{x \cdot 9}\right) - 1\right) \]
   2. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \left(\sqrt{x} \cdot 3\right) \cdot \left(\color{blue}{\left(y + \frac{1}{x \cdot 9}\right)} - 1\right) \]

      2. associate-*l* N/A

         \[\leadsto \sqrt{x} \cdot \color{blue}{\left(3 \cdot \left(\left(y + \frac{1}{x \cdot 9}\right) - 1\right)\right)} \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(\sqrt{x}\right), \color{blue}{\left(3 \cdot \left(\left(y + \frac{1}{x \cdot 9}\right) - 1\right)\right)}\right) \]

      4. sqrt-lowering-sqrt.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \left(\color{blue}{3} \cdot \left(\left(y + \frac{1}{x \cdot 9}\right) - 1\right)\right)\right) \]

      5. associate--l+ N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \left(3 \cdot \left(y + \color{blue}{\left(\frac{1}{x \cdot 9} - 1\right)}\right)\right)\right) \]

      6. distribute-lft-in N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \left(3 \cdot y + \color{blue}{3 \cdot \left(\frac{1}{x \cdot 9} - 1\right)}\right)\right) \]

      7. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \left(3 \cdot y + \left(\frac{1}{x \cdot 9} - 1\right) \cdot \color{blue}{3}\right)\right) \]

      8. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{+.f64}\left(\left(3 \cdot y\right), \color{blue}{\left(\left(\frac{1}{x \cdot 9} - 1\right) \cdot 3\right)}\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(3, y\right), \left(\color{blue}{\left(\frac{1}{x \cdot 9} - 1\right)} \cdot 3\right)\right)\right) \]

      10. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(3, y\right), \left(3 \cdot \color{blue}{\left(\frac{1}{x \cdot 9} - 1\right)}\right)\right)\right) \]

      11. sub-neg N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(3, y\right), \left(3 \cdot \left(\frac{1}{x \cdot 9} + \color{blue}{\left(\mathsf{neg}\left(1\right)\right)}\right)\right)\right)\right) \]

      12. +-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(3, y\right), \left(3 \cdot \left(\left(\mathsf{neg}\left(1\right)\right) + \color{blue}{\frac{1}{x \cdot 9}}\right)\right)\right)\right) \]

      13. distribute-lft-in N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(3, y\right), \left(3 \cdot \left(\mathsf{neg}\left(1\right)\right) + \color{blue}{3 \cdot \frac{1}{x \cdot 9}}\right)\right)\right) \]

      14. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(3, y\right), \left(3 \cdot \left(\mathsf{neg}\left(1\right)\right) + \frac{1}{x \cdot 9} \cdot \color{blue}{3}\right)\right)\right) \]

      15. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(3, y\right), \mathsf{+.f64}\left(\left(3 \cdot \left(\mathsf{neg}\left(1\right)\right)\right), \color{blue}{\left(\frac{1}{x \cdot 9} \cdot 3\right)}\right)\right)\right) \]

      16. metadata-eval N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(3, y\right), \mathsf{+.f64}\left(\left(3 \cdot -1\right), \left(\frac{1}{\color{blue}{x \cdot 9}} \cdot 3\right)\right)\right)\right) \]

      17. metadata-eval N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(3, y\right), \mathsf{+.f64}\left(-3, \left(\color{blue}{\frac{1}{x \cdot 9}} \cdot 3\right)\right)\right)\right) \]

      18. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(3, y\right), \mathsf{+.f64}\left(-3, \left(3 \cdot \color{blue}{\frac{1}{x \cdot 9}}\right)\right)\right)\right) \]

      19. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(3, y\right), \mathsf{+.f64}\left(-3, \left(3 \cdot \frac{1}{9 \cdot \color{blue}{x}}\right)\right)\right)\right) \]

      20. associate-/r* N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(3, y\right), \mathsf{+.f64}\left(-3, \left(3 \cdot \frac{\frac{1}{9}}{\color{blue}{x}}\right)\right)\right)\right) \]

      21. associate-*r/ N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(3, y\right), \mathsf{+.f64}\left(-3, \left(\frac{3 \cdot \frac{1}{9}}{\color{blue}{x}}\right)\right)\right)\right) \]

      22. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(3, y\right), \mathsf{+.f64}\left(-3, \mathsf{/.f64}\left(\left(3 \cdot \frac{1}{9}\right), \color{blue}{x}\right)\right)\right)\right) \]

   3. Simplified 99.6%

      \[\leadsto \color{blue}{\sqrt{x} \cdot \left(3 \cdot y + \left(-3 + \frac{0.3333333333333333}{x}\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf

      \[\leadsto \color{blue}{\sqrt{x} \cdot \left(3 \cdot y - 3\right)} \]
   6. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(\sqrt{x}\right), \color{blue}{\left(3 \cdot y - 3\right)}\right) \]

      2. sqrt-lowering-sqrt.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \left(\color{blue}{3 \cdot y} - 3\right)\right) \]

      3. sub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \left(3 \cdot y + \color{blue}{\left(\mathsf{neg}\left(3\right)\right)}\right)\right) \]

      4. metadata-eval N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \left(3 \cdot y + -3\right)\right) \]

      5. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{+.f64}\left(\left(3 \cdot y\right), \color{blue}{-3}\right)\right) \]

      6. *-lowering-*.f64 98.6%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(3, y\right), -3\right)\right) \]

   7. Simplified 98.6%

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

Alternative 8: 99.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \left(3 \cdot y + \left(-3 + \frac{0.3333333333333333}{x}\right)\right) \cdot \sqrt{x} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (* (+ (* 3.0 y) (+ -3.0 (/ 0.3333333333333333 x))) (sqrt x)))

C

double code(double x, double y) {
	return ((3.0 * y) + (-3.0 + (0.3333333333333333 / x))) * sqrt(x);
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = ((3.0d0 * y) + ((-3.0d0) + (0.3333333333333333d0 / x))) * sqrt(x)
end function

Java

public static double code(double x, double y) {
	return ((3.0 * y) + (-3.0 + (0.3333333333333333 / x))) * Math.sqrt(x);
}

Python

def code(x, y):
	return ((3.0 * y) + (-3.0 + (0.3333333333333333 / x))) * math.sqrt(x)

Julia

function code(x, y)
	return Float64(Float64(Float64(3.0 * y) + Float64(-3.0 + Float64(0.3333333333333333 / x))) * sqrt(x))
end

MATLAB

function tmp = code(x, y)
	tmp = ((3.0 * y) + (-3.0 + (0.3333333333333333 / x))) * sqrt(x);
end

Wolfram

code[x_, y_] := N[(N[(N[(3.0 * y), $MachinePrecision] + N[(-3.0 + N[(0.3333333333333333 / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision] * N[Sqrt[x], $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 99.4%

   \[\left(3 \cdot \sqrt{x}\right) \cdot \left(\left(y + \frac{1}{x \cdot 9}\right) - 1\right) \]
2. Step-by-step derivation

   1. *-commutative N/A

      \[\leadsto \left(\sqrt{x} \cdot 3\right) \cdot \left(\color{blue}{\left(y + \frac{1}{x \cdot 9}\right)} - 1\right) \]

   2. associate-*l* N/A

      \[\leadsto \sqrt{x} \cdot \color{blue}{\left(3 \cdot \left(\left(y + \frac{1}{x \cdot 9}\right) - 1\right)\right)} \]

   3. *-lowering-*.f64 N/A

      \[\leadsto \mathsf{*.f64}\left(\left(\sqrt{x}\right), \color{blue}{\left(3 \cdot \left(\left(y + \frac{1}{x \cdot 9}\right) - 1\right)\right)}\right) \]

   4. sqrt-lowering-sqrt.f64 N/A

      \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \left(\color{blue}{3} \cdot \left(\left(y + \frac{1}{x \cdot 9}\right) - 1\right)\right)\right) \]

   5. associate--l+ N/A

      \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \left(3 \cdot \left(y + \color{blue}{\left(\frac{1}{x \cdot 9} - 1\right)}\right)\right)\right) \]

   6. distribute-lft-in N/A

      \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \left(3 \cdot y + \color{blue}{3 \cdot \left(\frac{1}{x \cdot 9} - 1\right)}\right)\right) \]

   7. *-commutative N/A

      \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \left(3 \cdot y + \left(\frac{1}{x \cdot 9} - 1\right) \cdot \color{blue}{3}\right)\right) \]

   8. +-lowering-+.f64 N/A

      \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{+.f64}\left(\left(3 \cdot y\right), \color{blue}{\left(\left(\frac{1}{x \cdot 9} - 1\right) \cdot 3\right)}\right)\right) \]

   9. *-lowering-*.f64 N/A

      \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(3, y\right), \left(\color{blue}{\left(\frac{1}{x \cdot 9} - 1\right)} \cdot 3\right)\right)\right) \]

   10. *-commutative N/A

       \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(3, y\right), \left(3 \cdot \color{blue}{\left(\frac{1}{x \cdot 9} - 1\right)}\right)\right)\right) \]

   11. sub-neg N/A

       \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(3, y\right), \left(3 \cdot \left(\frac{1}{x \cdot 9} + \color{blue}{\left(\mathsf{neg}\left(1\right)\right)}\right)\right)\right)\right) \]

   12. +-commutative N/A

       \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(3, y\right), \left(3 \cdot \left(\left(\mathsf{neg}\left(1\right)\right) + \color{blue}{\frac{1}{x \cdot 9}}\right)\right)\right)\right) \]

   13. distribute-lft-in N/A

       \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(3, y\right), \left(3 \cdot \left(\mathsf{neg}\left(1\right)\right) + \color{blue}{3 \cdot \frac{1}{x \cdot 9}}\right)\right)\right) \]

   14. *-commutative N/A

       \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(3, y\right), \left(3 \cdot \left(\mathsf{neg}\left(1\right)\right) + \frac{1}{x \cdot 9} \cdot \color{blue}{3}\right)\right)\right) \]

   15. +-lowering-+.f64 N/A

       \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(3, y\right), \mathsf{+.f64}\left(\left(3 \cdot \left(\mathsf{neg}\left(1\right)\right)\right), \color{blue}{\left(\frac{1}{x \cdot 9} \cdot 3\right)}\right)\right)\right) \]

   16. metadata-eval N/A

       \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(3, y\right), \mathsf{+.f64}\left(\left(3 \cdot -1\right), \left(\frac{1}{\color{blue}{x \cdot 9}} \cdot 3\right)\right)\right)\right) \]

   17. metadata-eval N/A

       \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(3, y\right), \mathsf{+.f64}\left(-3, \left(\color{blue}{\frac{1}{x \cdot 9}} \cdot 3\right)\right)\right)\right) \]

   18. *-commutative N/A

       \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(3, y\right), \mathsf{+.f64}\left(-3, \left(3 \cdot \color{blue}{\frac{1}{x \cdot 9}}\right)\right)\right)\right) \]

   19. *-commutative N/A

       \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(3, y\right), \mathsf{+.f64}\left(-3, \left(3 \cdot \frac{1}{9 \cdot \color{blue}{x}}\right)\right)\right)\right) \]

   20. associate-/r* N/A

       \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(3, y\right), \mathsf{+.f64}\left(-3, \left(3 \cdot \frac{\frac{1}{9}}{\color{blue}{x}}\right)\right)\right)\right) \]

   21. associate-*r/ N/A

       \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(3, y\right), \mathsf{+.f64}\left(-3, \left(\frac{3 \cdot \frac{1}{9}}{\color{blue}{x}}\right)\right)\right)\right) \]

   22. /-lowering-/.f64 N/A

       \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(3, y\right), \mathsf{+.f64}\left(-3, \mathsf{/.f64}\left(\left(3 \cdot \frac{1}{9}\right), \color{blue}{x}\right)\right)\right)\right) \]

3. Simplified 99.4%

   \[\leadsto \color{blue}{\sqrt{x} \cdot \left(3 \cdot y + \left(-3 + \frac{0.3333333333333333}{x}\right)\right)} \]
4. Add Preprocessing

5. Final simplification 99.4%

   \[\leadsto \left(3 \cdot y + \left(-3 + \frac{0.3333333333333333}{x}\right)\right) \cdot \sqrt{x} \]
6. Add Preprocessing

Alternative 9: 60.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 0.00044:\\ \;\;\;\;\frac{{x}^{-0.5}}{3}\\ \mathbf{else}:\\ \;\;\;\;\frac{-3}{{x}^{-0.5}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x 0.00044) (/ (pow x -0.5) 3.0) (/ -3.0 (pow x -0.5))))

C

double code(double x, double y) {
	double tmp;
	if (x <= 0.00044) {
		tmp = pow(x, -0.5) / 3.0;
	} else {
		tmp = -3.0 / pow(x, -0.5);
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (x <= 0.00044d0) then
        tmp = (x ** (-0.5d0)) / 3.0d0
    else
        tmp = (-3.0d0) / (x ** (-0.5d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= 0.00044) {
		tmp = Math.pow(x, -0.5) / 3.0;
	} else {
		tmp = -3.0 / Math.pow(x, -0.5);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= 0.00044:
		tmp = math.pow(x, -0.5) / 3.0
	else:
		tmp = -3.0 / math.pow(x, -0.5)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= 0.00044)
		tmp = Float64((x ^ -0.5) / 3.0);
	else
		tmp = Float64(-3.0 / (x ^ -0.5));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= 0.00044)
		tmp = (x ^ -0.5) / 3.0;
	else
		tmp = -3.0 / (x ^ -0.5);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, 0.00044], N[(N[Power[x, -0.5], $MachinePrecision] / 3.0), $MachinePrecision], N[(-3.0 / N[Power[x, -0.5], $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < 4.40000000000000016e-4

   1. Initial program 99.2%

      \[\left(3 \cdot \sqrt{x}\right) \cdot \left(\left(y + \frac{1}{x \cdot 9}\right) - 1\right) \]
   2. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \left(\sqrt{x} \cdot 3\right) \cdot \left(\color{blue}{\left(y + \frac{1}{x \cdot 9}\right)} - 1\right) \]

      2. associate-*l* N/A

         \[\leadsto \sqrt{x} \cdot \color{blue}{\left(3 \cdot \left(\left(y + \frac{1}{x \cdot 9}\right) - 1\right)\right)} \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(\sqrt{x}\right), \color{blue}{\left(3 \cdot \left(\left(y + \frac{1}{x \cdot 9}\right) - 1\right)\right)}\right) \]

      4. sqrt-lowering-sqrt.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \left(\color{blue}{3} \cdot \left(\left(y + \frac{1}{x \cdot 9}\right) - 1\right)\right)\right) \]

      5. associate--l+ N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \left(3 \cdot \left(y + \color{blue}{\left(\frac{1}{x \cdot 9} - 1\right)}\right)\right)\right) \]

      6. distribute-lft-in N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \left(3 \cdot y + \color{blue}{3 \cdot \left(\frac{1}{x \cdot 9} - 1\right)}\right)\right) \]

      7. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \left(3 \cdot y + \left(\frac{1}{x \cdot 9} - 1\right) \cdot \color{blue}{3}\right)\right) \]

      8. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{+.f64}\left(\left(3 \cdot y\right), \color{blue}{\left(\left(\frac{1}{x \cdot 9} - 1\right) \cdot 3\right)}\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(3, y\right), \left(\color{blue}{\left(\frac{1}{x \cdot 9} - 1\right)} \cdot 3\right)\right)\right) \]

      10. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(3, y\right), \left(3 \cdot \color{blue}{\left(\frac{1}{x \cdot 9} - 1\right)}\right)\right)\right) \]

      11. sub-neg N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(3, y\right), \left(3 \cdot \left(\frac{1}{x \cdot 9} + \color{blue}{\left(\mathsf{neg}\left(1\right)\right)}\right)\right)\right)\right) \]

      12. +-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(3, y\right), \left(3 \cdot \left(\left(\mathsf{neg}\left(1\right)\right) + \color{blue}{\frac{1}{x \cdot 9}}\right)\right)\right)\right) \]

      13. distribute-lft-in N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(3, y\right), \left(3 \cdot \left(\mathsf{neg}\left(1\right)\right) + \color{blue}{3 \cdot \frac{1}{x \cdot 9}}\right)\right)\right) \]

      14. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(3, y\right), \left(3 \cdot \left(\mathsf{neg}\left(1\right)\right) + \frac{1}{x \cdot 9} \cdot \color{blue}{3}\right)\right)\right) \]

      15. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(3, y\right), \mathsf{+.f64}\left(\left(3 \cdot \left(\mathsf{neg}\left(1\right)\right)\right), \color{blue}{\left(\frac{1}{x \cdot 9} \cdot 3\right)}\right)\right)\right) \]

      16. metadata-eval N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(3, y\right), \mathsf{+.f64}\left(\left(3 \cdot -1\right), \left(\frac{1}{\color{blue}{x \cdot 9}} \cdot 3\right)\right)\right)\right) \]

      17. metadata-eval N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(3, y\right), \mathsf{+.f64}\left(-3, \left(\color{blue}{\frac{1}{x \cdot 9}} \cdot 3\right)\right)\right)\right) \]

      18. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(3, y\right), \mathsf{+.f64}\left(-3, \left(3 \cdot \color{blue}{\frac{1}{x \cdot 9}}\right)\right)\right)\right) \]

      19. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(3, y\right), \mathsf{+.f64}\left(-3, \left(3 \cdot \frac{1}{9 \cdot \color{blue}{x}}\right)\right)\right)\right) \]

      20. associate-/r* N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(3, y\right), \mathsf{+.f64}\left(-3, \left(3 \cdot \frac{\frac{1}{9}}{\color{blue}{x}}\right)\right)\right)\right) \]

      21. associate-*r/ N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(3, y\right), \mathsf{+.f64}\left(-3, \left(\frac{3 \cdot \frac{1}{9}}{\color{blue}{x}}\right)\right)\right)\right) \]

      22. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(3, y\right), \mathsf{+.f64}\left(-3, \mathsf{/.f64}\left(\left(3 \cdot \frac{1}{9}\right), \color{blue}{x}\right)\right)\right)\right) \]

   3. Simplified 99.3%

      \[\leadsto \color{blue}{\sqrt{x} \cdot \left(3 \cdot y + \left(-3 + \frac{0.3333333333333333}{x}\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in x around 0

      \[\leadsto \color{blue}{\frac{1}{3} \cdot \sqrt{\frac{1}{x}}} \]
   6. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\frac{1}{3}, \color{blue}{\left(\sqrt{\frac{1}{x}}\right)}\right) \]

      2. sqrt-lowering-sqrt.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\frac{1}{3}, \mathsf{sqrt.f64}\left(\left(\frac{1}{x}\right)\right)\right) \]

      3. /-lowering-/.f64 77.2%

         \[\leadsto \mathsf{*.f64}\left(\frac{1}{3}, \mathsf{sqrt.f64}\left(\mathsf{/.f64}\left(1, x\right)\right)\right) \]

   7. Simplified 77.2%

      \[\leadsto \color{blue}{0.3333333333333333 \cdot \sqrt{\frac{1}{x}}} \]
   8. Step-by-step derivation

      1. sqrt-div N/A

         \[\leadsto \frac{1}{3} \cdot \frac{\sqrt{1}}{\color{blue}{\sqrt{x}}} \]

      2. metadata-eval N/A

         \[\leadsto \frac{1}{3} \cdot \frac{1}{\sqrt{\color{blue}{x}}} \]

      3. un-div-inv N/A

         \[\leadsto \frac{\frac{1}{3}}{\color{blue}{\sqrt{x}}} \]

      4. metadata-eval N/A

         \[\leadsto \frac{1 \cdot \frac{1}{3}}{\sqrt{\color{blue}{x}}} \]

      5. pow1/2 N/A

         \[\leadsto \frac{1 \cdot \frac{1}{3}}{{x}^{\color{blue}{\frac{1}{2}}}} \]

      6. metadata-eval N/A

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

      7. pow-plus N/A

         \[\leadsto \frac{1 \cdot \frac{1}{3}}{{x}^{\frac{-1}{2}} \cdot \color{blue}{x}} \]

      8. frac-times N/A

         \[\leadsto \frac{1}{{x}^{\frac{-1}{2}}} \cdot \color{blue}{\frac{\frac{1}{3}}{x}} \]

      9. pow-flip N/A

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

      10. metadata-eval N/A

          \[\leadsto {x}^{\frac{1}{2}} \cdot \frac{\frac{1}{3}}{x} \]

      11. metadata-eval N/A

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

      12. pow-plus N/A

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

      13. associate-*l* N/A

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

      14. remove-double-div N/A

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

      15. clear-num N/A

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

      16. frac-times N/A

          \[\leadsto {x}^{\frac{-1}{2}} \cdot \frac{1 \cdot 1}{\color{blue}{\frac{1}{x} \cdot \frac{x}{\frac{1}{3}}}} \]

      17. metadata-eval N/A

          \[\leadsto {x}^{\frac{-1}{2}} \cdot \frac{1}{\color{blue}{\frac{1}{x}} \cdot \frac{x}{\frac{1}{3}}} \]

      18. un-div-inv N/A

          \[\leadsto \frac{{x}^{\frac{-1}{2}}}{\color{blue}{\frac{1}{x} \cdot \frac{x}{\frac{1}{3}}}} \]

      19. inv-pow N/A

          \[\leadsto \frac{{x}^{\frac{-1}{2}}}{{x}^{-1} \cdot \frac{\color{blue}{x}}{\frac{1}{3}}} \]

      20. clear-num N/A

          \[\leadsto \frac{{x}^{\frac{-1}{2}}}{{x}^{-1} \cdot \frac{1}{\color{blue}{\frac{\frac{1}{3}}{x}}}} \]

      21. inv-pow N/A

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

      22. pow-prod-down N/A

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

      23. *-commutative N/A

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

      24. div-inv N/A

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

      25. associate-*l* N/A

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

      26. lft-mult-inverse N/A

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

      27. metadata-eval N/A

          \[\leadsto \frac{{x}^{\frac{-1}{2}}}{{\frac{1}{3}}^{-1}} \]

   9. Applied egg-rr 77.3%

      \[\leadsto \color{blue}{\frac{{x}^{-0.5}}{3}} \]

   if 4.40000000000000016e-4 < x

   1. Initial program 99.6%

      \[\left(3 \cdot \sqrt{x}\right) \cdot \left(\left(y + \frac{1}{x \cdot 9}\right) - 1\right) \]
   2. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \left(\sqrt{x} \cdot 3\right) \cdot \left(\color{blue}{\left(y + \frac{1}{x \cdot 9}\right)} - 1\right) \]

      2. associate-*l* N/A

         \[\leadsto \sqrt{x} \cdot \color{blue}{\left(3 \cdot \left(\left(y + \frac{1}{x \cdot 9}\right) - 1\right)\right)} \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(\sqrt{x}\right), \color{blue}{\left(3 \cdot \left(\left(y + \frac{1}{x \cdot 9}\right) - 1\right)\right)}\right) \]

      4. sqrt-lowering-sqrt.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \left(\color{blue}{3} \cdot \left(\left(y + \frac{1}{x \cdot 9}\right) - 1\right)\right)\right) \]

      5. associate--l+ N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \left(3 \cdot \left(y + \color{blue}{\left(\frac{1}{x \cdot 9} - 1\right)}\right)\right)\right) \]

      6. distribute-lft-in N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \left(3 \cdot y + \color{blue}{3 \cdot \left(\frac{1}{x \cdot 9} - 1\right)}\right)\right) \]

      7. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \left(3 \cdot y + \left(\frac{1}{x \cdot 9} - 1\right) \cdot \color{blue}{3}\right)\right) \]

      8. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{+.f64}\left(\left(3 \cdot y\right), \color{blue}{\left(\left(\frac{1}{x \cdot 9} - 1\right) \cdot 3\right)}\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(3, y\right), \left(\color{blue}{\left(\frac{1}{x \cdot 9} - 1\right)} \cdot 3\right)\right)\right) \]

      10. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(3, y\right), \left(3 \cdot \color{blue}{\left(\frac{1}{x \cdot 9} - 1\right)}\right)\right)\right) \]

      11. sub-neg N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(3, y\right), \left(3 \cdot \left(\frac{1}{x \cdot 9} + \color{blue}{\left(\mathsf{neg}\left(1\right)\right)}\right)\right)\right)\right) \]

      12. +-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(3, y\right), \left(3 \cdot \left(\left(\mathsf{neg}\left(1\right)\right) + \color{blue}{\frac{1}{x \cdot 9}}\right)\right)\right)\right) \]

      13. distribute-lft-in N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(3, y\right), \left(3 \cdot \left(\mathsf{neg}\left(1\right)\right) + \color{blue}{3 \cdot \frac{1}{x \cdot 9}}\right)\right)\right) \]

      14. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(3, y\right), \left(3 \cdot \left(\mathsf{neg}\left(1\right)\right) + \frac{1}{x \cdot 9} \cdot \color{blue}{3}\right)\right)\right) \]

      15. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(3, y\right), \mathsf{+.f64}\left(\left(3 \cdot \left(\mathsf{neg}\left(1\right)\right)\right), \color{blue}{\left(\frac{1}{x \cdot 9} \cdot 3\right)}\right)\right)\right) \]

      16. metadata-eval N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(3, y\right), \mathsf{+.f64}\left(\left(3 \cdot -1\right), \left(\frac{1}{\color{blue}{x \cdot 9}} \cdot 3\right)\right)\right)\right) \]

      17. metadata-eval N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(3, y\right), \mathsf{+.f64}\left(-3, \left(\color{blue}{\frac{1}{x \cdot 9}} \cdot 3\right)\right)\right)\right) \]

      18. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(3, y\right), \mathsf{+.f64}\left(-3, \left(3 \cdot \color{blue}{\frac{1}{x \cdot 9}}\right)\right)\right)\right) \]

      19. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(3, y\right), \mathsf{+.f64}\left(-3, \left(3 \cdot \frac{1}{9 \cdot \color{blue}{x}}\right)\right)\right)\right) \]

      20. associate-/r* N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(3, y\right), \mathsf{+.f64}\left(-3, \left(3 \cdot \frac{\frac{1}{9}}{\color{blue}{x}}\right)\right)\right)\right) \]

      21. associate-*r/ N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(3, y\right), \mathsf{+.f64}\left(-3, \left(\frac{3 \cdot \frac{1}{9}}{\color{blue}{x}}\right)\right)\right)\right) \]

      22. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(3, y\right), \mathsf{+.f64}\left(-3, \mathsf{/.f64}\left(\left(3 \cdot \frac{1}{9}\right), \color{blue}{x}\right)\right)\right)\right) \]

   3. Simplified 99.6%

      \[\leadsto \color{blue}{\sqrt{x} \cdot \left(3 \cdot y + \left(-3 + \frac{0.3333333333333333}{x}\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf

      \[\leadsto \color{blue}{\sqrt{x} \cdot \left(3 \cdot y - 3\right)} \]
   6. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(\sqrt{x}\right), \color{blue}{\left(3 \cdot y - 3\right)}\right) \]

      2. sqrt-lowering-sqrt.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \left(\color{blue}{3 \cdot y} - 3\right)\right) \]

      3. sub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \left(3 \cdot y + \color{blue}{\left(\mathsf{neg}\left(3\right)\right)}\right)\right) \]

      4. metadata-eval N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \left(3 \cdot y + -3\right)\right) \]

      5. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{+.f64}\left(\left(3 \cdot y\right), \color{blue}{-3}\right)\right) \]

      6. *-lowering-*.f64 98.6%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(3, y\right), -3\right)\right) \]

   7. Simplified 98.6%

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

   8. Taylor expanded in y around 0

      \[\leadsto \color{blue}{-3 \cdot \sqrt{x}} \]
   9. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \sqrt{x} \cdot \color{blue}{-3} \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(\sqrt{x}\right), \color{blue}{-3}\right) \]

      3. sqrt-lowering-sqrt.f64 51.5%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), -3\right) \]

   10. Simplified 51.5%

       \[\leadsto \color{blue}{\sqrt{x} \cdot -3} \]
   11. Step-by-step derivation

       1. *-commutative N/A

          \[\leadsto -3 \cdot \color{blue}{\sqrt{x}} \]

       2. pow1/2 N/A

          \[\leadsto -3 \cdot {x}^{\color{blue}{\frac{1}{2}}} \]

       3. metadata-eval N/A

          \[\leadsto -3 \cdot {x}^{\left(\mathsf{neg}\left(\frac{-1}{2}\right)\right)} \]

       4. pow-flip N/A

          \[\leadsto -3 \cdot \frac{1}{\color{blue}{{x}^{\frac{-1}{2}}}} \]

       5. un-div-inv N/A

          \[\leadsto \frac{-3}{\color{blue}{{x}^{\frac{-1}{2}}}} \]

       6. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(-3, \color{blue}{\left({x}^{\frac{-1}{2}}\right)}\right) \]

       7. pow-lowering-pow.f64 51.6%

          \[\leadsto \mathsf{/.f64}\left(-3, \mathsf{pow.f64}\left(x, \color{blue}{\frac{-1}{2}}\right)\right) \]

   12. Applied egg-rr 51.6%

       \[\leadsto \color{blue}{\frac{-3}{{x}^{-0.5}}} \]
3. Recombined 2 regimes into one program.
4. Add Preprocessing

Alternative 10: 60.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 0.00044:\\ \;\;\;\;0.3333333333333333 \cdot {x}^{-0.5}\\ \mathbf{else}:\\ \;\;\;\;\frac{-3}{{x}^{-0.5}}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x 0.00044) (* 0.3333333333333333 (pow x -0.5)) (/ -3.0 (pow x -0.5))))

C

double code(double x, double y) {
	double tmp;
	if (x <= 0.00044) {
		tmp = 0.3333333333333333 * pow(x, -0.5);
	} else {
		tmp = -3.0 / pow(x, -0.5);
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (x <= 0.00044d0) then
        tmp = 0.3333333333333333d0 * (x ** (-0.5d0))
    else
        tmp = (-3.0d0) / (x ** (-0.5d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= 0.00044) {
		tmp = 0.3333333333333333 * Math.pow(x, -0.5);
	} else {
		tmp = -3.0 / Math.pow(x, -0.5);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= 0.00044:
		tmp = 0.3333333333333333 * math.pow(x, -0.5)
	else:
		tmp = -3.0 / math.pow(x, -0.5)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= 0.00044)
		tmp = Float64(0.3333333333333333 * (x ^ -0.5));
	else
		tmp = Float64(-3.0 / (x ^ -0.5));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= 0.00044)
		tmp = 0.3333333333333333 * (x ^ -0.5);
	else
		tmp = -3.0 / (x ^ -0.5);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, 0.00044], N[(0.3333333333333333 * N[Power[x, -0.5], $MachinePrecision]), $MachinePrecision], N[(-3.0 / N[Power[x, -0.5], $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < 4.40000000000000016e-4

   1. Initial program 99.2%

      \[\left(3 \cdot \sqrt{x}\right) \cdot \left(\left(y + \frac{1}{x \cdot 9}\right) - 1\right) \]
   2. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \left(\sqrt{x} \cdot 3\right) \cdot \left(\color{blue}{\left(y + \frac{1}{x \cdot 9}\right)} - 1\right) \]

      2. associate-*l* N/A

         \[\leadsto \sqrt{x} \cdot \color{blue}{\left(3 \cdot \left(\left(y + \frac{1}{x \cdot 9}\right) - 1\right)\right)} \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(\sqrt{x}\right), \color{blue}{\left(3 \cdot \left(\left(y + \frac{1}{x \cdot 9}\right) - 1\right)\right)}\right) \]

      4. sqrt-lowering-sqrt.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \left(\color{blue}{3} \cdot \left(\left(y + \frac{1}{x \cdot 9}\right) - 1\right)\right)\right) \]

      5. associate--l+ N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \left(3 \cdot \left(y + \color{blue}{\left(\frac{1}{x \cdot 9} - 1\right)}\right)\right)\right) \]

      6. distribute-lft-in N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \left(3 \cdot y + \color{blue}{3 \cdot \left(\frac{1}{x \cdot 9} - 1\right)}\right)\right) \]

      7. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \left(3 \cdot y + \left(\frac{1}{x \cdot 9} - 1\right) \cdot \color{blue}{3}\right)\right) \]

      8. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{+.f64}\left(\left(3 \cdot y\right), \color{blue}{\left(\left(\frac{1}{x \cdot 9} - 1\right) \cdot 3\right)}\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(3, y\right), \left(\color{blue}{\left(\frac{1}{x \cdot 9} - 1\right)} \cdot 3\right)\right)\right) \]

      10. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(3, y\right), \left(3 \cdot \color{blue}{\left(\frac{1}{x \cdot 9} - 1\right)}\right)\right)\right) \]

      11. sub-neg N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(3, y\right), \left(3 \cdot \left(\frac{1}{x \cdot 9} + \color{blue}{\left(\mathsf{neg}\left(1\right)\right)}\right)\right)\right)\right) \]

      12. +-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(3, y\right), \left(3 \cdot \left(\left(\mathsf{neg}\left(1\right)\right) + \color{blue}{\frac{1}{x \cdot 9}}\right)\right)\right)\right) \]

      13. distribute-lft-in N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(3, y\right), \left(3 \cdot \left(\mathsf{neg}\left(1\right)\right) + \color{blue}{3 \cdot \frac{1}{x \cdot 9}}\right)\right)\right) \]

      14. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(3, y\right), \left(3 \cdot \left(\mathsf{neg}\left(1\right)\right) + \frac{1}{x \cdot 9} \cdot \color{blue}{3}\right)\right)\right) \]

      15. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(3, y\right), \mathsf{+.f64}\left(\left(3 \cdot \left(\mathsf{neg}\left(1\right)\right)\right), \color{blue}{\left(\frac{1}{x \cdot 9} \cdot 3\right)}\right)\right)\right) \]

      16. metadata-eval N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(3, y\right), \mathsf{+.f64}\left(\left(3 \cdot -1\right), \left(\frac{1}{\color{blue}{x \cdot 9}} \cdot 3\right)\right)\right)\right) \]

      17. metadata-eval N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(3, y\right), \mathsf{+.f64}\left(-3, \left(\color{blue}{\frac{1}{x \cdot 9}} \cdot 3\right)\right)\right)\right) \]

      18. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(3, y\right), \mathsf{+.f64}\left(-3, \left(3 \cdot \color{blue}{\frac{1}{x \cdot 9}}\right)\right)\right)\right) \]

      19. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(3, y\right), \mathsf{+.f64}\left(-3, \left(3 \cdot \frac{1}{9 \cdot \color{blue}{x}}\right)\right)\right)\right) \]

      20. associate-/r* N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(3, y\right), \mathsf{+.f64}\left(-3, \left(3 \cdot \frac{\frac{1}{9}}{\color{blue}{x}}\right)\right)\right)\right) \]

      21. associate-*r/ N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(3, y\right), \mathsf{+.f64}\left(-3, \left(\frac{3 \cdot \frac{1}{9}}{\color{blue}{x}}\right)\right)\right)\right) \]

      22. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(3, y\right), \mathsf{+.f64}\left(-3, \mathsf{/.f64}\left(\left(3 \cdot \frac{1}{9}\right), \color{blue}{x}\right)\right)\right)\right) \]

   3. Simplified 99.3%

      \[\leadsto \color{blue}{\sqrt{x} \cdot \left(3 \cdot y + \left(-3 + \frac{0.3333333333333333}{x}\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in x around 0

      \[\leadsto \color{blue}{\frac{1}{3} \cdot \sqrt{\frac{1}{x}}} \]
   6. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\frac{1}{3}, \color{blue}{\left(\sqrt{\frac{1}{x}}\right)}\right) \]

      2. sqrt-lowering-sqrt.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\frac{1}{3}, \mathsf{sqrt.f64}\left(\left(\frac{1}{x}\right)\right)\right) \]

      3. /-lowering-/.f64 77.2%

         \[\leadsto \mathsf{*.f64}\left(\frac{1}{3}, \mathsf{sqrt.f64}\left(\mathsf{/.f64}\left(1, x\right)\right)\right) \]

   7. Simplified 77.2%

      \[\leadsto \color{blue}{0.3333333333333333 \cdot \sqrt{\frac{1}{x}}} \]
   8. Step-by-step derivation

      1. inv-pow N/A

         \[\leadsto \frac{1}{3} \cdot \sqrt{{x}^{-1}} \]

      2. sqrt-pow1 N/A

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

      3. metadata-eval N/A

         \[\leadsto \frac{1}{3} \cdot {x}^{\frac{-1}{2}} \]

      4. *-commutative N/A

         \[\leadsto {x}^{\frac{-1}{2}} \cdot \color{blue}{\frac{1}{3}} \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left({x}^{\frac{-1}{2}}\right), \color{blue}{\frac{1}{3}}\right) \]

      6. pow-lowering-pow.f64 77.3%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{pow.f64}\left(x, \frac{-1}{2}\right), \frac{1}{3}\right) \]

   9. Applied egg-rr 77.3%

      \[\leadsto \color{blue}{{x}^{-0.5} \cdot 0.3333333333333333} \]

   if 4.40000000000000016e-4 < x

   1. Initial program 99.6%

      \[\left(3 \cdot \sqrt{x}\right) \cdot \left(\left(y + \frac{1}{x \cdot 9}\right) - 1\right) \]
   2. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \left(\sqrt{x} \cdot 3\right) \cdot \left(\color{blue}{\left(y + \frac{1}{x \cdot 9}\right)} - 1\right) \]

      2. associate-*l* N/A

         \[\leadsto \sqrt{x} \cdot \color{blue}{\left(3 \cdot \left(\left(y + \frac{1}{x \cdot 9}\right) - 1\right)\right)} \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(\sqrt{x}\right), \color{blue}{\left(3 \cdot \left(\left(y + \frac{1}{x \cdot 9}\right) - 1\right)\right)}\right) \]

      4. sqrt-lowering-sqrt.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \left(\color{blue}{3} \cdot \left(\left(y + \frac{1}{x \cdot 9}\right) - 1\right)\right)\right) \]

      5. associate--l+ N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \left(3 \cdot \left(y + \color{blue}{\left(\frac{1}{x \cdot 9} - 1\right)}\right)\right)\right) \]

      6. distribute-lft-in N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \left(3 \cdot y + \color{blue}{3 \cdot \left(\frac{1}{x \cdot 9} - 1\right)}\right)\right) \]

      7. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \left(3 \cdot y + \left(\frac{1}{x \cdot 9} - 1\right) \cdot \color{blue}{3}\right)\right) \]

      8. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{+.f64}\left(\left(3 \cdot y\right), \color{blue}{\left(\left(\frac{1}{x \cdot 9} - 1\right) \cdot 3\right)}\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(3, y\right), \left(\color{blue}{\left(\frac{1}{x \cdot 9} - 1\right)} \cdot 3\right)\right)\right) \]

      10. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(3, y\right), \left(3 \cdot \color{blue}{\left(\frac{1}{x \cdot 9} - 1\right)}\right)\right)\right) \]

      11. sub-neg N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(3, y\right), \left(3 \cdot \left(\frac{1}{x \cdot 9} + \color{blue}{\left(\mathsf{neg}\left(1\right)\right)}\right)\right)\right)\right) \]

      12. +-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(3, y\right), \left(3 \cdot \left(\left(\mathsf{neg}\left(1\right)\right) + \color{blue}{\frac{1}{x \cdot 9}}\right)\right)\right)\right) \]

      13. distribute-lft-in N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(3, y\right), \left(3 \cdot \left(\mathsf{neg}\left(1\right)\right) + \color{blue}{3 \cdot \frac{1}{x \cdot 9}}\right)\right)\right) \]

      14. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(3, y\right), \left(3 \cdot \left(\mathsf{neg}\left(1\right)\right) + \frac{1}{x \cdot 9} \cdot \color{blue}{3}\right)\right)\right) \]

      15. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(3, y\right), \mathsf{+.f64}\left(\left(3 \cdot \left(\mathsf{neg}\left(1\right)\right)\right), \color{blue}{\left(\frac{1}{x \cdot 9} \cdot 3\right)}\right)\right)\right) \]

      16. metadata-eval N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(3, y\right), \mathsf{+.f64}\left(\left(3 \cdot -1\right), \left(\frac{1}{\color{blue}{x \cdot 9}} \cdot 3\right)\right)\right)\right) \]

      17. metadata-eval N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(3, y\right), \mathsf{+.f64}\left(-3, \left(\color{blue}{\frac{1}{x \cdot 9}} \cdot 3\right)\right)\right)\right) \]

      18. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(3, y\right), \mathsf{+.f64}\left(-3, \left(3 \cdot \color{blue}{\frac{1}{x \cdot 9}}\right)\right)\right)\right) \]

      19. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(3, y\right), \mathsf{+.f64}\left(-3, \left(3 \cdot \frac{1}{9 \cdot \color{blue}{x}}\right)\right)\right)\right) \]

      20. associate-/r* N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(3, y\right), \mathsf{+.f64}\left(-3, \left(3 \cdot \frac{\frac{1}{9}}{\color{blue}{x}}\right)\right)\right)\right) \]

      21. associate-*r/ N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(3, y\right), \mathsf{+.f64}\left(-3, \left(\frac{3 \cdot \frac{1}{9}}{\color{blue}{x}}\right)\right)\right)\right) \]

      22. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(3, y\right), \mathsf{+.f64}\left(-3, \mathsf{/.f64}\left(\left(3 \cdot \frac{1}{9}\right), \color{blue}{x}\right)\right)\right)\right) \]

   3. Simplified 99.6%

      \[\leadsto \color{blue}{\sqrt{x} \cdot \left(3 \cdot y + \left(-3 + \frac{0.3333333333333333}{x}\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf

      \[\leadsto \color{blue}{\sqrt{x} \cdot \left(3 \cdot y - 3\right)} \]
   6. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(\sqrt{x}\right), \color{blue}{\left(3 \cdot y - 3\right)}\right) \]

      2. sqrt-lowering-sqrt.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \left(\color{blue}{3 \cdot y} - 3\right)\right) \]

      3. sub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \left(3 \cdot y + \color{blue}{\left(\mathsf{neg}\left(3\right)\right)}\right)\right) \]

      4. metadata-eval N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \left(3 \cdot y + -3\right)\right) \]

      5. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{+.f64}\left(\left(3 \cdot y\right), \color{blue}{-3}\right)\right) \]

      6. *-lowering-*.f64 98.6%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(3, y\right), -3\right)\right) \]

   7. Simplified 98.6%

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

   8. Taylor expanded in y around 0

      \[\leadsto \color{blue}{-3 \cdot \sqrt{x}} \]
   9. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \sqrt{x} \cdot \color{blue}{-3} \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(\sqrt{x}\right), \color{blue}{-3}\right) \]

      3. sqrt-lowering-sqrt.f64 51.5%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), -3\right) \]

   10. Simplified 51.5%

       \[\leadsto \color{blue}{\sqrt{x} \cdot -3} \]
   11. Step-by-step derivation

       1. *-commutative N/A

          \[\leadsto -3 \cdot \color{blue}{\sqrt{x}} \]

       2. pow1/2 N/A

          \[\leadsto -3 \cdot {x}^{\color{blue}{\frac{1}{2}}} \]

       3. metadata-eval N/A

          \[\leadsto -3 \cdot {x}^{\left(\mathsf{neg}\left(\frac{-1}{2}\right)\right)} \]

       4. pow-flip N/A

          \[\leadsto -3 \cdot \frac{1}{\color{blue}{{x}^{\frac{-1}{2}}}} \]

       5. un-div-inv N/A

          \[\leadsto \frac{-3}{\color{blue}{{x}^{\frac{-1}{2}}}} \]

       6. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{/.f64}\left(-3, \color{blue}{\left({x}^{\frac{-1}{2}}\right)}\right) \]

       7. pow-lowering-pow.f64 51.6%

          \[\leadsto \mathsf{/.f64}\left(-3, \mathsf{pow.f64}\left(x, \color{blue}{\frac{-1}{2}}\right)\right) \]

   12. Applied egg-rr 51.6%

       \[\leadsto \color{blue}{\frac{-3}{{x}^{-0.5}}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 63.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 0.00044:\\ \;\;\;\;0.3333333333333333 \cdot {x}^{-0.5}\\ \mathbf{else}:\\ \;\;\;\;\frac{-3}{{x}^{-0.5}}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 60.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 0.00044:\\ \;\;\;\;0.3333333333333333 \cdot {x}^{-0.5}\\ \mathbf{else}:\\ \;\;\;\;-3 \cdot \sqrt{x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x 0.00044) (* 0.3333333333333333 (pow x -0.5)) (* -3.0 (sqrt x))))

C

double code(double x, double y) {
	double tmp;
	if (x <= 0.00044) {
		tmp = 0.3333333333333333 * pow(x, -0.5);
	} else {
		tmp = -3.0 * sqrt(x);
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (x <= 0.00044d0) then
        tmp = 0.3333333333333333d0 * (x ** (-0.5d0))
    else
        tmp = (-3.0d0) * sqrt(x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= 0.00044) {
		tmp = 0.3333333333333333 * Math.pow(x, -0.5);
	} else {
		tmp = -3.0 * Math.sqrt(x);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= 0.00044:
		tmp = 0.3333333333333333 * math.pow(x, -0.5)
	else:
		tmp = -3.0 * math.sqrt(x)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= 0.00044)
		tmp = Float64(0.3333333333333333 * (x ^ -0.5));
	else
		tmp = Float64(-3.0 * sqrt(x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= 0.00044)
		tmp = 0.3333333333333333 * (x ^ -0.5);
	else
		tmp = -3.0 * sqrt(x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, 0.00044], N[(0.3333333333333333 * N[Power[x, -0.5], $MachinePrecision]), $MachinePrecision], N[(-3.0 * N[Sqrt[x], $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < 4.40000000000000016e-4

   1. Initial program 99.2%

      \[\left(3 \cdot \sqrt{x}\right) \cdot \left(\left(y + \frac{1}{x \cdot 9}\right) - 1\right) \]
   2. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \left(\sqrt{x} \cdot 3\right) \cdot \left(\color{blue}{\left(y + \frac{1}{x \cdot 9}\right)} - 1\right) \]

      2. associate-*l* N/A

         \[\leadsto \sqrt{x} \cdot \color{blue}{\left(3 \cdot \left(\left(y + \frac{1}{x \cdot 9}\right) - 1\right)\right)} \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(\sqrt{x}\right), \color{blue}{\left(3 \cdot \left(\left(y + \frac{1}{x \cdot 9}\right) - 1\right)\right)}\right) \]

      4. sqrt-lowering-sqrt.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \left(\color{blue}{3} \cdot \left(\left(y + \frac{1}{x \cdot 9}\right) - 1\right)\right)\right) \]

      5. associate--l+ N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \left(3 \cdot \left(y + \color{blue}{\left(\frac{1}{x \cdot 9} - 1\right)}\right)\right)\right) \]

      6. distribute-lft-in N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \left(3 \cdot y + \color{blue}{3 \cdot \left(\frac{1}{x \cdot 9} - 1\right)}\right)\right) \]

      7. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \left(3 \cdot y + \left(\frac{1}{x \cdot 9} - 1\right) \cdot \color{blue}{3}\right)\right) \]

      8. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{+.f64}\left(\left(3 \cdot y\right), \color{blue}{\left(\left(\frac{1}{x \cdot 9} - 1\right) \cdot 3\right)}\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(3, y\right), \left(\color{blue}{\left(\frac{1}{x \cdot 9} - 1\right)} \cdot 3\right)\right)\right) \]

      10. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(3, y\right), \left(3 \cdot \color{blue}{\left(\frac{1}{x \cdot 9} - 1\right)}\right)\right)\right) \]

      11. sub-neg N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(3, y\right), \left(3 \cdot \left(\frac{1}{x \cdot 9} + \color{blue}{\left(\mathsf{neg}\left(1\right)\right)}\right)\right)\right)\right) \]

      12. +-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(3, y\right), \left(3 \cdot \left(\left(\mathsf{neg}\left(1\right)\right) + \color{blue}{\frac{1}{x \cdot 9}}\right)\right)\right)\right) \]

      13. distribute-lft-in N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(3, y\right), \left(3 \cdot \left(\mathsf{neg}\left(1\right)\right) + \color{blue}{3 \cdot \frac{1}{x \cdot 9}}\right)\right)\right) \]

      14. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(3, y\right), \left(3 \cdot \left(\mathsf{neg}\left(1\right)\right) + \frac{1}{x \cdot 9} \cdot \color{blue}{3}\right)\right)\right) \]

      15. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(3, y\right), \mathsf{+.f64}\left(\left(3 \cdot \left(\mathsf{neg}\left(1\right)\right)\right), \color{blue}{\left(\frac{1}{x \cdot 9} \cdot 3\right)}\right)\right)\right) \]

      16. metadata-eval N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(3, y\right), \mathsf{+.f64}\left(\left(3 \cdot -1\right), \left(\frac{1}{\color{blue}{x \cdot 9}} \cdot 3\right)\right)\right)\right) \]

      17. metadata-eval N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(3, y\right), \mathsf{+.f64}\left(-3, \left(\color{blue}{\frac{1}{x \cdot 9}} \cdot 3\right)\right)\right)\right) \]

      18. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(3, y\right), \mathsf{+.f64}\left(-3, \left(3 \cdot \color{blue}{\frac{1}{x \cdot 9}}\right)\right)\right)\right) \]

      19. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(3, y\right), \mathsf{+.f64}\left(-3, \left(3 \cdot \frac{1}{9 \cdot \color{blue}{x}}\right)\right)\right)\right) \]

      20. associate-/r* N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(3, y\right), \mathsf{+.f64}\left(-3, \left(3 \cdot \frac{\frac{1}{9}}{\color{blue}{x}}\right)\right)\right)\right) \]

      21. associate-*r/ N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(3, y\right), \mathsf{+.f64}\left(-3, \left(\frac{3 \cdot \frac{1}{9}}{\color{blue}{x}}\right)\right)\right)\right) \]

      22. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(3, y\right), \mathsf{+.f64}\left(-3, \mathsf{/.f64}\left(\left(3 \cdot \frac{1}{9}\right), \color{blue}{x}\right)\right)\right)\right) \]

   3. Simplified 99.3%

      \[\leadsto \color{blue}{\sqrt{x} \cdot \left(3 \cdot y + \left(-3 + \frac{0.3333333333333333}{x}\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in x around 0

      \[\leadsto \color{blue}{\frac{1}{3} \cdot \sqrt{\frac{1}{x}}} \]
   6. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\frac{1}{3}, \color{blue}{\left(\sqrt{\frac{1}{x}}\right)}\right) \]

      2. sqrt-lowering-sqrt.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\frac{1}{3}, \mathsf{sqrt.f64}\left(\left(\frac{1}{x}\right)\right)\right) \]

      3. /-lowering-/.f64 77.2%

         \[\leadsto \mathsf{*.f64}\left(\frac{1}{3}, \mathsf{sqrt.f64}\left(\mathsf{/.f64}\left(1, x\right)\right)\right) \]

   7. Simplified 77.2%

      \[\leadsto \color{blue}{0.3333333333333333 \cdot \sqrt{\frac{1}{x}}} \]
   8. Step-by-step derivation

      1. inv-pow N/A

         \[\leadsto \frac{1}{3} \cdot \sqrt{{x}^{-1}} \]

      2. sqrt-pow1 N/A

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

      3. metadata-eval N/A

         \[\leadsto \frac{1}{3} \cdot {x}^{\frac{-1}{2}} \]

      4. *-commutative N/A

         \[\leadsto {x}^{\frac{-1}{2}} \cdot \color{blue}{\frac{1}{3}} \]

      5. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left({x}^{\frac{-1}{2}}\right), \color{blue}{\frac{1}{3}}\right) \]

      6. pow-lowering-pow.f64 77.3%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{pow.f64}\left(x, \frac{-1}{2}\right), \frac{1}{3}\right) \]

   9. Applied egg-rr 77.3%

      \[\leadsto \color{blue}{{x}^{-0.5} \cdot 0.3333333333333333} \]

   if 4.40000000000000016e-4 < x

   1. Initial program 99.6%

      \[\left(3 \cdot \sqrt{x}\right) \cdot \left(\left(y + \frac{1}{x \cdot 9}\right) - 1\right) \]
   2. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \left(\sqrt{x} \cdot 3\right) \cdot \left(\color{blue}{\left(y + \frac{1}{x \cdot 9}\right)} - 1\right) \]

      2. associate-*l* N/A

         \[\leadsto \sqrt{x} \cdot \color{blue}{\left(3 \cdot \left(\left(y + \frac{1}{x \cdot 9}\right) - 1\right)\right)} \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(\sqrt{x}\right), \color{blue}{\left(3 \cdot \left(\left(y + \frac{1}{x \cdot 9}\right) - 1\right)\right)}\right) \]

      4. sqrt-lowering-sqrt.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \left(\color{blue}{3} \cdot \left(\left(y + \frac{1}{x \cdot 9}\right) - 1\right)\right)\right) \]

      5. associate--l+ N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \left(3 \cdot \left(y + \color{blue}{\left(\frac{1}{x \cdot 9} - 1\right)}\right)\right)\right) \]

      6. distribute-lft-in N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \left(3 \cdot y + \color{blue}{3 \cdot \left(\frac{1}{x \cdot 9} - 1\right)}\right)\right) \]

      7. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \left(3 \cdot y + \left(\frac{1}{x \cdot 9} - 1\right) \cdot \color{blue}{3}\right)\right) \]

      8. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{+.f64}\left(\left(3 \cdot y\right), \color{blue}{\left(\left(\frac{1}{x \cdot 9} - 1\right) \cdot 3\right)}\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(3, y\right), \left(\color{blue}{\left(\frac{1}{x \cdot 9} - 1\right)} \cdot 3\right)\right)\right) \]

      10. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(3, y\right), \left(3 \cdot \color{blue}{\left(\frac{1}{x \cdot 9} - 1\right)}\right)\right)\right) \]

      11. sub-neg N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(3, y\right), \left(3 \cdot \left(\frac{1}{x \cdot 9} + \color{blue}{\left(\mathsf{neg}\left(1\right)\right)}\right)\right)\right)\right) \]

      12. +-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(3, y\right), \left(3 \cdot \left(\left(\mathsf{neg}\left(1\right)\right) + \color{blue}{\frac{1}{x \cdot 9}}\right)\right)\right)\right) \]

      13. distribute-lft-in N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(3, y\right), \left(3 \cdot \left(\mathsf{neg}\left(1\right)\right) + \color{blue}{3 \cdot \frac{1}{x \cdot 9}}\right)\right)\right) \]

      14. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(3, y\right), \left(3 \cdot \left(\mathsf{neg}\left(1\right)\right) + \frac{1}{x \cdot 9} \cdot \color{blue}{3}\right)\right)\right) \]

      15. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(3, y\right), \mathsf{+.f64}\left(\left(3 \cdot \left(\mathsf{neg}\left(1\right)\right)\right), \color{blue}{\left(\frac{1}{x \cdot 9} \cdot 3\right)}\right)\right)\right) \]

      16. metadata-eval N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(3, y\right), \mathsf{+.f64}\left(\left(3 \cdot -1\right), \left(\frac{1}{\color{blue}{x \cdot 9}} \cdot 3\right)\right)\right)\right) \]

      17. metadata-eval N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(3, y\right), \mathsf{+.f64}\left(-3, \left(\color{blue}{\frac{1}{x \cdot 9}} \cdot 3\right)\right)\right)\right) \]

      18. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(3, y\right), \mathsf{+.f64}\left(-3, \left(3 \cdot \color{blue}{\frac{1}{x \cdot 9}}\right)\right)\right)\right) \]

      19. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(3, y\right), \mathsf{+.f64}\left(-3, \left(3 \cdot \frac{1}{9 \cdot \color{blue}{x}}\right)\right)\right)\right) \]

      20. associate-/r* N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(3, y\right), \mathsf{+.f64}\left(-3, \left(3 \cdot \frac{\frac{1}{9}}{\color{blue}{x}}\right)\right)\right)\right) \]

      21. associate-*r/ N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(3, y\right), \mathsf{+.f64}\left(-3, \left(\frac{3 \cdot \frac{1}{9}}{\color{blue}{x}}\right)\right)\right)\right) \]

      22. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(3, y\right), \mathsf{+.f64}\left(-3, \mathsf{/.f64}\left(\left(3 \cdot \frac{1}{9}\right), \color{blue}{x}\right)\right)\right)\right) \]

   3. Simplified 99.6%

      \[\leadsto \color{blue}{\sqrt{x} \cdot \left(3 \cdot y + \left(-3 + \frac{0.3333333333333333}{x}\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf

      \[\leadsto \color{blue}{\sqrt{x} \cdot \left(3 \cdot y - 3\right)} \]
   6. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(\sqrt{x}\right), \color{blue}{\left(3 \cdot y - 3\right)}\right) \]

      2. sqrt-lowering-sqrt.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \left(\color{blue}{3 \cdot y} - 3\right)\right) \]

      3. sub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \left(3 \cdot y + \color{blue}{\left(\mathsf{neg}\left(3\right)\right)}\right)\right) \]

      4. metadata-eval N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \left(3 \cdot y + -3\right)\right) \]

      5. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{+.f64}\left(\left(3 \cdot y\right), \color{blue}{-3}\right)\right) \]

      6. *-lowering-*.f64 98.6%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(3, y\right), -3\right)\right) \]

   7. Simplified 98.6%

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

   8. Taylor expanded in y around 0

      \[\leadsto \color{blue}{-3 \cdot \sqrt{x}} \]
   9. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \sqrt{x} \cdot \color{blue}{-3} \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(\sqrt{x}\right), \color{blue}{-3}\right) \]

      3. sqrt-lowering-sqrt.f64 51.5%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), -3\right) \]

   10. Simplified 51.5%

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

4. Final simplification 63.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 0.00044:\\ \;\;\;\;0.3333333333333333 \cdot {x}^{-0.5}\\ \mathbf{else}:\\ \;\;\;\;-3 \cdot \sqrt{x}\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 60.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 0.00044:\\ \;\;\;\;\frac{0.3333333333333333}{\sqrt{x}}\\ \mathbf{else}:\\ \;\;\;\;-3 \cdot \sqrt{x}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x 0.00044) (/ 0.3333333333333333 (sqrt x)) (* -3.0 (sqrt x))))

C

double code(double x, double y) {
	double tmp;
	if (x <= 0.00044) {
		tmp = 0.3333333333333333 / sqrt(x);
	} else {
		tmp = -3.0 * sqrt(x);
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (x <= 0.00044d0) then
        tmp = 0.3333333333333333d0 / sqrt(x)
    else
        tmp = (-3.0d0) * sqrt(x)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= 0.00044) {
		tmp = 0.3333333333333333 / Math.sqrt(x);
	} else {
		tmp = -3.0 * Math.sqrt(x);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= 0.00044:
		tmp = 0.3333333333333333 / math.sqrt(x)
	else:
		tmp = -3.0 * math.sqrt(x)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= 0.00044)
		tmp = Float64(0.3333333333333333 / sqrt(x));
	else
		tmp = Float64(-3.0 * sqrt(x));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= 0.00044)
		tmp = 0.3333333333333333 / sqrt(x);
	else
		tmp = -3.0 * sqrt(x);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, 0.00044], N[(0.3333333333333333 / N[Sqrt[x], $MachinePrecision]), $MachinePrecision], N[(-3.0 * N[Sqrt[x], $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < 4.40000000000000016e-4

   1. Initial program 99.2%

      \[\left(3 \cdot \sqrt{x}\right) \cdot \left(\left(y + \frac{1}{x \cdot 9}\right) - 1\right) \]
   2. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \left(\sqrt{x} \cdot 3\right) \cdot \left(\color{blue}{\left(y + \frac{1}{x \cdot 9}\right)} - 1\right) \]

      2. associate-*l* N/A

         \[\leadsto \sqrt{x} \cdot \color{blue}{\left(3 \cdot \left(\left(y + \frac{1}{x \cdot 9}\right) - 1\right)\right)} \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(\sqrt{x}\right), \color{blue}{\left(3 \cdot \left(\left(y + \frac{1}{x \cdot 9}\right) - 1\right)\right)}\right) \]

      4. sqrt-lowering-sqrt.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \left(\color{blue}{3} \cdot \left(\left(y + \frac{1}{x \cdot 9}\right) - 1\right)\right)\right) \]

      5. associate--l+ N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \left(3 \cdot \left(y + \color{blue}{\left(\frac{1}{x \cdot 9} - 1\right)}\right)\right)\right) \]

      6. distribute-lft-in N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \left(3 \cdot y + \color{blue}{3 \cdot \left(\frac{1}{x \cdot 9} - 1\right)}\right)\right) \]

      7. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \left(3 \cdot y + \left(\frac{1}{x \cdot 9} - 1\right) \cdot \color{blue}{3}\right)\right) \]

      8. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{+.f64}\left(\left(3 \cdot y\right), \color{blue}{\left(\left(\frac{1}{x \cdot 9} - 1\right) \cdot 3\right)}\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(3, y\right), \left(\color{blue}{\left(\frac{1}{x \cdot 9} - 1\right)} \cdot 3\right)\right)\right) \]

      10. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(3, y\right), \left(3 \cdot \color{blue}{\left(\frac{1}{x \cdot 9} - 1\right)}\right)\right)\right) \]

      11. sub-neg N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(3, y\right), \left(3 \cdot \left(\frac{1}{x \cdot 9} + \color{blue}{\left(\mathsf{neg}\left(1\right)\right)}\right)\right)\right)\right) \]

      12. +-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(3, y\right), \left(3 \cdot \left(\left(\mathsf{neg}\left(1\right)\right) + \color{blue}{\frac{1}{x \cdot 9}}\right)\right)\right)\right) \]

      13. distribute-lft-in N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(3, y\right), \left(3 \cdot \left(\mathsf{neg}\left(1\right)\right) + \color{blue}{3 \cdot \frac{1}{x \cdot 9}}\right)\right)\right) \]

      14. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(3, y\right), \left(3 \cdot \left(\mathsf{neg}\left(1\right)\right) + \frac{1}{x \cdot 9} \cdot \color{blue}{3}\right)\right)\right) \]

      15. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(3, y\right), \mathsf{+.f64}\left(\left(3 \cdot \left(\mathsf{neg}\left(1\right)\right)\right), \color{blue}{\left(\frac{1}{x \cdot 9} \cdot 3\right)}\right)\right)\right) \]

      16. metadata-eval N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(3, y\right), \mathsf{+.f64}\left(\left(3 \cdot -1\right), \left(\frac{1}{\color{blue}{x \cdot 9}} \cdot 3\right)\right)\right)\right) \]

      17. metadata-eval N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(3, y\right), \mathsf{+.f64}\left(-3, \left(\color{blue}{\frac{1}{x \cdot 9}} \cdot 3\right)\right)\right)\right) \]

      18. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(3, y\right), \mathsf{+.f64}\left(-3, \left(3 \cdot \color{blue}{\frac{1}{x \cdot 9}}\right)\right)\right)\right) \]

      19. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(3, y\right), \mathsf{+.f64}\left(-3, \left(3 \cdot \frac{1}{9 \cdot \color{blue}{x}}\right)\right)\right)\right) \]

      20. associate-/r* N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(3, y\right), \mathsf{+.f64}\left(-3, \left(3 \cdot \frac{\frac{1}{9}}{\color{blue}{x}}\right)\right)\right)\right) \]

      21. associate-*r/ N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(3, y\right), \mathsf{+.f64}\left(-3, \left(\frac{3 \cdot \frac{1}{9}}{\color{blue}{x}}\right)\right)\right)\right) \]

      22. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(3, y\right), \mathsf{+.f64}\left(-3, \mathsf{/.f64}\left(\left(3 \cdot \frac{1}{9}\right), \color{blue}{x}\right)\right)\right)\right) \]

   3. Simplified 99.3%

      \[\leadsto \color{blue}{\sqrt{x} \cdot \left(3 \cdot y + \left(-3 + \frac{0.3333333333333333}{x}\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in x around 0

      \[\leadsto \color{blue}{\frac{1}{3} \cdot \sqrt{\frac{1}{x}}} \]
   6. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\frac{1}{3}, \color{blue}{\left(\sqrt{\frac{1}{x}}\right)}\right) \]

      2. sqrt-lowering-sqrt.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\frac{1}{3}, \mathsf{sqrt.f64}\left(\left(\frac{1}{x}\right)\right)\right) \]

      3. /-lowering-/.f64 77.2%

         \[\leadsto \mathsf{*.f64}\left(\frac{1}{3}, \mathsf{sqrt.f64}\left(\mathsf{/.f64}\left(1, x\right)\right)\right) \]

   7. Simplified 77.2%

      \[\leadsto \color{blue}{0.3333333333333333 \cdot \sqrt{\frac{1}{x}}} \]
   8. Step-by-step derivation

      1. sqrt-div N/A

         \[\leadsto \frac{1}{3} \cdot \frac{\sqrt{1}}{\color{blue}{\sqrt{x}}} \]

      2. metadata-eval N/A

         \[\leadsto \frac{1}{3} \cdot \frac{1}{\sqrt{\color{blue}{x}}} \]

      3. un-div-inv N/A

         \[\leadsto \frac{\frac{1}{3}}{\color{blue}{\sqrt{x}}} \]

      4. /-lowering-/.f64 N/A

         \[\leadsto \mathsf{/.f64}\left(\frac{1}{3}, \color{blue}{\left(\sqrt{x}\right)}\right) \]

      5. sqrt-lowering-sqrt.f64 77.2%

         \[\leadsto \mathsf{/.f64}\left(\frac{1}{3}, \mathsf{sqrt.f64}\left(x\right)\right) \]

   9. Applied egg-rr 77.2%

      \[\leadsto \color{blue}{\frac{0.3333333333333333}{\sqrt{x}}} \]

   if 4.40000000000000016e-4 < x

   1. Initial program 99.6%

      \[\left(3 \cdot \sqrt{x}\right) \cdot \left(\left(y + \frac{1}{x \cdot 9}\right) - 1\right) \]
   2. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \left(\sqrt{x} \cdot 3\right) \cdot \left(\color{blue}{\left(y + \frac{1}{x \cdot 9}\right)} - 1\right) \]

      2. associate-*l* N/A

         \[\leadsto \sqrt{x} \cdot \color{blue}{\left(3 \cdot \left(\left(y + \frac{1}{x \cdot 9}\right) - 1\right)\right)} \]

      3. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(\sqrt{x}\right), \color{blue}{\left(3 \cdot \left(\left(y + \frac{1}{x \cdot 9}\right) - 1\right)\right)}\right) \]

      4. sqrt-lowering-sqrt.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \left(\color{blue}{3} \cdot \left(\left(y + \frac{1}{x \cdot 9}\right) - 1\right)\right)\right) \]

      5. associate--l+ N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \left(3 \cdot \left(y + \color{blue}{\left(\frac{1}{x \cdot 9} - 1\right)}\right)\right)\right) \]

      6. distribute-lft-in N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \left(3 \cdot y + \color{blue}{3 \cdot \left(\frac{1}{x \cdot 9} - 1\right)}\right)\right) \]

      7. *-commutative N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \left(3 \cdot y + \left(\frac{1}{x \cdot 9} - 1\right) \cdot \color{blue}{3}\right)\right) \]

      8. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{+.f64}\left(\left(3 \cdot y\right), \color{blue}{\left(\left(\frac{1}{x \cdot 9} - 1\right) \cdot 3\right)}\right)\right) \]

      9. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(3, y\right), \left(\color{blue}{\left(\frac{1}{x \cdot 9} - 1\right)} \cdot 3\right)\right)\right) \]

      10. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(3, y\right), \left(3 \cdot \color{blue}{\left(\frac{1}{x \cdot 9} - 1\right)}\right)\right)\right) \]

      11. sub-neg N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(3, y\right), \left(3 \cdot \left(\frac{1}{x \cdot 9} + \color{blue}{\left(\mathsf{neg}\left(1\right)\right)}\right)\right)\right)\right) \]

      12. +-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(3, y\right), \left(3 \cdot \left(\left(\mathsf{neg}\left(1\right)\right) + \color{blue}{\frac{1}{x \cdot 9}}\right)\right)\right)\right) \]

      13. distribute-lft-in N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(3, y\right), \left(3 \cdot \left(\mathsf{neg}\left(1\right)\right) + \color{blue}{3 \cdot \frac{1}{x \cdot 9}}\right)\right)\right) \]

      14. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(3, y\right), \left(3 \cdot \left(\mathsf{neg}\left(1\right)\right) + \frac{1}{x \cdot 9} \cdot \color{blue}{3}\right)\right)\right) \]

      15. +-lowering-+.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(3, y\right), \mathsf{+.f64}\left(\left(3 \cdot \left(\mathsf{neg}\left(1\right)\right)\right), \color{blue}{\left(\frac{1}{x \cdot 9} \cdot 3\right)}\right)\right)\right) \]

      16. metadata-eval N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(3, y\right), \mathsf{+.f64}\left(\left(3 \cdot -1\right), \left(\frac{1}{\color{blue}{x \cdot 9}} \cdot 3\right)\right)\right)\right) \]

      17. metadata-eval N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(3, y\right), \mathsf{+.f64}\left(-3, \left(\color{blue}{\frac{1}{x \cdot 9}} \cdot 3\right)\right)\right)\right) \]

      18. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(3, y\right), \mathsf{+.f64}\left(-3, \left(3 \cdot \color{blue}{\frac{1}{x \cdot 9}}\right)\right)\right)\right) \]

      19. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(3, y\right), \mathsf{+.f64}\left(-3, \left(3 \cdot \frac{1}{9 \cdot \color{blue}{x}}\right)\right)\right)\right) \]

      20. associate-/r* N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(3, y\right), \mathsf{+.f64}\left(-3, \left(3 \cdot \frac{\frac{1}{9}}{\color{blue}{x}}\right)\right)\right)\right) \]

      21. associate-*r/ N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(3, y\right), \mathsf{+.f64}\left(-3, \left(\frac{3 \cdot \frac{1}{9}}{\color{blue}{x}}\right)\right)\right)\right) \]

      22. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(3, y\right), \mathsf{+.f64}\left(-3, \mathsf{/.f64}\left(\left(3 \cdot \frac{1}{9}\right), \color{blue}{x}\right)\right)\right)\right) \]

   3. Simplified 99.6%

      \[\leadsto \color{blue}{\sqrt{x} \cdot \left(3 \cdot y + \left(-3 + \frac{0.3333333333333333}{x}\right)\right)} \]
   4. Add Preprocessing

   5. Taylor expanded in x around inf

      \[\leadsto \color{blue}{\sqrt{x} \cdot \left(3 \cdot y - 3\right)} \]
   6. Step-by-step derivation

      1. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(\sqrt{x}\right), \color{blue}{\left(3 \cdot y - 3\right)}\right) \]

      2. sqrt-lowering-sqrt.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \left(\color{blue}{3 \cdot y} - 3\right)\right) \]

      3. sub-neg N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \left(3 \cdot y + \color{blue}{\left(\mathsf{neg}\left(3\right)\right)}\right)\right) \]

      4. metadata-eval N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \left(3 \cdot y + -3\right)\right) \]

      5. +-lowering-+.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{+.f64}\left(\left(3 \cdot y\right), \color{blue}{-3}\right)\right) \]

      6. *-lowering-*.f64 98.6%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(3, y\right), -3\right)\right) \]

   7. Simplified 98.6%

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

   8. Taylor expanded in y around 0

      \[\leadsto \color{blue}{-3 \cdot \sqrt{x}} \]
   9. Step-by-step derivation

      1. *-commutative N/A

         \[\leadsto \sqrt{x} \cdot \color{blue}{-3} \]

      2. *-lowering-*.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\left(\sqrt{x}\right), \color{blue}{-3}\right) \]

      3. sqrt-lowering-sqrt.f64 51.5%

         \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), -3\right) \]

   10. Simplified 51.5%

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

4. Final simplification 63.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 0.00044:\\ \;\;\;\;\frac{0.3333333333333333}{\sqrt{x}}\\ \mathbf{else}:\\ \;\;\;\;-3 \cdot \sqrt{x}\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 25.0% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ -3 \cdot \sqrt{x} \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (* -3.0 (sqrt x)))

C

double code(double x, double y) {
	return -3.0 * sqrt(x);
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = (-3.0d0) * sqrt(x)
end function

Java

public static double code(double x, double y) {
	return -3.0 * Math.sqrt(x);
}

Python

def code(x, y):
	return -3.0 * math.sqrt(x)

Julia

function code(x, y)
	return Float64(-3.0 * sqrt(x))
end

MATLAB

function tmp = code(x, y)
	tmp = -3.0 * sqrt(x);
end

Wolfram

code[x_, y_] := N[(-3.0 * N[Sqrt[x], $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 99.4%

   \[\left(3 \cdot \sqrt{x}\right) \cdot \left(\left(y + \frac{1}{x \cdot 9}\right) - 1\right) \]
2. Step-by-step derivation

   1. *-commutative N/A

      \[\leadsto \left(\sqrt{x} \cdot 3\right) \cdot \left(\color{blue}{\left(y + \frac{1}{x \cdot 9}\right)} - 1\right) \]

   2. associate-*l* N/A

      \[\leadsto \sqrt{x} \cdot \color{blue}{\left(3 \cdot \left(\left(y + \frac{1}{x \cdot 9}\right) - 1\right)\right)} \]

   3. *-lowering-*.f64 N/A

      \[\leadsto \mathsf{*.f64}\left(\left(\sqrt{x}\right), \color{blue}{\left(3 \cdot \left(\left(y + \frac{1}{x \cdot 9}\right) - 1\right)\right)}\right) \]

   4. sqrt-lowering-sqrt.f64 N/A

      \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \left(\color{blue}{3} \cdot \left(\left(y + \frac{1}{x \cdot 9}\right) - 1\right)\right)\right) \]

   5. associate--l+ N/A

      \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \left(3 \cdot \left(y + \color{blue}{\left(\frac{1}{x \cdot 9} - 1\right)}\right)\right)\right) \]

   6. distribute-lft-in N/A

      \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \left(3 \cdot y + \color{blue}{3 \cdot \left(\frac{1}{x \cdot 9} - 1\right)}\right)\right) \]

   7. *-commutative N/A

      \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \left(3 \cdot y + \left(\frac{1}{x \cdot 9} - 1\right) \cdot \color{blue}{3}\right)\right) \]

   8. +-lowering-+.f64 N/A

      \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{+.f64}\left(\left(3 \cdot y\right), \color{blue}{\left(\left(\frac{1}{x \cdot 9} - 1\right) \cdot 3\right)}\right)\right) \]

   9. *-lowering-*.f64 N/A

      \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(3, y\right), \left(\color{blue}{\left(\frac{1}{x \cdot 9} - 1\right)} \cdot 3\right)\right)\right) \]

   10. *-commutative N/A

       \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(3, y\right), \left(3 \cdot \color{blue}{\left(\frac{1}{x \cdot 9} - 1\right)}\right)\right)\right) \]

   11. sub-neg N/A

       \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(3, y\right), \left(3 \cdot \left(\frac{1}{x \cdot 9} + \color{blue}{\left(\mathsf{neg}\left(1\right)\right)}\right)\right)\right)\right) \]

   12. +-commutative N/A

       \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(3, y\right), \left(3 \cdot \left(\left(\mathsf{neg}\left(1\right)\right) + \color{blue}{\frac{1}{x \cdot 9}}\right)\right)\right)\right) \]

   13. distribute-lft-in N/A

       \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(3, y\right), \left(3 \cdot \left(\mathsf{neg}\left(1\right)\right) + \color{blue}{3 \cdot \frac{1}{x \cdot 9}}\right)\right)\right) \]

   14. *-commutative N/A

       \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(3, y\right), \left(3 \cdot \left(\mathsf{neg}\left(1\right)\right) + \frac{1}{x \cdot 9} \cdot \color{blue}{3}\right)\right)\right) \]

   15. +-lowering-+.f64 N/A

       \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(3, y\right), \mathsf{+.f64}\left(\left(3 \cdot \left(\mathsf{neg}\left(1\right)\right)\right), \color{blue}{\left(\frac{1}{x \cdot 9} \cdot 3\right)}\right)\right)\right) \]

   16. metadata-eval N/A

       \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(3, y\right), \mathsf{+.f64}\left(\left(3 \cdot -1\right), \left(\frac{1}{\color{blue}{x \cdot 9}} \cdot 3\right)\right)\right)\right) \]

   17. metadata-eval N/A

       \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(3, y\right), \mathsf{+.f64}\left(-3, \left(\color{blue}{\frac{1}{x \cdot 9}} \cdot 3\right)\right)\right)\right) \]

   18. *-commutative N/A

       \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(3, y\right), \mathsf{+.f64}\left(-3, \left(3 \cdot \color{blue}{\frac{1}{x \cdot 9}}\right)\right)\right)\right) \]

   19. *-commutative N/A

       \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(3, y\right), \mathsf{+.f64}\left(-3, \left(3 \cdot \frac{1}{9 \cdot \color{blue}{x}}\right)\right)\right)\right) \]

   20. associate-/r* N/A

       \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(3, y\right), \mathsf{+.f64}\left(-3, \left(3 \cdot \frac{\frac{1}{9}}{\color{blue}{x}}\right)\right)\right)\right) \]

   21. associate-*r/ N/A

       \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(3, y\right), \mathsf{+.f64}\left(-3, \left(\frac{3 \cdot \frac{1}{9}}{\color{blue}{x}}\right)\right)\right)\right) \]

   22. /-lowering-/.f64 N/A

       \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(3, y\right), \mathsf{+.f64}\left(-3, \mathsf{/.f64}\left(\left(3 \cdot \frac{1}{9}\right), \color{blue}{x}\right)\right)\right)\right) \]

3. Simplified 99.4%

   \[\leadsto \color{blue}{\sqrt{x} \cdot \left(3 \cdot y + \left(-3 + \frac{0.3333333333333333}{x}\right)\right)} \]
4. Add Preprocessing

5. Taylor expanded in x around inf

   \[\leadsto \color{blue}{\sqrt{x} \cdot \left(3 \cdot y - 3\right)} \]
6. Step-by-step derivation

   1. *-lowering-*.f64 N/A

      \[\leadsto \mathsf{*.f64}\left(\left(\sqrt{x}\right), \color{blue}{\left(3 \cdot y - 3\right)}\right) \]

   2. sqrt-lowering-sqrt.f64 N/A

      \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \left(\color{blue}{3 \cdot y} - 3\right)\right) \]

   3. sub-neg N/A

      \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \left(3 \cdot y + \color{blue}{\left(\mathsf{neg}\left(3\right)\right)}\right)\right) \]

   4. metadata-eval N/A

      \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \left(3 \cdot y + -3\right)\right) \]

   5. +-lowering-+.f64 N/A

      \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{+.f64}\left(\left(3 \cdot y\right), \color{blue}{-3}\right)\right) \]

   6. *-lowering-*.f64 62.0%

      \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), \mathsf{+.f64}\left(\mathsf{*.f64}\left(3, y\right), -3\right)\right) \]

7. Simplified 62.0%

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

8. Taylor expanded in y around 0

   \[\leadsto \color{blue}{-3 \cdot \sqrt{x}} \]
9. Step-by-step derivation

   1. *-commutative N/A

      \[\leadsto \sqrt{x} \cdot \color{blue}{-3} \]

   2. *-lowering-*.f64 N/A

      \[\leadsto \mathsf{*.f64}\left(\left(\sqrt{x}\right), \color{blue}{-3}\right) \]

   3. sqrt-lowering-sqrt.f64 27.6%

      \[\leadsto \mathsf{*.f64}\left(\mathsf{sqrt.f64}\left(x\right), -3\right) \]

10. Simplified 27.6%

    \[\leadsto \color{blue}{\sqrt{x} \cdot -3} \]

11. Final simplification 27.6%

    \[\leadsto -3 \cdot \sqrt{x} \]
12. Add Preprocessing

Developer Target 1: 99.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ 3 \cdot \left(y \cdot \sqrt{x} + \left(\frac{1}{x \cdot 9} - 1\right) \cdot \sqrt{x}\right) \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (* 3.0 (+ (* y (sqrt x)) (* (- (/ 1.0 (* x 9.0)) 1.0) (sqrt x)))))

C

double code(double x, double y) {
	return 3.0 * ((y * sqrt(x)) + (((1.0 / (x * 9.0)) - 1.0) * sqrt(x)));
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = 3.0d0 * ((y * sqrt(x)) + (((1.0d0 / (x * 9.0d0)) - 1.0d0) * sqrt(x)))
end function

Java

public static double code(double x, double y) {
	return 3.0 * ((y * Math.sqrt(x)) + (((1.0 / (x * 9.0)) - 1.0) * Math.sqrt(x)));
}

Python

def code(x, y):
	return 3.0 * ((y * math.sqrt(x)) + (((1.0 / (x * 9.0)) - 1.0) * math.sqrt(x)))

Julia

function code(x, y)
	return Float64(3.0 * Float64(Float64(y * sqrt(x)) + Float64(Float64(Float64(1.0 / Float64(x * 9.0)) - 1.0) * sqrt(x))))
end

MATLAB

function tmp = code(x, y)
	tmp = 3.0 * ((y * sqrt(x)) + (((1.0 / (x * 9.0)) - 1.0) * sqrt(x)));
end

Wolfram

code[x_, y_] := N[(3.0 * N[(N[(y * N[Sqrt[x], $MachinePrecision]), $MachinePrecision] + N[(N[(N[(1.0 / N[(x * 9.0), $MachinePrecision]), $MachinePrecision] - 1.0), $MachinePrecision] * N[Sqrt[x], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Reproduce

herbie shell --seed 2024164 
(FPCore (x y)
  :name "Numeric.SpecFunctions:incompleteGamma from math-functions-0.1.5.2, B"
  :precision binary64

  :alt
  (! :herbie-platform default (* 3 (+ (* y (sqrt x)) (* (- (/ 1 (* x 9)) 1) (sqrt x)))))

  (* (* 3.0 (sqrt x)) (- (+ y (/ 1.0 (* x 9.0))) 1.0)))