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

Percentage Accurate: 99.4% → 99.4%

Time: 12.5s

Alternatives: 12

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

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

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]

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. Add Preprocessing

3. Final simplification 99.4%

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

Alternative 2: 61.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \sqrt{x} \cdot -3\\ \mathbf{if}\;x \leq 3.1 \cdot 10^{-49}:\\ \;\;\;\;\frac{{x}^{-0.5}}{3}\\ \mathbf{elif}\;x \leq 8 \cdot 10^{+31}:\\ \;\;\;\;\left(3 \cdot \sqrt{x}\right) \cdot y\\ \mathbf{elif}\;x \leq 3.45 \cdot 10^{+106}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 1.05 \cdot 10^{+196}:\\ \;\;\;\;3 \cdot \left(\sqrt{x} \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (* (sqrt x) -3.0)))
   (if (<= x 3.1e-49)
     (/ (pow x -0.5) 3.0)
     (if (<= x 8e+31)
       (* (* 3.0 (sqrt x)) y)
       (if (<= x 3.45e+106)
         t_0
         (if (<= x 1.05e+196) (* 3.0 (* (sqrt x) y)) t_0))))))

C

double code(double x, double y) {
	double t_0 = sqrt(x) * -3.0;
	double tmp;
	if (x <= 3.1e-49) {
		tmp = pow(x, -0.5) / 3.0;
	} else if (x <= 8e+31) {
		tmp = (3.0 * sqrt(x)) * y;
	} else if (x <= 3.45e+106) {
		tmp = t_0;
	} else if (x <= 1.05e+196) {
		tmp = 3.0 * (sqrt(x) * y);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: t_0
    real(8) :: tmp
    t_0 = sqrt(x) * (-3.0d0)
    if (x <= 3.1d-49) then
        tmp = (x ** (-0.5d0)) / 3.0d0
    else if (x <= 8d+31) then
        tmp = (3.0d0 * sqrt(x)) * y
    else if (x <= 3.45d+106) then
        tmp = t_0
    else if (x <= 1.05d+196) then
        tmp = 3.0d0 * (sqrt(x) * y)
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double t_0 = Math.sqrt(x) * -3.0;
	double tmp;
	if (x <= 3.1e-49) {
		tmp = Math.pow(x, -0.5) / 3.0;
	} else if (x <= 8e+31) {
		tmp = (3.0 * Math.sqrt(x)) * y;
	} else if (x <= 3.45e+106) {
		tmp = t_0;
	} else if (x <= 1.05e+196) {
		tmp = 3.0 * (Math.sqrt(x) * y);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = math.sqrt(x) * -3.0
	tmp = 0
	if x <= 3.1e-49:
		tmp = math.pow(x, -0.5) / 3.0
	elif x <= 8e+31:
		tmp = (3.0 * math.sqrt(x)) * y
	elif x <= 3.45e+106:
		tmp = t_0
	elif x <= 1.05e+196:
		tmp = 3.0 * (math.sqrt(x) * y)
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y)
	t_0 = Float64(sqrt(x) * -3.0)
	tmp = 0.0
	if (x <= 3.1e-49)
		tmp = Float64((x ^ -0.5) / 3.0);
	elseif (x <= 8e+31)
		tmp = Float64(Float64(3.0 * sqrt(x)) * y);
	elseif (x <= 3.45e+106)
		tmp = t_0;
	elseif (x <= 1.05e+196)
		tmp = Float64(3.0 * Float64(sqrt(x) * y));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = sqrt(x) * -3.0;
	tmp = 0.0;
	if (x <= 3.1e-49)
		tmp = (x ^ -0.5) / 3.0;
	elseif (x <= 8e+31)
		tmp = (3.0 * sqrt(x)) * y;
	elseif (x <= 3.45e+106)
		tmp = t_0;
	elseif (x <= 1.05e+196)
		tmp = 3.0 * (sqrt(x) * y);
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(N[Sqrt[x], $MachinePrecision] * -3.0), $MachinePrecision]}, If[LessEqual[x, 3.1e-49], N[(N[Power[x, -0.5], $MachinePrecision] / 3.0), $MachinePrecision], If[LessEqual[x, 8e+31], N[(N[(3.0 * N[Sqrt[x], $MachinePrecision]), $MachinePrecision] * y), $MachinePrecision], If[LessEqual[x, 3.45e+106], t$95$0, If[LessEqual[x, 1.05e+196], N[(3.0 * N[(N[Sqrt[x], $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision], t$95$0]]]]]

Derivation

1. Split input into 4 regimes

2. if x < 3.1e-49

   1. Initial program 99.3%

      \[\left(3 \cdot \sqrt{x}\right) \cdot \left(\left(y + \frac{1}{x \cdot 9}\right) - 1\right) \]
   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 99.2%

      \[\leadsto \color{blue}{\sqrt{x} \cdot \left(3 \cdot y + \left(-3 + \frac{0.3333333333333333}{x}\right)\right)} \]
   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 80.7%

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

   7. Simplified 80.7%

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

      1. *-commutative N/A

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

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

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

      3. pow1/2 N/A

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

      4. inv-pow N/A

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

      5. metadata-eval N/A

         \[\leadsto \mathsf{*.f64}\left(\left({\left({x}^{\left(\mathsf{neg}\left(1\right)\right)}\right)}^{\frac{1}{2}}\right), \frac{1}{3}\right) \]

      6. pow-pow N/A

         \[\leadsto \mathsf{*.f64}\left(\left({x}^{\left(\left(\mathsf{neg}\left(1\right)\right) \cdot \frac{1}{2}\right)}\right), \frac{1}{3}\right) \]

      7. pow-lowering-pow.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{pow.f64}\left(x, \left(\left(\mathsf{neg}\left(1\right)\right) \cdot \frac{1}{2}\right)\right), \frac{1}{3}\right) \]

      8. metadata-eval N/A

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

      9. metadata-eval 80.7%

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

   9. Applied egg-rr 80.7%

      \[\leadsto \color{blue}{{x}^{-0.5} \cdot 0.3333333333333333} \]
   10. Step-by-step derivation

       1. metadata-eval N/A

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

       2. div-inv N/A

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

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

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

       4. pow-lowering-pow.f64 80.8%

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

   11. Applied egg-rr 80.8%

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

   if 3.1e-49 < x < 7.9999999999999997e31

   1. Initial program 99.5%

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

   3. Taylor expanded in y around inf

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

   5. Simplified 66.5%

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

   if 7.9999999999999997e31 < x < 3.4499999999999999e106 or 1.05000000000000007e196 < x

   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 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 65.8%

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

   7. Simplified 65.8%

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

   8. Taylor expanded in x around inf

      \[\leadsto \color{blue}{-3 \cdot \sqrt{x}} \]
   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 65.8%

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

   10. Simplified 65.8%

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

   if 3.4499999999999999e106 < x < 1.05000000000000007e196

   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. Step-by-step derivation

      1. clear-num N/A

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

      2. associate-/r/ N/A

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

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

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

      4. /-lowering-/.f64 99.6%

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

   6. Applied egg-rr 99.6%

      \[\leadsto \sqrt{x} \cdot \left(3 \cdot y + \left(-3 + \color{blue}{\frac{1}{x} \cdot 0.3333333333333333}\right)\right) \]

   7. Taylor expanded in y around inf

      \[\leadsto \color{blue}{3 \cdot \left(\sqrt{x} \cdot y\right)} \]
   8. 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 66.7%

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

   9. Simplified 66.7%

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

Alternative 3: 61.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \sqrt{x} \cdot -3\\ \mathbf{if}\;x \leq 2 \cdot 10^{-49}:\\ \;\;\;\;\frac{{x}^{-0.5}}{3}\\ \mathbf{elif}\;x \leq 9 \cdot 10^{+29}:\\ \;\;\;\;\sqrt{x} \cdot \left(3 \cdot y\right)\\ \mathbf{elif}\;x \leq 4.6 \cdot 10^{+106}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 3.1 \cdot 10^{+205}:\\ \;\;\;\;3 \cdot \left(\sqrt{x} \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (* (sqrt x) -3.0)))
   (if (<= x 2e-49)
     (/ (pow x -0.5) 3.0)
     (if (<= x 9e+29)
       (* (sqrt x) (* 3.0 y))
       (if (<= x 4.6e+106)
         t_0
         (if (<= x 3.1e+205) (* 3.0 (* (sqrt x) y)) t_0))))))

C

double code(double x, double y) {
	double t_0 = sqrt(x) * -3.0;
	double tmp;
	if (x <= 2e-49) {
		tmp = pow(x, -0.5) / 3.0;
	} else if (x <= 9e+29) {
		tmp = sqrt(x) * (3.0 * y);
	} else if (x <= 4.6e+106) {
		tmp = t_0;
	} else if (x <= 3.1e+205) {
		tmp = 3.0 * (sqrt(x) * y);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: t_0
    real(8) :: tmp
    t_0 = sqrt(x) * (-3.0d0)
    if (x <= 2d-49) then
        tmp = (x ** (-0.5d0)) / 3.0d0
    else if (x <= 9d+29) then
        tmp = sqrt(x) * (3.0d0 * y)
    else if (x <= 4.6d+106) then
        tmp = t_0
    else if (x <= 3.1d+205) then
        tmp = 3.0d0 * (sqrt(x) * y)
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double t_0 = Math.sqrt(x) * -3.0;
	double tmp;
	if (x <= 2e-49) {
		tmp = Math.pow(x, -0.5) / 3.0;
	} else if (x <= 9e+29) {
		tmp = Math.sqrt(x) * (3.0 * y);
	} else if (x <= 4.6e+106) {
		tmp = t_0;
	} else if (x <= 3.1e+205) {
		tmp = 3.0 * (Math.sqrt(x) * y);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = math.sqrt(x) * -3.0
	tmp = 0
	if x <= 2e-49:
		tmp = math.pow(x, -0.5) / 3.0
	elif x <= 9e+29:
		tmp = math.sqrt(x) * (3.0 * y)
	elif x <= 4.6e+106:
		tmp = t_0
	elif x <= 3.1e+205:
		tmp = 3.0 * (math.sqrt(x) * y)
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y)
	t_0 = Float64(sqrt(x) * -3.0)
	tmp = 0.0
	if (x <= 2e-49)
		tmp = Float64((x ^ -0.5) / 3.0);
	elseif (x <= 9e+29)
		tmp = Float64(sqrt(x) * Float64(3.0 * y));
	elseif (x <= 4.6e+106)
		tmp = t_0;
	elseif (x <= 3.1e+205)
		tmp = Float64(3.0 * Float64(sqrt(x) * y));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = sqrt(x) * -3.0;
	tmp = 0.0;
	if (x <= 2e-49)
		tmp = (x ^ -0.5) / 3.0;
	elseif (x <= 9e+29)
		tmp = sqrt(x) * (3.0 * y);
	elseif (x <= 4.6e+106)
		tmp = t_0;
	elseif (x <= 3.1e+205)
		tmp = 3.0 * (sqrt(x) * y);
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(N[Sqrt[x], $MachinePrecision] * -3.0), $MachinePrecision]}, If[LessEqual[x, 2e-49], N[(N[Power[x, -0.5], $MachinePrecision] / 3.0), $MachinePrecision], If[LessEqual[x, 9e+29], N[(N[Sqrt[x], $MachinePrecision] * N[(3.0 * y), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 4.6e+106], t$95$0, If[LessEqual[x, 3.1e+205], N[(3.0 * N[(N[Sqrt[x], $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision], t$95$0]]]]]

Derivation

1. Split input into 4 regimes

2. if x < 1.99999999999999987e-49

   1. Initial program 99.3%

      \[\left(3 \cdot \sqrt{x}\right) \cdot \left(\left(y + \frac{1}{x \cdot 9}\right) - 1\right) \]
   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 99.2%

      \[\leadsto \color{blue}{\sqrt{x} \cdot \left(3 \cdot y + \left(-3 + \frac{0.3333333333333333}{x}\right)\right)} \]
   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 80.7%

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

   7. Simplified 80.7%

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

      1. *-commutative N/A

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

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

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

      3. pow1/2 N/A

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

      4. inv-pow N/A

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

      5. metadata-eval N/A

         \[\leadsto \mathsf{*.f64}\left(\left({\left({x}^{\left(\mathsf{neg}\left(1\right)\right)}\right)}^{\frac{1}{2}}\right), \frac{1}{3}\right) \]

      6. pow-pow N/A

         \[\leadsto \mathsf{*.f64}\left(\left({x}^{\left(\left(\mathsf{neg}\left(1\right)\right) \cdot \frac{1}{2}\right)}\right), \frac{1}{3}\right) \]

      7. pow-lowering-pow.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{pow.f64}\left(x, \left(\left(\mathsf{neg}\left(1\right)\right) \cdot \frac{1}{2}\right)\right), \frac{1}{3}\right) \]

      8. metadata-eval N/A

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

      9. metadata-eval 80.7%

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

   9. Applied egg-rr 80.7%

      \[\leadsto \color{blue}{{x}^{-0.5} \cdot 0.3333333333333333} \]
   10. Step-by-step derivation

       1. metadata-eval N/A

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

       2. div-inv N/A

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

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

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

       4. pow-lowering-pow.f64 80.8%

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

   11. Applied egg-rr 80.8%

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

   if 1.99999999999999987e-49 < x < 9.0000000000000005e29

   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 y around inf

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

      1. *-commutative N/A

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

      2. associate-*l* N/A

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

      3. *-commutative N/A

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

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

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

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

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

      6. *-lowering-*.f64 66.5%

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

   7. Simplified 66.5%

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

   if 9.0000000000000005e29 < x < 4.6000000000000004e106 or 3.10000000000000017e205 < x

   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 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 65.8%

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

   7. Simplified 65.8%

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

   8. Taylor expanded in x around inf

      \[\leadsto \color{blue}{-3 \cdot \sqrt{x}} \]
   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 65.8%

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

   10. Simplified 65.8%

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

   if 4.6000000000000004e106 < x < 3.10000000000000017e205

   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. Step-by-step derivation

      1. clear-num N/A

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

      2. associate-/r/ N/A

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

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

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

      4. /-lowering-/.f64 99.6%

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

   6. Applied egg-rr 99.6%

      \[\leadsto \sqrt{x} \cdot \left(3 \cdot y + \left(-3 + \color{blue}{\frac{1}{x} \cdot 0.3333333333333333}\right)\right) \]

   7. Taylor expanded in y around inf

      \[\leadsto \color{blue}{3 \cdot \left(\sqrt{x} \cdot y\right)} \]
   8. 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 66.7%

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

   9. Simplified 66.7%

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

Alternative 4: 61.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \sqrt{x} \cdot -3\\ t_1 := 3 \cdot \left(\sqrt{x} \cdot y\right)\\ \mathbf{if}\;x \leq 3.1 \cdot 10^{-49}:\\ \;\;\;\;\frac{{x}^{-0.5}}{3}\\ \mathbf{elif}\;x \leq 4.1 \cdot 10^{+30}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 5.7 \cdot 10^{+106}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 4.2 \cdot 10^{+200}:\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (* (sqrt x) -3.0)) (t_1 (* 3.0 (* (sqrt x) y))))
   (if (<= x 3.1e-49)
     (/ (pow x -0.5) 3.0)
     (if (<= x 4.1e+30)
       t_1
       (if (<= x 5.7e+106) t_0 (if (<= x 4.2e+200) t_1 t_0))))))

C

double code(double x, double y) {
	double t_0 = sqrt(x) * -3.0;
	double t_1 = 3.0 * (sqrt(x) * y);
	double tmp;
	if (x <= 3.1e-49) {
		tmp = pow(x, -0.5) / 3.0;
	} else if (x <= 4.1e+30) {
		tmp = t_1;
	} else if (x <= 5.7e+106) {
		tmp = t_0;
	} else if (x <= 4.2e+200) {
		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 = sqrt(x) * (-3.0d0)
    t_1 = 3.0d0 * (sqrt(x) * y)
    if (x <= 3.1d-49) then
        tmp = (x ** (-0.5d0)) / 3.0d0
    else if (x <= 4.1d+30) then
        tmp = t_1
    else if (x <= 5.7d+106) then
        tmp = t_0
    else if (x <= 4.2d+200) 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 = Math.sqrt(x) * -3.0;
	double t_1 = 3.0 * (Math.sqrt(x) * y);
	double tmp;
	if (x <= 3.1e-49) {
		tmp = Math.pow(x, -0.5) / 3.0;
	} else if (x <= 4.1e+30) {
		tmp = t_1;
	} else if (x <= 5.7e+106) {
		tmp = t_0;
	} else if (x <= 4.2e+200) {
		tmp = t_1;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = math.sqrt(x) * -3.0
	t_1 = 3.0 * (math.sqrt(x) * y)
	tmp = 0
	if x <= 3.1e-49:
		tmp = math.pow(x, -0.5) / 3.0
	elif x <= 4.1e+30:
		tmp = t_1
	elif x <= 5.7e+106:
		tmp = t_0
	elif x <= 4.2e+200:
		tmp = t_1
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y)
	t_0 = Float64(sqrt(x) * -3.0)
	t_1 = Float64(3.0 * Float64(sqrt(x) * y))
	tmp = 0.0
	if (x <= 3.1e-49)
		tmp = Float64((x ^ -0.5) / 3.0);
	elseif (x <= 4.1e+30)
		tmp = t_1;
	elseif (x <= 5.7e+106)
		tmp = t_0;
	elseif (x <= 4.2e+200)
		tmp = t_1;
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = sqrt(x) * -3.0;
	t_1 = 3.0 * (sqrt(x) * y);
	tmp = 0.0;
	if (x <= 3.1e-49)
		tmp = (x ^ -0.5) / 3.0;
	elseif (x <= 4.1e+30)
		tmp = t_1;
	elseif (x <= 5.7e+106)
		tmp = t_0;
	elseif (x <= 4.2e+200)
		tmp = t_1;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(N[Sqrt[x], $MachinePrecision] * -3.0), $MachinePrecision]}, Block[{t$95$1 = N[(3.0 * N[(N[Sqrt[x], $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, 3.1e-49], N[(N[Power[x, -0.5], $MachinePrecision] / 3.0), $MachinePrecision], If[LessEqual[x, 4.1e+30], t$95$1, If[LessEqual[x, 5.7e+106], t$95$0, If[LessEqual[x, 4.2e+200], t$95$1, t$95$0]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < 3.1e-49

   1. Initial program 99.3%

      \[\left(3 \cdot \sqrt{x}\right) \cdot \left(\left(y + \frac{1}{x \cdot 9}\right) - 1\right) \]
   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 99.2%

      \[\leadsto \color{blue}{\sqrt{x} \cdot \left(3 \cdot y + \left(-3 + \frac{0.3333333333333333}{x}\right)\right)} \]
   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 80.7%

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

   7. Simplified 80.7%

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

      1. *-commutative N/A

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

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

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

      3. pow1/2 N/A

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

      4. inv-pow N/A

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

      5. metadata-eval N/A

         \[\leadsto \mathsf{*.f64}\left(\left({\left({x}^{\left(\mathsf{neg}\left(1\right)\right)}\right)}^{\frac{1}{2}}\right), \frac{1}{3}\right) \]

      6. pow-pow N/A

         \[\leadsto \mathsf{*.f64}\left(\left({x}^{\left(\left(\mathsf{neg}\left(1\right)\right) \cdot \frac{1}{2}\right)}\right), \frac{1}{3}\right) \]

      7. pow-lowering-pow.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{pow.f64}\left(x, \left(\left(\mathsf{neg}\left(1\right)\right) \cdot \frac{1}{2}\right)\right), \frac{1}{3}\right) \]

      8. metadata-eval N/A

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

      9. metadata-eval 80.7%

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

   9. Applied egg-rr 80.7%

      \[\leadsto \color{blue}{{x}^{-0.5} \cdot 0.3333333333333333} \]
   10. Step-by-step derivation

       1. metadata-eval N/A

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

       2. div-inv N/A

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

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

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

       4. pow-lowering-pow.f64 80.8%

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

   11. Applied egg-rr 80.8%

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

   if 3.1e-49 < x < 4.10000000000000005e30 or 5.6999999999999997e106 < x < 4.19999999999999994e200

   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 99.5%

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

      1. clear-num N/A

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

      2. associate-/r/ N/A

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

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

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

      4. /-lowering-/.f64 99.5%

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

   6. Applied egg-rr 99.5%

      \[\leadsto \sqrt{x} \cdot \left(3 \cdot y + \left(-3 + \color{blue}{\frac{1}{x} \cdot 0.3333333333333333}\right)\right) \]

   7. Taylor expanded in y around inf

      \[\leadsto \color{blue}{3 \cdot \left(\sqrt{x} \cdot y\right)} \]
   8. 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 66.5%

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

   9. Simplified 66.5%

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

   if 4.10000000000000005e30 < x < 5.6999999999999997e106 or 4.19999999999999994e200 < x

   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 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 65.8%

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

   7. Simplified 65.8%

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

   8. Taylor expanded in x around inf

      \[\leadsto \color{blue}{-3 \cdot \sqrt{x}} \]
   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 65.8%

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

   10. Simplified 65.8%

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

Alternative 5: 98.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 0.0042:\\ \;\;\;\;\sqrt{x} \cdot \left(3 \cdot y + \frac{0.3333333333333333}{x}\right)\\ \mathbf{else}:\\ \;\;\;\;3 \cdot \left(\sqrt{x} \cdot \left(y + -1\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x 0.0042)
   (* (sqrt x) (+ (* 3.0 y) (/ 0.3333333333333333 x)))
   (* 3.0 (* (sqrt x) (+ y -1.0)))))

C

double code(double x, double y) {
	double tmp;
	if (x <= 0.0042) {
		tmp = sqrt(x) * ((3.0 * y) + (0.3333333333333333 / x));
	} else {
		tmp = 3.0 * (sqrt(x) * (y + -1.0));
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (x <= 0.0042d0) then
        tmp = sqrt(x) * ((3.0d0 * y) + (0.3333333333333333d0 / x))
    else
        tmp = 3.0d0 * (sqrt(x) * (y + (-1.0d0)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= 0.0042) {
		tmp = Math.sqrt(x) * ((3.0 * y) + (0.3333333333333333 / x));
	} else {
		tmp = 3.0 * (Math.sqrt(x) * (y + -1.0));
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= 0.0042:
		tmp = math.sqrt(x) * ((3.0 * y) + (0.3333333333333333 / x))
	else:
		tmp = 3.0 * (math.sqrt(x) * (y + -1.0))
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= 0.0042)
		tmp = Float64(sqrt(x) * Float64(Float64(3.0 * y) + Float64(0.3333333333333333 / x)));
	else
		tmp = Float64(3.0 * Float64(sqrt(x) * Float64(y + -1.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= 0.0042)
		tmp = sqrt(x) * ((3.0 * y) + (0.3333333333333333 / x));
	else
		tmp = 3.0 * (sqrt(x) * (y + -1.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, 0.0042], N[(N[Sqrt[x], $MachinePrecision] * N[(N[(3.0 * y), $MachinePrecision] + N[(0.3333333333333333 / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(3.0 * N[(N[Sqrt[x], $MachinePrecision] * N[(y + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < 0.00419999999999999974

   1. Initial program 99.3%

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

      1. clear-num N/A

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

      2. associate-/r/ N/A

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

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

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

      4. /-lowering-/.f64 99.3%

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

   6. Applied egg-rr 99.3%

      \[\leadsto \sqrt{x} \cdot \left(3 \cdot y + \left(-3 + \color{blue}{\frac{1}{x} \cdot 0.3333333333333333}\right)\right) \]

   7. Taylor expanded in x around 0

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

      1. /-lowering-/.f64 98.2%

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

   9. Simplified 98.2%

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

   if 0.00419999999999999974 < x

   1. Initial program 99.5%

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

      1. +-commutative N/A

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

      2. flip-+ N/A

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

      3. div-inv N/A

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

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

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

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

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

      6. associate-/r* N/A

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

      7. associate-/r* N/A

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

      8. frac-times N/A

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

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

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

      10. un-div-inv N/A

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

      11. /-lowering-/.f64 N/A

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

      12. /-lowering-/.f64 N/A

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

      13. metadata-eval N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(3, \mathsf{sqrt.f64}\left(x\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{/.f64}\left(\mathsf{/.f64}\left(1, x\right), x\right), 81\right), \left(y \cdot y\right)\right), \left(\frac{1}{\frac{1}{x \cdot 9} - y}\right)\right), 1\right)\right) \]

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

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(3, \mathsf{sqrt.f64}\left(x\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{/.f64}\left(\mathsf{/.f64}\left(1, x\right), x\right), 81\right), \mathsf{*.f64}\left(y, y\right)\right), \left(\frac{1}{\frac{1}{x \cdot 9} - y}\right)\right), 1\right)\right) \]

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

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(3, \mathsf{sqrt.f64}\left(x\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{/.f64}\left(\mathsf{/.f64}\left(1, x\right), x\right), 81\right), \mathsf{*.f64}\left(y, y\right)\right), \mathsf{/.f64}\left(1, \left(\frac{1}{x \cdot 9} - y\right)\right)\right), 1\right)\right) \]

      16. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(3, \mathsf{sqrt.f64}\left(x\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{/.f64}\left(\mathsf{/.f64}\left(1, x\right), x\right), 81\right), \mathsf{*.f64}\left(y, y\right)\right), \mathsf{/.f64}\left(1, \mathsf{\_.f64}\left(\left(\frac{1}{x \cdot 9}\right), y\right)\right)\right), 1\right)\right) \]

      17. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(3, \mathsf{sqrt.f64}\left(x\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{/.f64}\left(\mathsf{/.f64}\left(1, x\right), x\right), 81\right), \mathsf{*.f64}\left(y, y\right)\right), \mathsf{/.f64}\left(1, \mathsf{\_.f64}\left(\left(\frac{1}{9 \cdot x}\right), y\right)\right)\right), 1\right)\right) \]

      18. associate-/r* N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(3, \mathsf{sqrt.f64}\left(x\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{/.f64}\left(\mathsf{/.f64}\left(1, x\right), x\right), 81\right), \mathsf{*.f64}\left(y, y\right)\right), \mathsf{/.f64}\left(1, \mathsf{\_.f64}\left(\left(\frac{\frac{1}{9}}{x}\right), y\right)\right)\right), 1\right)\right) \]

      19. metadata-eval N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(3, \mathsf{sqrt.f64}\left(x\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{/.f64}\left(\mathsf{/.f64}\left(1, x\right), x\right), 81\right), \mathsf{*.f64}\left(y, y\right)\right), \mathsf{/.f64}\left(1, \mathsf{\_.f64}\left(\left(\frac{\frac{1}{9}}{x}\right), y\right)\right)\right), 1\right)\right) \]

      20. metadata-eval N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(3, \mathsf{sqrt.f64}\left(x\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{/.f64}\left(\mathsf{/.f64}\left(1, x\right), x\right), 81\right), \mathsf{*.f64}\left(y, y\right)\right), \mathsf{/.f64}\left(1, \mathsf{\_.f64}\left(\left(\frac{{9}^{-1}}{x}\right), y\right)\right)\right), 1\right)\right) \]

      21. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(3, \mathsf{sqrt.f64}\left(x\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{/.f64}\left(\mathsf{/.f64}\left(1, x\right), x\right), 81\right), \mathsf{*.f64}\left(y, y\right)\right), \mathsf{/.f64}\left(1, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\left({9}^{-1}\right), x\right), y\right)\right)\right), 1\right)\right) \]

      22. metadata-eval 90.6%

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(3, \mathsf{sqrt.f64}\left(x\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{/.f64}\left(\mathsf{/.f64}\left(1, x\right), x\right), 81\right), \mathsf{*.f64}\left(y, y\right)\right), \mathsf{/.f64}\left(1, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\frac{1}{9}, x\right), y\right)\right)\right), 1\right)\right) \]

   4. Applied egg-rr 90.6%

      \[\leadsto \left(3 \cdot \sqrt{x}\right) \cdot \left(\color{blue}{\left(\frac{\frac{\frac{1}{x}}{x}}{81} - y \cdot y\right) \cdot \frac{1}{\frac{0.1111111111111111}{x} - y}} - 1\right) \]
   5. Step-by-step derivation

      1. associate-*l* N/A

         \[\leadsto 3 \cdot \color{blue}{\left(\sqrt{x} \cdot \left(\left(\frac{\frac{\frac{1}{x}}{x}}{81} - y \cdot y\right) \cdot \frac{1}{\frac{\frac{1}{9}}{x} - y} - 1\right)\right)} \]

      2. *-commutative N/A

         \[\leadsto \left(\sqrt{x} \cdot \left(\left(\frac{\frac{\frac{1}{x}}{x}}{81} - y \cdot y\right) \cdot \frac{1}{\frac{\frac{1}{9}}{x} - y} - 1\right)\right) \cdot \color{blue}{3} \]

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

         \[\leadsto \mathsf{*.f64}\left(\left(\sqrt{x} \cdot \left(\left(\frac{\frac{\frac{1}{x}}{x}}{81} - y \cdot y\right) \cdot \frac{1}{\frac{\frac{1}{9}}{x} - y} - 1\right)\right), \color{blue}{3}\right) \]

   6. Applied egg-rr 99.6%

      \[\leadsto \color{blue}{\left(\sqrt{x} \cdot \left(\left(y + \frac{0.1111111111111111}{x}\right) + -1\right)\right) \cdot 3} \]

   7. Taylor expanded in x around inf

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

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

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

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

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

      3. sub-neg N/A

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

      4. metadata-eval N/A

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

      5. +-lowering-+.f64 99.1%

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

   9. Simplified 99.1%

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

4. Final simplification 98.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 0.0042:\\ \;\;\;\;\sqrt{x} \cdot \left(3 \cdot y + \frac{0.3333333333333333}{x}\right)\\ \mathbf{else}:\\ \;\;\;\;3 \cdot \left(\sqrt{x} \cdot \left(y + -1\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 85.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 3.1 \cdot 10^{-49}:\\ \;\;\;\;\frac{{x}^{-0.5}}{3}\\ \mathbf{else}:\\ \;\;\;\;3 \cdot \left(\sqrt{x} \cdot \left(y + -1\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x 3.1e-49) (/ (pow x -0.5) 3.0) (* 3.0 (* (sqrt x) (+ y -1.0)))))

C

double code(double x, double y) {
	double tmp;
	if (x <= 3.1e-49) {
		tmp = pow(x, -0.5) / 3.0;
	} else {
		tmp = 3.0 * (sqrt(x) * (y + -1.0));
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (x <= 3.1d-49) then
        tmp = (x ** (-0.5d0)) / 3.0d0
    else
        tmp = 3.0d0 * (sqrt(x) * (y + (-1.0d0)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= 3.1e-49) {
		tmp = Math.pow(x, -0.5) / 3.0;
	} else {
		tmp = 3.0 * (Math.sqrt(x) * (y + -1.0));
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= 3.1e-49:
		tmp = math.pow(x, -0.5) / 3.0
	else:
		tmp = 3.0 * (math.sqrt(x) * (y + -1.0))
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= 3.1e-49)
		tmp = Float64((x ^ -0.5) / 3.0);
	else
		tmp = Float64(3.0 * Float64(sqrt(x) * Float64(y + -1.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= 3.1e-49)
		tmp = (x ^ -0.5) / 3.0;
	else
		tmp = 3.0 * (sqrt(x) * (y + -1.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, 3.1e-49], N[(N[Power[x, -0.5], $MachinePrecision] / 3.0), $MachinePrecision], N[(3.0 * N[(N[Sqrt[x], $MachinePrecision] * N[(y + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < 3.1e-49

   1. Initial program 99.3%

      \[\left(3 \cdot \sqrt{x}\right) \cdot \left(\left(y + \frac{1}{x \cdot 9}\right) - 1\right) \]
   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 99.2%

      \[\leadsto \color{blue}{\sqrt{x} \cdot \left(3 \cdot y + \left(-3 + \frac{0.3333333333333333}{x}\right)\right)} \]
   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 80.7%

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

   7. Simplified 80.7%

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

      1. *-commutative N/A

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

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

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

      3. pow1/2 N/A

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

      4. inv-pow N/A

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

      5. metadata-eval N/A

         \[\leadsto \mathsf{*.f64}\left(\left({\left({x}^{\left(\mathsf{neg}\left(1\right)\right)}\right)}^{\frac{1}{2}}\right), \frac{1}{3}\right) \]

      6. pow-pow N/A

         \[\leadsto \mathsf{*.f64}\left(\left({x}^{\left(\left(\mathsf{neg}\left(1\right)\right) \cdot \frac{1}{2}\right)}\right), \frac{1}{3}\right) \]

      7. pow-lowering-pow.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{pow.f64}\left(x, \left(\left(\mathsf{neg}\left(1\right)\right) \cdot \frac{1}{2}\right)\right), \frac{1}{3}\right) \]

      8. metadata-eval N/A

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

      9. metadata-eval 80.7%

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

   9. Applied egg-rr 80.7%

      \[\leadsto \color{blue}{{x}^{-0.5} \cdot 0.3333333333333333} \]
   10. Step-by-step derivation

       1. metadata-eval N/A

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

       2. div-inv N/A

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

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

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

       4. pow-lowering-pow.f64 80.8%

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

   11. Applied egg-rr 80.8%

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

   if 3.1e-49 < x

   1. Initial program 99.5%

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

      1. +-commutative N/A

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

      2. flip-+ N/A

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

      3. div-inv N/A

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

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

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

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

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

      6. associate-/r* N/A

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

      7. associate-/r* N/A

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

      8. frac-times N/A

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

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

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

      10. un-div-inv N/A

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

      11. /-lowering-/.f64 N/A

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

      12. /-lowering-/.f64 N/A

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

      13. metadata-eval N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(3, \mathsf{sqrt.f64}\left(x\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{/.f64}\left(\mathsf{/.f64}\left(1, x\right), x\right), 81\right), \left(y \cdot y\right)\right), \left(\frac{1}{\frac{1}{x \cdot 9} - y}\right)\right), 1\right)\right) \]

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

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(3, \mathsf{sqrt.f64}\left(x\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{/.f64}\left(\mathsf{/.f64}\left(1, x\right), x\right), 81\right), \mathsf{*.f64}\left(y, y\right)\right), \left(\frac{1}{\frac{1}{x \cdot 9} - y}\right)\right), 1\right)\right) \]

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

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(3, \mathsf{sqrt.f64}\left(x\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{/.f64}\left(\mathsf{/.f64}\left(1, x\right), x\right), 81\right), \mathsf{*.f64}\left(y, y\right)\right), \mathsf{/.f64}\left(1, \left(\frac{1}{x \cdot 9} - y\right)\right)\right), 1\right)\right) \]

      16. --lowering--.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(3, \mathsf{sqrt.f64}\left(x\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{/.f64}\left(\mathsf{/.f64}\left(1, x\right), x\right), 81\right), \mathsf{*.f64}\left(y, y\right)\right), \mathsf{/.f64}\left(1, \mathsf{\_.f64}\left(\left(\frac{1}{x \cdot 9}\right), y\right)\right)\right), 1\right)\right) \]

      17. *-commutative N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(3, \mathsf{sqrt.f64}\left(x\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{/.f64}\left(\mathsf{/.f64}\left(1, x\right), x\right), 81\right), \mathsf{*.f64}\left(y, y\right)\right), \mathsf{/.f64}\left(1, \mathsf{\_.f64}\left(\left(\frac{1}{9 \cdot x}\right), y\right)\right)\right), 1\right)\right) \]

      18. associate-/r* N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(3, \mathsf{sqrt.f64}\left(x\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{/.f64}\left(\mathsf{/.f64}\left(1, x\right), x\right), 81\right), \mathsf{*.f64}\left(y, y\right)\right), \mathsf{/.f64}\left(1, \mathsf{\_.f64}\left(\left(\frac{\frac{1}{9}}{x}\right), y\right)\right)\right), 1\right)\right) \]

      19. metadata-eval N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(3, \mathsf{sqrt.f64}\left(x\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{/.f64}\left(\mathsf{/.f64}\left(1, x\right), x\right), 81\right), \mathsf{*.f64}\left(y, y\right)\right), \mathsf{/.f64}\left(1, \mathsf{\_.f64}\left(\left(\frac{\frac{1}{9}}{x}\right), y\right)\right)\right), 1\right)\right) \]

      20. metadata-eval N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(3, \mathsf{sqrt.f64}\left(x\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{/.f64}\left(\mathsf{/.f64}\left(1, x\right), x\right), 81\right), \mathsf{*.f64}\left(y, y\right)\right), \mathsf{/.f64}\left(1, \mathsf{\_.f64}\left(\left(\frac{{9}^{-1}}{x}\right), y\right)\right)\right), 1\right)\right) \]

      21. /-lowering-/.f64 N/A

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(3, \mathsf{sqrt.f64}\left(x\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{/.f64}\left(\mathsf{/.f64}\left(1, x\right), x\right), 81\right), \mathsf{*.f64}\left(y, y\right)\right), \mathsf{/.f64}\left(1, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\left({9}^{-1}\right), x\right), y\right)\right)\right), 1\right)\right) \]

      22. metadata-eval 88.3%

          \[\leadsto \mathsf{*.f64}\left(\mathsf{*.f64}\left(3, \mathsf{sqrt.f64}\left(x\right)\right), \mathsf{\_.f64}\left(\mathsf{*.f64}\left(\mathsf{\_.f64}\left(\mathsf{/.f64}\left(\mathsf{/.f64}\left(\mathsf{/.f64}\left(1, x\right), x\right), 81\right), \mathsf{*.f64}\left(y, y\right)\right), \mathsf{/.f64}\left(1, \mathsf{\_.f64}\left(\mathsf{/.f64}\left(\frac{1}{9}, x\right), y\right)\right)\right), 1\right)\right) \]

   4. Applied egg-rr 88.3%

      \[\leadsto \left(3 \cdot \sqrt{x}\right) \cdot \left(\color{blue}{\left(\frac{\frac{\frac{1}{x}}{x}}{81} - y \cdot y\right) \cdot \frac{1}{\frac{0.1111111111111111}{x} - y}} - 1\right) \]
   5. Step-by-step derivation

      1. associate-*l* N/A

         \[\leadsto 3 \cdot \color{blue}{\left(\sqrt{x} \cdot \left(\left(\frac{\frac{\frac{1}{x}}{x}}{81} - y \cdot y\right) \cdot \frac{1}{\frac{\frac{1}{9}}{x} - y} - 1\right)\right)} \]

      2. *-commutative N/A

         \[\leadsto \left(\sqrt{x} \cdot \left(\left(\frac{\frac{\frac{1}{x}}{x}}{81} - y \cdot y\right) \cdot \frac{1}{\frac{\frac{1}{9}}{x} - y} - 1\right)\right) \cdot \color{blue}{3} \]

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

         \[\leadsto \mathsf{*.f64}\left(\left(\sqrt{x} \cdot \left(\left(\frac{\frac{\frac{1}{x}}{x}}{81} - y \cdot y\right) \cdot \frac{1}{\frac{\frac{1}{9}}{x} - y} - 1\right)\right), \color{blue}{3}\right) \]

   6. Applied egg-rr 99.5%

      \[\leadsto \color{blue}{\left(\sqrt{x} \cdot \left(\left(y + \frac{0.1111111111111111}{x}\right) + -1\right)\right) \cdot 3} \]

   7. Taylor expanded in x around inf

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

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

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

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

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

      3. sub-neg N/A

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

      4. metadata-eval N/A

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

      5. +-lowering-+.f64 92.5%

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

   9. Simplified 92.5%

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

4. Final simplification 88.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 3.1 \cdot 10^{-49}:\\ \;\;\;\;\frac{{x}^{-0.5}}{3}\\ \mathbf{else}:\\ \;\;\;\;3 \cdot \left(\sqrt{x} \cdot \left(y + -1\right)\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 85.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 3.1 \cdot 10^{-49}:\\ \;\;\;\;\frac{{x}^{-0.5}}{3}\\ \mathbf{else}:\\ \;\;\;\;\sqrt{x} \cdot \left(3 \cdot y + -3\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x 3.1e-49) (/ (pow x -0.5) 3.0) (* (sqrt x) (+ (* 3.0 y) -3.0))))

C

double code(double x, double y) {
	double tmp;
	if (x <= 3.1e-49) {
		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 <= 3.1d-49) 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 <= 3.1e-49) {
		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 <= 3.1e-49:
		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 <= 3.1e-49)
		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 <= 3.1e-49)
		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, 3.1e-49], 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 < 3.1e-49

   1. Initial program 99.3%

      \[\left(3 \cdot \sqrt{x}\right) \cdot \left(\left(y + \frac{1}{x \cdot 9}\right) - 1\right) \]
   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 99.2%

      \[\leadsto \color{blue}{\sqrt{x} \cdot \left(3 \cdot y + \left(-3 + \frac{0.3333333333333333}{x}\right)\right)} \]
   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 80.7%

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

   7. Simplified 80.7%

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

      1. *-commutative N/A

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

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

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

      3. pow1/2 N/A

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

      4. inv-pow N/A

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

      5. metadata-eval N/A

         \[\leadsto \mathsf{*.f64}\left(\left({\left({x}^{\left(\mathsf{neg}\left(1\right)\right)}\right)}^{\frac{1}{2}}\right), \frac{1}{3}\right) \]

      6. pow-pow N/A

         \[\leadsto \mathsf{*.f64}\left(\left({x}^{\left(\left(\mathsf{neg}\left(1\right)\right) \cdot \frac{1}{2}\right)}\right), \frac{1}{3}\right) \]

      7. pow-lowering-pow.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{pow.f64}\left(x, \left(\left(\mathsf{neg}\left(1\right)\right) \cdot \frac{1}{2}\right)\right), \frac{1}{3}\right) \]

      8. metadata-eval N/A

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

      9. metadata-eval 80.7%

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

   9. Applied egg-rr 80.7%

      \[\leadsto \color{blue}{{x}^{-0.5} \cdot 0.3333333333333333} \]
   10. Step-by-step derivation

       1. metadata-eval N/A

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

       2. div-inv N/A

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

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

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

       4. pow-lowering-pow.f64 80.8%

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

   11. Applied egg-rr 80.8%

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

   if 3.1e-49 < x

   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 92.5%

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

   7. Simplified 92.5%

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

Alternative 8: 99.4% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_] := N[(N[Sqrt[x], $MachinePrecision] * N[(N[(3.0 * y), $MachinePrecision] + N[(-3.0 + N[(0.3333333333333333 / x), $MachinePrecision]), $MachinePrecision]), $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. Add Preprocessing

Alternative 9: 60.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 0.0042:\\ \;\;\;\;\frac{{x}^{-0.5}}{3}\\ \mathbf{else}:\\ \;\;\;\;\sqrt{x} \cdot -3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x 0.0042) (/ (pow x -0.5) 3.0) (* (sqrt x) -3.0)))

C

double code(double x, double y) {
	double tmp;
	if (x <= 0.0042) {
		tmp = pow(x, -0.5) / 3.0;
	} else {
		tmp = sqrt(x) * -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 <= 0.0042d0) then
        tmp = (x ** (-0.5d0)) / 3.0d0
    else
        tmp = sqrt(x) * (-3.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= 0.0042) {
		tmp = Math.pow(x, -0.5) / 3.0;
	} else {
		tmp = Math.sqrt(x) * -3.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= 0.0042:
		tmp = math.pow(x, -0.5) / 3.0
	else:
		tmp = math.sqrt(x) * -3.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= 0.0042)
		tmp = Float64((x ^ -0.5) / 3.0);
	else
		tmp = Float64(sqrt(x) * -3.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= 0.0042)
		tmp = (x ^ -0.5) / 3.0;
	else
		tmp = sqrt(x) * -3.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, 0.0042], N[(N[Power[x, -0.5], $MachinePrecision] / 3.0), $MachinePrecision], N[(N[Sqrt[x], $MachinePrecision] * -3.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < 0.00419999999999999974

   1. Initial program 99.3%

      \[\left(3 \cdot \sqrt{x}\right) \cdot \left(\left(y + \frac{1}{x \cdot 9}\right) - 1\right) \]
   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 72.7%

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

   7. Simplified 72.7%

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

      1. *-commutative N/A

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

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

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

      3. pow1/2 N/A

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

      4. inv-pow N/A

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

      5. metadata-eval N/A

         \[\leadsto \mathsf{*.f64}\left(\left({\left({x}^{\left(\mathsf{neg}\left(1\right)\right)}\right)}^{\frac{1}{2}}\right), \frac{1}{3}\right) \]

      6. pow-pow N/A

         \[\leadsto \mathsf{*.f64}\left(\left({x}^{\left(\left(\mathsf{neg}\left(1\right)\right) \cdot \frac{1}{2}\right)}\right), \frac{1}{3}\right) \]

      7. pow-lowering-pow.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{pow.f64}\left(x, \left(\left(\mathsf{neg}\left(1\right)\right) \cdot \frac{1}{2}\right)\right), \frac{1}{3}\right) \]

      8. metadata-eval N/A

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

      9. metadata-eval 72.7%

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

   9. Applied egg-rr 72.7%

      \[\leadsto \color{blue}{{x}^{-0.5} \cdot 0.3333333333333333} \]
   10. Step-by-step derivation

       1. metadata-eval N/A

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

       2. div-inv N/A

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

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

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

       4. pow-lowering-pow.f64 72.8%

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

   11. Applied egg-rr 72.8%

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

   if 0.00419999999999999974 < x

   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 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 52.2%

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

   7. Simplified 52.2%

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

   8. Taylor expanded in x around inf

      \[\leadsto \color{blue}{-3 \cdot \sqrt{x}} \]
   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 51.8%

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

   10. Simplified 51.8%

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

Alternative 10: 60.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 0.0042:\\ \;\;\;\;0.3333333333333333 \cdot {x}^{-0.5}\\ \mathbf{else}:\\ \;\;\;\;\sqrt{x} \cdot -3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x 0.0042) (* 0.3333333333333333 (pow x -0.5)) (* (sqrt x) -3.0)))

C

double code(double x, double y) {
	double tmp;
	if (x <= 0.0042) {
		tmp = 0.3333333333333333 * pow(x, -0.5);
	} else {
		tmp = sqrt(x) * -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 <= 0.0042d0) then
        tmp = 0.3333333333333333d0 * (x ** (-0.5d0))
    else
        tmp = sqrt(x) * (-3.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= 0.0042) {
		tmp = 0.3333333333333333 * Math.pow(x, -0.5);
	} else {
		tmp = Math.sqrt(x) * -3.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= 0.0042:
		tmp = 0.3333333333333333 * math.pow(x, -0.5)
	else:
		tmp = math.sqrt(x) * -3.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= 0.0042)
		tmp = Float64(0.3333333333333333 * (x ^ -0.5));
	else
		tmp = Float64(sqrt(x) * -3.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= 0.0042)
		tmp = 0.3333333333333333 * (x ^ -0.5);
	else
		tmp = sqrt(x) * -3.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, 0.0042], N[(0.3333333333333333 * N[Power[x, -0.5], $MachinePrecision]), $MachinePrecision], N[(N[Sqrt[x], $MachinePrecision] * -3.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < 0.00419999999999999974

   1. Initial program 99.3%

      \[\left(3 \cdot \sqrt{x}\right) \cdot \left(\left(y + \frac{1}{x \cdot 9}\right) - 1\right) \]
   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 72.7%

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

   7. Simplified 72.7%

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

      1. *-commutative N/A

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

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

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

      3. pow1/2 N/A

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

      4. inv-pow N/A

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

      5. metadata-eval N/A

         \[\leadsto \mathsf{*.f64}\left(\left({\left({x}^{\left(\mathsf{neg}\left(1\right)\right)}\right)}^{\frac{1}{2}}\right), \frac{1}{3}\right) \]

      6. pow-pow N/A

         \[\leadsto \mathsf{*.f64}\left(\left({x}^{\left(\left(\mathsf{neg}\left(1\right)\right) \cdot \frac{1}{2}\right)}\right), \frac{1}{3}\right) \]

      7. pow-lowering-pow.f64 N/A

         \[\leadsto \mathsf{*.f64}\left(\mathsf{pow.f64}\left(x, \left(\left(\mathsf{neg}\left(1\right)\right) \cdot \frac{1}{2}\right)\right), \frac{1}{3}\right) \]

      8. metadata-eval N/A

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

      9. metadata-eval 72.7%

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

   9. Applied egg-rr 72.7%

      \[\leadsto \color{blue}{{x}^{-0.5} \cdot 0.3333333333333333} \]

   if 0.00419999999999999974 < x

   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 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 52.2%

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

   7. Simplified 52.2%

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

   8. Taylor expanded in x around inf

      \[\leadsto \color{blue}{-3 \cdot \sqrt{x}} \]
   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 51.8%

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

   10. Simplified 51.8%

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

4. Final simplification 61.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 0.0042:\\ \;\;\;\;0.3333333333333333 \cdot {x}^{-0.5}\\ \mathbf{else}:\\ \;\;\;\;\sqrt{x} \cdot -3\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 60.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 0.0042:\\ \;\;\;\;\frac{0.3333333333333333}{\sqrt{x}}\\ \mathbf{else}:\\ \;\;\;\;\sqrt{x} \cdot -3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x 0.0042) (/ 0.3333333333333333 (sqrt x)) (* (sqrt x) -3.0)))

C

double code(double x, double y) {
	double tmp;
	if (x <= 0.0042) {
		tmp = 0.3333333333333333 / sqrt(x);
	} else {
		tmp = sqrt(x) * -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 <= 0.0042d0) then
        tmp = 0.3333333333333333d0 / sqrt(x)
    else
        tmp = sqrt(x) * (-3.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= 0.0042) {
		tmp = 0.3333333333333333 / Math.sqrt(x);
	} else {
		tmp = Math.sqrt(x) * -3.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= 0.0042:
		tmp = 0.3333333333333333 / math.sqrt(x)
	else:
		tmp = math.sqrt(x) * -3.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= 0.0042)
		tmp = Float64(0.3333333333333333 / sqrt(x));
	else
		tmp = Float64(sqrt(x) * -3.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= 0.0042)
		tmp = 0.3333333333333333 / sqrt(x);
	else
		tmp = sqrt(x) * -3.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, 0.0042], N[(0.3333333333333333 / N[Sqrt[x], $MachinePrecision]), $MachinePrecision], N[(N[Sqrt[x], $MachinePrecision] * -3.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < 0.00419999999999999974

   1. Initial program 99.3%

      \[\left(3 \cdot \sqrt{x}\right) \cdot \left(\left(y + \frac{1}{x \cdot 9}\right) - 1\right) \]
   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 72.7%

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

   7. Simplified 72.7%

      \[\leadsto \color{blue}{0.3333333333333333 \cdot \sqrt{\frac{1}{x}}} \]
   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 72.6%

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

   9. Applied egg-rr 72.6%

      \[\leadsto \color{blue}{\frac{0.3333333333333333}{\sqrt{x}}} \]

   if 0.00419999999999999974 < x

   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 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 52.2%

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

   7. Simplified 52.2%

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

   8. Taylor expanded in x around inf

      \[\leadsto \color{blue}{-3 \cdot \sqrt{x}} \]
   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 51.8%

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

   10. Simplified 51.8%

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

Alternative 12: 25.1% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \sqrt{x} \cdot -3 \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (* (sqrt x) -3.0))

C

double code(double x, double y) {
	return sqrt(x) * -3.0;
}

Fortran

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

Java

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

Python

def code(x, y):
	return math.sqrt(x) * -3.0

Julia

function code(x, y)
	return Float64(sqrt(x) * -3.0)
end

MATLAB

function tmp = code(x, y)
	tmp = sqrt(x) * -3.0;
end

Wolfram

code[x_, y_] := N[(N[Sqrt[x], $MachinePrecision] * -3.0), $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 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 62.3%

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

7. Simplified 62.3%

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

8. Taylor expanded in x around inf

   \[\leadsto \color{blue}{-3 \cdot \sqrt{x}} \]
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 28.3%

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

10. Simplified 28.3%

    \[\leadsto \color{blue}{\sqrt{x} \cdot -3} \]
11. 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 2024158 
(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)))