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

Percentage Accurate: 99.4% → 99.5%

Time: 12.6s

Alternatives: 16

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: 99.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \frac{y + \left(\frac{0.1111111111111111}{x} + -1\right)}{\sqrt{\frac{0.1111111111111111}{x}}} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (/ (+ y (+ (/ 0.1111111111111111 x) -1.0)) (sqrt (/ 0.1111111111111111 x))))

C

double code(double x, double y) {
	return (y + ((0.1111111111111111 / x) + -1.0)) / sqrt((0.1111111111111111 / x));
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = (y + ((0.1111111111111111d0 / x) + (-1.0d0))) / sqrt((0.1111111111111111d0 / x))
end function

Java

public static double code(double x, double y) {
	return (y + ((0.1111111111111111 / x) + -1.0)) / Math.sqrt((0.1111111111111111 / x));
}

Python

def code(x, y):
	return (y + ((0.1111111111111111 / x) + -1.0)) / math.sqrt((0.1111111111111111 / x))

Julia

function code(x, y)
	return Float64(Float64(y + Float64(Float64(0.1111111111111111 / x) + -1.0)) / sqrt(Float64(0.1111111111111111 / x)))
end

MATLAB

function tmp = code(x, y)
	tmp = (y + ((0.1111111111111111 / x) + -1.0)) / sqrt((0.1111111111111111 / x));
end

Wolfram

code[x_, y_] := N[(N[(y + N[(N[(0.1111111111111111 / x), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision] / N[Sqrt[N[(0.1111111111111111 / x), $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. Add Preprocessing
3. Step-by-step derivation

   1. +-commutative 99.4%

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

   2. metadata-eval 99.4%

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

   3. div-inv 99.4%

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

   4. clear-num 99.4%

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

   5. add-sqr-sqrt 99.3%

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

   6. fma-define 99.3%

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

   7. sqrt-div 99.3%

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

   8. metadata-eval 99.3%

      \[\leadsto \left(3 \cdot \sqrt{x}\right) \cdot \left(\mathsf{fma}\left(\frac{\color{blue}{0.3333333333333333}}{\sqrt{x}}, \sqrt{\frac{0.1111111111111111}{x}}, y\right) - 1\right) \]

   9. sqrt-div 99.3%

      \[\leadsto \left(3 \cdot \sqrt{x}\right) \cdot \left(\mathsf{fma}\left(\frac{0.3333333333333333}{\sqrt{x}}, \color{blue}{\frac{\sqrt{0.1111111111111111}}{\sqrt{x}}}, y\right) - 1\right) \]

   10. metadata-eval 99.3%

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

4. Applied egg-rr 99.3%

   \[\leadsto \left(3 \cdot \sqrt{x}\right) \cdot \left(\color{blue}{\mathsf{fma}\left(\frac{0.3333333333333333}{\sqrt{x}}, \frac{0.3333333333333333}{\sqrt{x}}, y\right)} - 1\right) \]
5. Step-by-step derivation

   1. fma-undefine 99.3%

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

   2. unpow2 99.3%

      \[\leadsto \left(3 \cdot \sqrt{x}\right) \cdot \left(\left(\color{blue}{{\left(\frac{0.3333333333333333}{\sqrt{x}}\right)}^{2}} + y\right) - 1\right) \]

6. Simplified 99.3%

   \[\leadsto \left(3 \cdot \sqrt{x}\right) \cdot \left(\color{blue}{\left({\left(\frac{0.3333333333333333}{\sqrt{x}}\right)}^{2} + y\right)} - 1\right) \]

8. Applied egg-rr 99.5%

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

9. Final simplification 99.5%

   \[\leadsto \frac{y + \left(\frac{0.1111111111111111}{x} + -1\right)}{\sqrt{\frac{0.1111111111111111}{x}}} \]
10. Add Preprocessing

Alternative 2: 62.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 2.7 \cdot 10^{-18}:\\ \;\;\;\;\sqrt{\frac{0.1111111111111111}{x} + -2}\\ \mathbf{elif}\;x \leq 2.9 \cdot 10^{+119} \lor \neg \left(x \leq 4.2 \cdot 10^{+150}\right) \land \left(x \leq 4.2 \cdot 10^{+182} \lor \neg \left(x \leq 5.5 \cdot 10^{+217}\right) \land x \leq 4.5 \cdot 10^{+267}\right):\\ \;\;\;\;3 \cdot \left(y \cdot \sqrt{x}\right)\\ \mathbf{else}:\\ \;\;\;\;\sqrt{x} \cdot -3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x 2.7e-18)
   (sqrt (+ (/ 0.1111111111111111 x) -2.0))
   (if (or (<= x 2.9e+119)
           (and (not (<= x 4.2e+150))
                (or (<= x 4.2e+182)
                    (and (not (<= x 5.5e+217)) (<= x 4.5e+267)))))
     (* 3.0 (* y (sqrt x)))
     (* (sqrt x) -3.0))))

C

double code(double x, double y) {
	double tmp;
	if (x <= 2.7e-18) {
		tmp = sqrt(((0.1111111111111111 / x) + -2.0));
	} else if ((x <= 2.9e+119) || (!(x <= 4.2e+150) && ((x <= 4.2e+182) || (!(x <= 5.5e+217) && (x <= 4.5e+267))))) {
		tmp = 3.0 * (y * 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 <= 2.7d-18) then
        tmp = sqrt(((0.1111111111111111d0 / x) + (-2.0d0)))
    else if ((x <= 2.9d+119) .or. (.not. (x <= 4.2d+150)) .and. (x <= 4.2d+182) .or. (.not. (x <= 5.5d+217)) .and. (x <= 4.5d+267)) then
        tmp = 3.0d0 * (y * 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 <= 2.7e-18) {
		tmp = Math.sqrt(((0.1111111111111111 / x) + -2.0));
	} else if ((x <= 2.9e+119) || (!(x <= 4.2e+150) && ((x <= 4.2e+182) || (!(x <= 5.5e+217) && (x <= 4.5e+267))))) {
		tmp = 3.0 * (y * Math.sqrt(x));
	} else {
		tmp = Math.sqrt(x) * -3.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= 2.7e-18:
		tmp = math.sqrt(((0.1111111111111111 / x) + -2.0))
	elif (x <= 2.9e+119) or (not (x <= 4.2e+150) and ((x <= 4.2e+182) or (not (x <= 5.5e+217) and (x <= 4.5e+267)))):
		tmp = 3.0 * (y * math.sqrt(x))
	else:
		tmp = math.sqrt(x) * -3.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= 2.7e-18)
		tmp = sqrt(Float64(Float64(0.1111111111111111 / x) + -2.0));
	elseif ((x <= 2.9e+119) || (!(x <= 4.2e+150) && ((x <= 4.2e+182) || (!(x <= 5.5e+217) && (x <= 4.5e+267)))))
		tmp = Float64(3.0 * Float64(y * 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 <= 2.7e-18)
		tmp = sqrt(((0.1111111111111111 / x) + -2.0));
	elseif ((x <= 2.9e+119) || (~((x <= 4.2e+150)) && ((x <= 4.2e+182) || (~((x <= 5.5e+217)) && (x <= 4.5e+267)))))
		tmp = 3.0 * (y * sqrt(x));
	else
		tmp = sqrt(x) * -3.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, 2.7e-18], N[Sqrt[N[(N[(0.1111111111111111 / x), $MachinePrecision] + -2.0), $MachinePrecision]], $MachinePrecision], If[Or[LessEqual[x, 2.9e+119], And[N[Not[LessEqual[x, 4.2e+150]], $MachinePrecision], Or[LessEqual[x, 4.2e+182], And[N[Not[LessEqual[x, 5.5e+217]], $MachinePrecision], LessEqual[x, 4.5e+267]]]]], N[(3.0 * N[(y * N[Sqrt[x], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[Sqrt[x], $MachinePrecision] * -3.0), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < 2.69999999999999989e-18

   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. associate-*l* 99.2%

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

      2. sub-neg 99.2%

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

      3. +-commutative 99.2%

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

      4. associate-+l+ 99.2%

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

      5. *-commutative 99.2%

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

      6. associate-/r* 99.2%

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

      7. metadata-eval 99.2%

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

      8. metadata-eval 99.2%

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

   3. Simplified 99.2%

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

   6. Applied egg-rr 34.0%

      \[\leadsto \color{blue}{\sqrt{9 \cdot \left(x \cdot {\left(\frac{0.1111111111111111}{x} + \left(y + -1\right)\right)}^{2}\right)}} \]
   7. Step-by-step derivation

      1. *-commutative 34.0%

         \[\leadsto \sqrt{\color{blue}{\left(x \cdot {\left(\frac{0.1111111111111111}{x} + \left(y + -1\right)\right)}^{2}\right) \cdot 9}} \]

      2. associate-*l* 33.9%

         \[\leadsto \sqrt{\color{blue}{x \cdot \left({\left(\frac{0.1111111111111111}{x} + \left(y + -1\right)\right)}^{2} \cdot 9\right)}} \]

      3. associate-+r+ 33.9%

         \[\leadsto \sqrt{x \cdot \left({\color{blue}{\left(\left(\frac{0.1111111111111111}{x} + y\right) + -1\right)}}^{2} \cdot 9\right)} \]

      4. +-commutative 33.9%

         \[\leadsto \sqrt{x \cdot \left({\left(\color{blue}{\left(y + \frac{0.1111111111111111}{x}\right)} + -1\right)}^{2} \cdot 9\right)} \]

      5. associate-+r+ 33.9%

         \[\leadsto \sqrt{x \cdot \left({\color{blue}{\left(y + \left(\frac{0.1111111111111111}{x} + -1\right)\right)}}^{2} \cdot 9\right)} \]

   8. Simplified 33.9%

      \[\leadsto \color{blue}{\sqrt{x \cdot \left({\left(y + \left(\frac{0.1111111111111111}{x} + -1\right)\right)}^{2} \cdot 9\right)}} \]

   9. Taylor expanded in x around 0 75.5%

      \[\leadsto \sqrt{\color{blue}{2 \cdot \left(y - 1\right) + 0.1111111111111111 \cdot \frac{1}{x}}} \]

   10. Taylor expanded in y around 0 75.4%

       \[\leadsto \color{blue}{\sqrt{0.1111111111111111 \cdot \frac{1}{x} - 2}} \]
   11. Step-by-step derivation

       1. sub-neg 75.4%

          \[\leadsto \sqrt{\color{blue}{0.1111111111111111 \cdot \frac{1}{x} + \left(-2\right)}} \]

       2. associate-*r/ 75.4%

          \[\leadsto \sqrt{\color{blue}{\frac{0.1111111111111111 \cdot 1}{x}} + \left(-2\right)} \]

       3. metadata-eval 75.4%

          \[\leadsto \sqrt{\frac{\color{blue}{0.1111111111111111}}{x} + \left(-2\right)} \]

       4. metadata-eval 75.4%

          \[\leadsto \sqrt{\frac{0.1111111111111111}{x} + \color{blue}{-2}} \]

   12. Simplified 75.4%

       \[\leadsto \color{blue}{\sqrt{\frac{0.1111111111111111}{x} + -2}} \]

   if 2.69999999999999989e-18 < x < 2.90000000000000007e119 or 4.19999999999999996e150 < x < 4.1999999999999998e182 or 5.5e217 < x < 4.49999999999999988e267

   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. associate-*l* 99.5%

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

      2. sub-neg 99.5%

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

      3. +-commutative 99.5%

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

      4. associate-+l+ 99.5%

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

      5. *-commutative 99.5%

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

      6. associate-/r* 99.5%

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

      7. metadata-eval 99.5%

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

      8. metadata-eval 99.5%

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

   3. Simplified 99.5%

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

   5. Taylor expanded in y around inf 69.1%

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

   if 2.90000000000000007e119 < x < 4.19999999999999996e150 or 4.1999999999999998e182 < x < 5.5e217 or 4.49999999999999988e267 < x

   1. Initial program 99.6%

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

      1. remove-double-neg 99.6%

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

      2. distribute-lft-neg-out 99.6%

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

      3. distribute-rgt-neg-in 99.6%

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

      4. +-commutative 99.6%

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

      5. associate--l+ 99.6%

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

      6. distribute-neg-in 99.6%

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

      7. distribute-frac-neg2 99.6%

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

      8. distribute-lft-neg-out 99.6%

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

      9. *-commutative 99.6%

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

      10. distribute-rgt-neg-in 99.6%

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

      11. metadata-eval 99.6%

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

   3. Simplified 99.6%

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

   5. Taylor expanded in y around 0 68.6%

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

      1. *-commutative 68.6%

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

      2. associate-*l* 68.6%

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

      3. sub-neg 68.6%

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

      4. associate-*r/ 68.6%

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

      5. metadata-eval 68.6%

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

      6. distribute-neg-frac 68.6%

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

      7. metadata-eval 68.6%

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

   7. Simplified 68.6%

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

   8. Taylor expanded in x around inf 68.6%

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

4. Final simplification 71.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 2.7 \cdot 10^{-18}:\\ \;\;\;\;\sqrt{\frac{0.1111111111111111}{x} + -2}\\ \mathbf{elif}\;x \leq 2.9 \cdot 10^{+119} \lor \neg \left(x \leq 4.2 \cdot 10^{+150}\right) \land \left(x \leq 4.2 \cdot 10^{+182} \lor \neg \left(x \leq 5.5 \cdot 10^{+217}\right) \land x \leq 4.5 \cdot 10^{+267}\right):\\ \;\;\;\;3 \cdot \left(y \cdot \sqrt{x}\right)\\ \mathbf{else}:\\ \;\;\;\;\sqrt{x} \cdot -3\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 62.5% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 5.2 \cdot 10^{-18}:\\ \;\;\;\;\sqrt{\frac{0.1111111111111111}{x} + -2}\\ \mathbf{elif}\;x \leq 3.15 \cdot 10^{+119} \lor \neg \left(x \leq 4.7 \cdot 10^{+150}\right) \land \left(x \leq 1.5 \cdot 10^{+182} \lor \neg \left(x \leq 2.35 \cdot 10^{+215}\right) \land x \leq 6 \cdot 10^{+267}\right):\\ \;\;\;\;y \cdot \sqrt{x \cdot 9}\\ \mathbf{else}:\\ \;\;\;\;\sqrt{x} \cdot -3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x 5.2e-18)
   (sqrt (+ (/ 0.1111111111111111 x) -2.0))
   (if (or (<= x 3.15e+119)
           (and (not (<= x 4.7e+150))
                (or (<= x 1.5e+182)
                    (and (not (<= x 2.35e+215)) (<= x 6e+267)))))
     (* y (sqrt (* x 9.0)))
     (* (sqrt x) -3.0))))

C

double code(double x, double y) {
	double tmp;
	if (x <= 5.2e-18) {
		tmp = sqrt(((0.1111111111111111 / x) + -2.0));
	} else if ((x <= 3.15e+119) || (!(x <= 4.7e+150) && ((x <= 1.5e+182) || (!(x <= 2.35e+215) && (x <= 6e+267))))) {
		tmp = y * sqrt((x * 9.0));
	} 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 <= 5.2d-18) then
        tmp = sqrt(((0.1111111111111111d0 / x) + (-2.0d0)))
    else if ((x <= 3.15d+119) .or. (.not. (x <= 4.7d+150)) .and. (x <= 1.5d+182) .or. (.not. (x <= 2.35d+215)) .and. (x <= 6d+267)) then
        tmp = y * sqrt((x * 9.0d0))
    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 <= 5.2e-18) {
		tmp = Math.sqrt(((0.1111111111111111 / x) + -2.0));
	} else if ((x <= 3.15e+119) || (!(x <= 4.7e+150) && ((x <= 1.5e+182) || (!(x <= 2.35e+215) && (x <= 6e+267))))) {
		tmp = y * Math.sqrt((x * 9.0));
	} else {
		tmp = Math.sqrt(x) * -3.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= 5.2e-18:
		tmp = math.sqrt(((0.1111111111111111 / x) + -2.0))
	elif (x <= 3.15e+119) or (not (x <= 4.7e+150) and ((x <= 1.5e+182) or (not (x <= 2.35e+215) and (x <= 6e+267)))):
		tmp = y * math.sqrt((x * 9.0))
	else:
		tmp = math.sqrt(x) * -3.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= 5.2e-18)
		tmp = sqrt(Float64(Float64(0.1111111111111111 / x) + -2.0));
	elseif ((x <= 3.15e+119) || (!(x <= 4.7e+150) && ((x <= 1.5e+182) || (!(x <= 2.35e+215) && (x <= 6e+267)))))
		tmp = Float64(y * sqrt(Float64(x * 9.0)));
	else
		tmp = Float64(sqrt(x) * -3.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= 5.2e-18)
		tmp = sqrt(((0.1111111111111111 / x) + -2.0));
	elseif ((x <= 3.15e+119) || (~((x <= 4.7e+150)) && ((x <= 1.5e+182) || (~((x <= 2.35e+215)) && (x <= 6e+267)))))
		tmp = y * sqrt((x * 9.0));
	else
		tmp = sqrt(x) * -3.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, 5.2e-18], N[Sqrt[N[(N[(0.1111111111111111 / x), $MachinePrecision] + -2.0), $MachinePrecision]], $MachinePrecision], If[Or[LessEqual[x, 3.15e+119], And[N[Not[LessEqual[x, 4.7e+150]], $MachinePrecision], Or[LessEqual[x, 1.5e+182], And[N[Not[LessEqual[x, 2.35e+215]], $MachinePrecision], LessEqual[x, 6e+267]]]]], N[(y * N[Sqrt[N[(x * 9.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], N[(N[Sqrt[x], $MachinePrecision] * -3.0), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < 5.2000000000000001e-18

   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. associate-*l* 99.2%

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

      2. sub-neg 99.2%

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

      3. +-commutative 99.2%

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

      4. associate-+l+ 99.2%

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

      5. *-commutative 99.2%

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

      6. associate-/r* 99.2%

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

      7. metadata-eval 99.2%

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

      8. metadata-eval 99.2%

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

   3. Simplified 99.2%

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

   6. Applied egg-rr 34.0%

      \[\leadsto \color{blue}{\sqrt{9 \cdot \left(x \cdot {\left(\frac{0.1111111111111111}{x} + \left(y + -1\right)\right)}^{2}\right)}} \]
   7. Step-by-step derivation

      1. *-commutative 34.0%

         \[\leadsto \sqrt{\color{blue}{\left(x \cdot {\left(\frac{0.1111111111111111}{x} + \left(y + -1\right)\right)}^{2}\right) \cdot 9}} \]

      2. associate-*l* 33.9%

         \[\leadsto \sqrt{\color{blue}{x \cdot \left({\left(\frac{0.1111111111111111}{x} + \left(y + -1\right)\right)}^{2} \cdot 9\right)}} \]

      3. associate-+r+ 33.9%

         \[\leadsto \sqrt{x \cdot \left({\color{blue}{\left(\left(\frac{0.1111111111111111}{x} + y\right) + -1\right)}}^{2} \cdot 9\right)} \]

      4. +-commutative 33.9%

         \[\leadsto \sqrt{x \cdot \left({\left(\color{blue}{\left(y + \frac{0.1111111111111111}{x}\right)} + -1\right)}^{2} \cdot 9\right)} \]

      5. associate-+r+ 33.9%

         \[\leadsto \sqrt{x \cdot \left({\color{blue}{\left(y + \left(\frac{0.1111111111111111}{x} + -1\right)\right)}}^{2} \cdot 9\right)} \]

   8. Simplified 33.9%

      \[\leadsto \color{blue}{\sqrt{x \cdot \left({\left(y + \left(\frac{0.1111111111111111}{x} + -1\right)\right)}^{2} \cdot 9\right)}} \]

   9. Taylor expanded in x around 0 75.5%

      \[\leadsto \sqrt{\color{blue}{2 \cdot \left(y - 1\right) + 0.1111111111111111 \cdot \frac{1}{x}}} \]

   10. Taylor expanded in y around 0 75.4%

       \[\leadsto \color{blue}{\sqrt{0.1111111111111111 \cdot \frac{1}{x} - 2}} \]
   11. Step-by-step derivation

       1. sub-neg 75.4%

          \[\leadsto \sqrt{\color{blue}{0.1111111111111111 \cdot \frac{1}{x} + \left(-2\right)}} \]

       2. associate-*r/ 75.4%

          \[\leadsto \sqrt{\color{blue}{\frac{0.1111111111111111 \cdot 1}{x}} + \left(-2\right)} \]

       3. metadata-eval 75.4%

          \[\leadsto \sqrt{\frac{\color{blue}{0.1111111111111111}}{x} + \left(-2\right)} \]

       4. metadata-eval 75.4%

          \[\leadsto \sqrt{\frac{0.1111111111111111}{x} + \color{blue}{-2}} \]

   12. Simplified 75.4%

       \[\leadsto \color{blue}{\sqrt{\frac{0.1111111111111111}{x} + -2}} \]

   if 5.2000000000000001e-18 < x < 3.1499999999999999e119 or 4.70000000000000004e150 < x < 1.5000000000000001e182 or 2.3500000000000001e215 < x < 5.9999999999999998e267

   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. associate-*l* 99.5%

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

      2. sub-neg 99.5%

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

      3. +-commutative 99.5%

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

      4. associate-+l+ 99.5%

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

      5. *-commutative 99.5%

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

      6. associate-/r* 99.5%

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

      7. metadata-eval 99.5%

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

      8. metadata-eval 99.5%

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

   3. Simplified 99.5%

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

   5. Taylor expanded in y around inf 69.1%

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

      1. add0 69.1%

         \[\leadsto \color{blue}{3 \cdot \left(\sqrt{x} \cdot y\right) + 0} \]

      2. associate-*r* 69.1%

         \[\leadsto \color{blue}{\left(3 \cdot \sqrt{x}\right) \cdot y} + 0 \]

      3. *-commutative 69.1%

         \[\leadsto \color{blue}{\left(\sqrt{x} \cdot 3\right)} \cdot y + 0 \]

      4. metadata-eval 69.1%

         \[\leadsto \left(\sqrt{x} \cdot \color{blue}{\sqrt{9}}\right) \cdot y + 0 \]

      5. sqrt-prod 69.2%

         \[\leadsto \color{blue}{\sqrt{x \cdot 9}} \cdot y + 0 \]

   7. Applied egg-rr 69.2%

      \[\leadsto \color{blue}{\sqrt{x \cdot 9} \cdot y + 0} \]
   8. Step-by-step derivation

      1. add0 69.2%

         \[\leadsto \color{blue}{\sqrt{x \cdot 9} \cdot y} \]

      2. *-commutative 69.2%

         \[\leadsto \color{blue}{y \cdot \sqrt{x \cdot 9}} \]

   9. Simplified 69.2%

      \[\leadsto \color{blue}{y \cdot \sqrt{x \cdot 9}} \]

   if 3.1499999999999999e119 < x < 4.70000000000000004e150 or 1.5000000000000001e182 < x < 2.3500000000000001e215 or 5.9999999999999998e267 < x

   1. Initial program 99.6%

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

      1. remove-double-neg 99.6%

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

      2. distribute-lft-neg-out 99.6%

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

      3. distribute-rgt-neg-in 99.6%

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

      4. +-commutative 99.6%

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

      5. associate--l+ 99.6%

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

      6. distribute-neg-in 99.6%

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

      7. distribute-frac-neg2 99.6%

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

      8. distribute-lft-neg-out 99.6%

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

      9. *-commutative 99.6%

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

      10. distribute-rgt-neg-in 99.6%

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

      11. metadata-eval 99.6%

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

   3. Simplified 99.6%

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

   5. Taylor expanded in y around 0 68.6%

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

      1. *-commutative 68.6%

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

      2. associate-*l* 68.6%

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

      3. sub-neg 68.6%

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

      4. associate-*r/ 68.6%

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

      5. metadata-eval 68.6%

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

      6. distribute-neg-frac 68.6%

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

      7. metadata-eval 68.6%

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

   7. Simplified 68.6%

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

   8. Taylor expanded in x around inf 68.6%

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

4. Final simplification 71.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 5.2 \cdot 10^{-18}:\\ \;\;\;\;\sqrt{\frac{0.1111111111111111}{x} + -2}\\ \mathbf{elif}\;x \leq 3.15 \cdot 10^{+119} \lor \neg \left(x \leq 4.7 \cdot 10^{+150}\right) \land \left(x \leq 1.5 \cdot 10^{+182} \lor \neg \left(x \leq 2.35 \cdot 10^{+215}\right) \land x \leq 6 \cdot 10^{+267}\right):\\ \;\;\;\;y \cdot \sqrt{x \cdot 9}\\ \mathbf{else}:\\ \;\;\;\;\sqrt{x} \cdot -3\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 62.7% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \sqrt{x} \cdot -3\\ t_1 := y \cdot \sqrt{x \cdot 9}\\ \mathbf{if}\;x \leq 1.55 \cdot 10^{-18}:\\ \;\;\;\;\sqrt{\frac{0.1111111111111111}{x} + -2}\\ \mathbf{elif}\;x \leq 4 \cdot 10^{+119}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 4 \cdot 10^{+150}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 4.5 \cdot 10^{+181}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 5.4 \cdot 10^{+217} \lor \neg \left(x \leq 1.8 \cdot 10^{+267}\right):\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;\sqrt{x} \cdot \left(y \cdot 3\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (* (sqrt x) -3.0)) (t_1 (* y (sqrt (* x 9.0)))))
   (if (<= x 1.55e-18)
     (sqrt (+ (/ 0.1111111111111111 x) -2.0))
     (if (<= x 4e+119)
       t_1
       (if (<= x 4e+150)
         t_0
         (if (<= x 4.5e+181)
           t_1
           (if (or (<= x 5.4e+217) (not (<= x 1.8e+267)))
             t_0
             (* (sqrt x) (* y 3.0)))))))))

C

double code(double x, double y) {
	double t_0 = sqrt(x) * -3.0;
	double t_1 = y * sqrt((x * 9.0));
	double tmp;
	if (x <= 1.55e-18) {
		tmp = sqrt(((0.1111111111111111 / x) + -2.0));
	} else if (x <= 4e+119) {
		tmp = t_1;
	} else if (x <= 4e+150) {
		tmp = t_0;
	} else if (x <= 4.5e+181) {
		tmp = t_1;
	} else if ((x <= 5.4e+217) || !(x <= 1.8e+267)) {
		tmp = t_0;
	} else {
		tmp = sqrt(x) * (y * 3.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = sqrt(x) * (-3.0d0)
    t_1 = y * sqrt((x * 9.0d0))
    if (x <= 1.55d-18) then
        tmp = sqrt(((0.1111111111111111d0 / x) + (-2.0d0)))
    else if (x <= 4d+119) then
        tmp = t_1
    else if (x <= 4d+150) then
        tmp = t_0
    else if (x <= 4.5d+181) then
        tmp = t_1
    else if ((x <= 5.4d+217) .or. (.not. (x <= 1.8d+267))) then
        tmp = t_0
    else
        tmp = sqrt(x) * (y * 3.0d0)
    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 = y * Math.sqrt((x * 9.0));
	double tmp;
	if (x <= 1.55e-18) {
		tmp = Math.sqrt(((0.1111111111111111 / x) + -2.0));
	} else if (x <= 4e+119) {
		tmp = t_1;
	} else if (x <= 4e+150) {
		tmp = t_0;
	} else if (x <= 4.5e+181) {
		tmp = t_1;
	} else if ((x <= 5.4e+217) || !(x <= 1.8e+267)) {
		tmp = t_0;
	} else {
		tmp = Math.sqrt(x) * (y * 3.0);
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = math.sqrt(x) * -3.0
	t_1 = y * math.sqrt((x * 9.0))
	tmp = 0
	if x <= 1.55e-18:
		tmp = math.sqrt(((0.1111111111111111 / x) + -2.0))
	elif x <= 4e+119:
		tmp = t_1
	elif x <= 4e+150:
		tmp = t_0
	elif x <= 4.5e+181:
		tmp = t_1
	elif (x <= 5.4e+217) or not (x <= 1.8e+267):
		tmp = t_0
	else:
		tmp = math.sqrt(x) * (y * 3.0)
	return tmp

Julia

function code(x, y)
	t_0 = Float64(sqrt(x) * -3.0)
	t_1 = Float64(y * sqrt(Float64(x * 9.0)))
	tmp = 0.0
	if (x <= 1.55e-18)
		tmp = sqrt(Float64(Float64(0.1111111111111111 / x) + -2.0));
	elseif (x <= 4e+119)
		tmp = t_1;
	elseif (x <= 4e+150)
		tmp = t_0;
	elseif (x <= 4.5e+181)
		tmp = t_1;
	elseif ((x <= 5.4e+217) || !(x <= 1.8e+267))
		tmp = t_0;
	else
		tmp = Float64(sqrt(x) * Float64(y * 3.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = sqrt(x) * -3.0;
	t_1 = y * sqrt((x * 9.0));
	tmp = 0.0;
	if (x <= 1.55e-18)
		tmp = sqrt(((0.1111111111111111 / x) + -2.0));
	elseif (x <= 4e+119)
		tmp = t_1;
	elseif (x <= 4e+150)
		tmp = t_0;
	elseif (x <= 4.5e+181)
		tmp = t_1;
	elseif ((x <= 5.4e+217) || ~((x <= 1.8e+267)))
		tmp = t_0;
	else
		tmp = sqrt(x) * (y * 3.0);
	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[(y * N[Sqrt[N[(x * 9.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, 1.55e-18], N[Sqrt[N[(N[(0.1111111111111111 / x), $MachinePrecision] + -2.0), $MachinePrecision]], $MachinePrecision], If[LessEqual[x, 4e+119], t$95$1, If[LessEqual[x, 4e+150], t$95$0, If[LessEqual[x, 4.5e+181], t$95$1, If[Or[LessEqual[x, 5.4e+217], N[Not[LessEqual[x, 1.8e+267]], $MachinePrecision]], t$95$0, N[(N[Sqrt[x], $MachinePrecision] * N[(y * 3.0), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if x < 1.55000000000000003e-18

   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. associate-*l* 99.2%

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

      2. sub-neg 99.2%

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

      3. +-commutative 99.2%

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

      4. associate-+l+ 99.2%

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

      5. *-commutative 99.2%

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

      6. associate-/r* 99.2%

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

      7. metadata-eval 99.2%

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

      8. metadata-eval 99.2%

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

   3. Simplified 99.2%

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

   6. Applied egg-rr 34.0%

      \[\leadsto \color{blue}{\sqrt{9 \cdot \left(x \cdot {\left(\frac{0.1111111111111111}{x} + \left(y + -1\right)\right)}^{2}\right)}} \]
   7. Step-by-step derivation

      1. *-commutative 34.0%

         \[\leadsto \sqrt{\color{blue}{\left(x \cdot {\left(\frac{0.1111111111111111}{x} + \left(y + -1\right)\right)}^{2}\right) \cdot 9}} \]

      2. associate-*l* 33.9%

         \[\leadsto \sqrt{\color{blue}{x \cdot \left({\left(\frac{0.1111111111111111}{x} + \left(y + -1\right)\right)}^{2} \cdot 9\right)}} \]

      3. associate-+r+ 33.9%

         \[\leadsto \sqrt{x \cdot \left({\color{blue}{\left(\left(\frac{0.1111111111111111}{x} + y\right) + -1\right)}}^{2} \cdot 9\right)} \]

      4. +-commutative 33.9%

         \[\leadsto \sqrt{x \cdot \left({\left(\color{blue}{\left(y + \frac{0.1111111111111111}{x}\right)} + -1\right)}^{2} \cdot 9\right)} \]

      5. associate-+r+ 33.9%

         \[\leadsto \sqrt{x \cdot \left({\color{blue}{\left(y + \left(\frac{0.1111111111111111}{x} + -1\right)\right)}}^{2} \cdot 9\right)} \]

   8. Simplified 33.9%

      \[\leadsto \color{blue}{\sqrt{x \cdot \left({\left(y + \left(\frac{0.1111111111111111}{x} + -1\right)\right)}^{2} \cdot 9\right)}} \]

   9. Taylor expanded in x around 0 75.5%

      \[\leadsto \sqrt{\color{blue}{2 \cdot \left(y - 1\right) + 0.1111111111111111 \cdot \frac{1}{x}}} \]

   10. Taylor expanded in y around 0 75.4%

       \[\leadsto \color{blue}{\sqrt{0.1111111111111111 \cdot \frac{1}{x} - 2}} \]
   11. Step-by-step derivation

       1. sub-neg 75.4%

          \[\leadsto \sqrt{\color{blue}{0.1111111111111111 \cdot \frac{1}{x} + \left(-2\right)}} \]

       2. associate-*r/ 75.4%

          \[\leadsto \sqrt{\color{blue}{\frac{0.1111111111111111 \cdot 1}{x}} + \left(-2\right)} \]

       3. metadata-eval 75.4%

          \[\leadsto \sqrt{\frac{\color{blue}{0.1111111111111111}}{x} + \left(-2\right)} \]

       4. metadata-eval 75.4%

          \[\leadsto \sqrt{\frac{0.1111111111111111}{x} + \color{blue}{-2}} \]

   12. Simplified 75.4%

       \[\leadsto \color{blue}{\sqrt{\frac{0.1111111111111111}{x} + -2}} \]

   if 1.55000000000000003e-18 < x < 3.99999999999999978e119 or 3.99999999999999992e150 < x < 4.5e181

   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. associate-*l* 99.5%

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

      2. sub-neg 99.5%

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

      3. +-commutative 99.5%

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

      4. associate-+l+ 99.5%

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

      5. *-commutative 99.5%

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

      6. associate-/r* 99.5%

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

      7. metadata-eval 99.5%

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

      8. metadata-eval 99.5%

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

   3. Simplified 99.5%

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

   5. Taylor expanded in y around inf 68.7%

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

      1. add0 68.7%

         \[\leadsto \color{blue}{3 \cdot \left(\sqrt{x} \cdot y\right) + 0} \]

      2. associate-*r* 68.7%

         \[\leadsto \color{blue}{\left(3 \cdot \sqrt{x}\right) \cdot y} + 0 \]

      3. *-commutative 68.7%

         \[\leadsto \color{blue}{\left(\sqrt{x} \cdot 3\right)} \cdot y + 0 \]

      4. metadata-eval 68.7%

         \[\leadsto \left(\sqrt{x} \cdot \color{blue}{\sqrt{9}}\right) \cdot y + 0 \]

      5. sqrt-prod 68.8%

         \[\leadsto \color{blue}{\sqrt{x \cdot 9}} \cdot y + 0 \]

   7. Applied egg-rr 68.8%

      \[\leadsto \color{blue}{\sqrt{x \cdot 9} \cdot y + 0} \]
   8. Step-by-step derivation

      1. add0 68.8%

         \[\leadsto \color{blue}{\sqrt{x \cdot 9} \cdot y} \]

      2. *-commutative 68.8%

         \[\leadsto \color{blue}{y \cdot \sqrt{x \cdot 9}} \]

   9. Simplified 68.8%

      \[\leadsto \color{blue}{y \cdot \sqrt{x \cdot 9}} \]

   if 3.99999999999999978e119 < x < 3.99999999999999992e150 or 4.5e181 < x < 5.40000000000000005e217 or 1.8e267 < x

   1. Initial program 99.6%

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

      1. remove-double-neg 99.6%

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

      2. distribute-lft-neg-out 99.6%

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

      3. distribute-rgt-neg-in 99.6%

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

      4. +-commutative 99.6%

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

      5. associate--l+ 99.6%

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

      6. distribute-neg-in 99.6%

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

      7. distribute-frac-neg2 99.6%

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

      8. distribute-lft-neg-out 99.6%

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

      9. *-commutative 99.6%

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

      10. distribute-rgt-neg-in 99.6%

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

      11. metadata-eval 99.6%

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

   3. Simplified 99.6%

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

   5. Taylor expanded in y around 0 68.6%

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

      1. *-commutative 68.6%

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

      2. associate-*l* 68.6%

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

      3. sub-neg 68.6%

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

      4. associate-*r/ 68.6%

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

      5. metadata-eval 68.6%

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

      6. distribute-neg-frac 68.6%

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

      7. metadata-eval 68.6%

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

   7. Simplified 68.6%

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

   8. Taylor expanded in x around inf 68.6%

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

   if 5.40000000000000005e217 < x < 1.8e267

   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. associate-*l* 99.5%

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

      2. sub-neg 99.5%

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

      3. +-commutative 99.5%

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

      4. associate-+l+ 99.5%

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

      5. *-commutative 99.5%

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

      6. associate-/r* 99.5%

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

      7. metadata-eval 99.5%

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

      8. metadata-eval 99.5%

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

   3. Simplified 99.5%

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

   5. Taylor expanded in y around inf 70.2%

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

      1. *-commutative 70.2%

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

      2. associate-*r* 70.4%

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

   7. Simplified 70.4%

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

4. Final simplification 71.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 1.55 \cdot 10^{-18}:\\ \;\;\;\;\sqrt{\frac{0.1111111111111111}{x} + -2}\\ \mathbf{elif}\;x \leq 4 \cdot 10^{+119}:\\ \;\;\;\;y \cdot \sqrt{x \cdot 9}\\ \mathbf{elif}\;x \leq 4 \cdot 10^{+150}:\\ \;\;\;\;\sqrt{x} \cdot -3\\ \mathbf{elif}\;x \leq 4.5 \cdot 10^{+181}:\\ \;\;\;\;y \cdot \sqrt{x \cdot 9}\\ \mathbf{elif}\;x \leq 5.4 \cdot 10^{+217} \lor \neg \left(x \leq 1.8 \cdot 10^{+267}\right):\\ \;\;\;\;\sqrt{x} \cdot -3\\ \mathbf{else}:\\ \;\;\;\;\sqrt{x} \cdot \left(y \cdot 3\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 62.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := y \cdot \sqrt{x \cdot 9}\\ t_1 := \sqrt{x} \cdot -3\\ \mathbf{if}\;x \leq 4.6 \cdot 10^{-18}:\\ \;\;\;\;\sqrt{0.1111111111111111 \cdot \frac{1}{x} - 2}\\ \mathbf{elif}\;x \leq 2.8 \cdot 10^{+119}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 4.2 \cdot 10^{+150}:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 1.7 \cdot 10^{+182}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 1.82 \cdot 10^{+217} \lor \neg \left(x \leq 4 \cdot 10^{+266}\right):\\ \;\;\;\;t\_1\\ \mathbf{else}:\\ \;\;\;\;\sqrt{x} \cdot \left(y \cdot 3\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (* y (sqrt (* x 9.0)))) (t_1 (* (sqrt x) -3.0)))
   (if (<= x 4.6e-18)
     (sqrt (- (* 0.1111111111111111 (/ 1.0 x)) 2.0))
     (if (<= x 2.8e+119)
       t_0
       (if (<= x 4.2e+150)
         t_1
         (if (<= x 1.7e+182)
           t_0
           (if (or (<= x 1.82e+217) (not (<= x 4e+266)))
             t_1
             (* (sqrt x) (* y 3.0)))))))))

C

double code(double x, double y) {
	double t_0 = y * sqrt((x * 9.0));
	double t_1 = sqrt(x) * -3.0;
	double tmp;
	if (x <= 4.6e-18) {
		tmp = sqrt(((0.1111111111111111 * (1.0 / x)) - 2.0));
	} else if (x <= 2.8e+119) {
		tmp = t_0;
	} else if (x <= 4.2e+150) {
		tmp = t_1;
	} else if (x <= 1.7e+182) {
		tmp = t_0;
	} else if ((x <= 1.82e+217) || !(x <= 4e+266)) {
		tmp = t_1;
	} else {
		tmp = sqrt(x) * (y * 3.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = y * sqrt((x * 9.0d0))
    t_1 = sqrt(x) * (-3.0d0)
    if (x <= 4.6d-18) then
        tmp = sqrt(((0.1111111111111111d0 * (1.0d0 / x)) - 2.0d0))
    else if (x <= 2.8d+119) then
        tmp = t_0
    else if (x <= 4.2d+150) then
        tmp = t_1
    else if (x <= 1.7d+182) then
        tmp = t_0
    else if ((x <= 1.82d+217) .or. (.not. (x <= 4d+266))) then
        tmp = t_1
    else
        tmp = sqrt(x) * (y * 3.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double t_0 = y * Math.sqrt((x * 9.0));
	double t_1 = Math.sqrt(x) * -3.0;
	double tmp;
	if (x <= 4.6e-18) {
		tmp = Math.sqrt(((0.1111111111111111 * (1.0 / x)) - 2.0));
	} else if (x <= 2.8e+119) {
		tmp = t_0;
	} else if (x <= 4.2e+150) {
		tmp = t_1;
	} else if (x <= 1.7e+182) {
		tmp = t_0;
	} else if ((x <= 1.82e+217) || !(x <= 4e+266)) {
		tmp = t_1;
	} else {
		tmp = Math.sqrt(x) * (y * 3.0);
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = y * math.sqrt((x * 9.0))
	t_1 = math.sqrt(x) * -3.0
	tmp = 0
	if x <= 4.6e-18:
		tmp = math.sqrt(((0.1111111111111111 * (1.0 / x)) - 2.0))
	elif x <= 2.8e+119:
		tmp = t_0
	elif x <= 4.2e+150:
		tmp = t_1
	elif x <= 1.7e+182:
		tmp = t_0
	elif (x <= 1.82e+217) or not (x <= 4e+266):
		tmp = t_1
	else:
		tmp = math.sqrt(x) * (y * 3.0)
	return tmp

Julia

function code(x, y)
	t_0 = Float64(y * sqrt(Float64(x * 9.0)))
	t_1 = Float64(sqrt(x) * -3.0)
	tmp = 0.0
	if (x <= 4.6e-18)
		tmp = sqrt(Float64(Float64(0.1111111111111111 * Float64(1.0 / x)) - 2.0));
	elseif (x <= 2.8e+119)
		tmp = t_0;
	elseif (x <= 4.2e+150)
		tmp = t_1;
	elseif (x <= 1.7e+182)
		tmp = t_0;
	elseif ((x <= 1.82e+217) || !(x <= 4e+266))
		tmp = t_1;
	else
		tmp = Float64(sqrt(x) * Float64(y * 3.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = y * sqrt((x * 9.0));
	t_1 = sqrt(x) * -3.0;
	tmp = 0.0;
	if (x <= 4.6e-18)
		tmp = sqrt(((0.1111111111111111 * (1.0 / x)) - 2.0));
	elseif (x <= 2.8e+119)
		tmp = t_0;
	elseif (x <= 4.2e+150)
		tmp = t_1;
	elseif (x <= 1.7e+182)
		tmp = t_0;
	elseif ((x <= 1.82e+217) || ~((x <= 4e+266)))
		tmp = t_1;
	else
		tmp = sqrt(x) * (y * 3.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(y * N[Sqrt[N[(x * 9.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(N[Sqrt[x], $MachinePrecision] * -3.0), $MachinePrecision]}, If[LessEqual[x, 4.6e-18], N[Sqrt[N[(N[(0.1111111111111111 * N[(1.0 / x), $MachinePrecision]), $MachinePrecision] - 2.0), $MachinePrecision]], $MachinePrecision], If[LessEqual[x, 2.8e+119], t$95$0, If[LessEqual[x, 4.2e+150], t$95$1, If[LessEqual[x, 1.7e+182], t$95$0, If[Or[LessEqual[x, 1.82e+217], N[Not[LessEqual[x, 4e+266]], $MachinePrecision]], t$95$1, N[(N[Sqrt[x], $MachinePrecision] * N[(y * 3.0), $MachinePrecision]), $MachinePrecision]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if x < 4.6000000000000002e-18

   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. associate-*l* 99.2%

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

      2. sub-neg 99.2%

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

      3. +-commutative 99.2%

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

      4. associate-+l+ 99.2%

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

      5. *-commutative 99.2%

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

      6. associate-/r* 99.2%

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

      7. metadata-eval 99.2%

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

      8. metadata-eval 99.2%

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

   3. Simplified 99.2%

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

   6. Applied egg-rr 34.0%

      \[\leadsto \color{blue}{\sqrt{9 \cdot \left(x \cdot {\left(\frac{0.1111111111111111}{x} + \left(y + -1\right)\right)}^{2}\right)}} \]
   7. Step-by-step derivation

      1. *-commutative 34.0%

         \[\leadsto \sqrt{\color{blue}{\left(x \cdot {\left(\frac{0.1111111111111111}{x} + \left(y + -1\right)\right)}^{2}\right) \cdot 9}} \]

      2. associate-*l* 33.9%

         \[\leadsto \sqrt{\color{blue}{x \cdot \left({\left(\frac{0.1111111111111111}{x} + \left(y + -1\right)\right)}^{2} \cdot 9\right)}} \]

      3. associate-+r+ 33.9%

         \[\leadsto \sqrt{x \cdot \left({\color{blue}{\left(\left(\frac{0.1111111111111111}{x} + y\right) + -1\right)}}^{2} \cdot 9\right)} \]

      4. +-commutative 33.9%

         \[\leadsto \sqrt{x \cdot \left({\left(\color{blue}{\left(y + \frac{0.1111111111111111}{x}\right)} + -1\right)}^{2} \cdot 9\right)} \]

      5. associate-+r+ 33.9%

         \[\leadsto \sqrt{x \cdot \left({\color{blue}{\left(y + \left(\frac{0.1111111111111111}{x} + -1\right)\right)}}^{2} \cdot 9\right)} \]

   8. Simplified 33.9%

      \[\leadsto \color{blue}{\sqrt{x \cdot \left({\left(y + \left(\frac{0.1111111111111111}{x} + -1\right)\right)}^{2} \cdot 9\right)}} \]

   9. Taylor expanded in x around 0 75.5%

      \[\leadsto \sqrt{\color{blue}{2 \cdot \left(y - 1\right) + 0.1111111111111111 \cdot \frac{1}{x}}} \]

   10. Taylor expanded in y around 0 75.4%

       \[\leadsto \color{blue}{\sqrt{0.1111111111111111 \cdot \frac{1}{x} - 2}} \]

   if 4.6000000000000002e-18 < x < 2.80000000000000013e119 or 4.19999999999999996e150 < x < 1.69999999999999993e182

   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. associate-*l* 99.5%

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

      2. sub-neg 99.5%

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

      3. +-commutative 99.5%

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

      4. associate-+l+ 99.5%

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

      5. *-commutative 99.5%

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

      6. associate-/r* 99.5%

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

      7. metadata-eval 99.5%

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

      8. metadata-eval 99.5%

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

   3. Simplified 99.5%

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

   5. Taylor expanded in y around inf 68.7%

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

      1. add0 68.7%

         \[\leadsto \color{blue}{3 \cdot \left(\sqrt{x} \cdot y\right) + 0} \]

      2. associate-*r* 68.7%

         \[\leadsto \color{blue}{\left(3 \cdot \sqrt{x}\right) \cdot y} + 0 \]

      3. *-commutative 68.7%

         \[\leadsto \color{blue}{\left(\sqrt{x} \cdot 3\right)} \cdot y + 0 \]

      4. metadata-eval 68.7%

         \[\leadsto \left(\sqrt{x} \cdot \color{blue}{\sqrt{9}}\right) \cdot y + 0 \]

      5. sqrt-prod 68.8%

         \[\leadsto \color{blue}{\sqrt{x \cdot 9}} \cdot y + 0 \]

   7. Applied egg-rr 68.8%

      \[\leadsto \color{blue}{\sqrt{x \cdot 9} \cdot y + 0} \]
   8. Step-by-step derivation

      1. add0 68.8%

         \[\leadsto \color{blue}{\sqrt{x \cdot 9} \cdot y} \]

      2. *-commutative 68.8%

         \[\leadsto \color{blue}{y \cdot \sqrt{x \cdot 9}} \]

   9. Simplified 68.8%

      \[\leadsto \color{blue}{y \cdot \sqrt{x \cdot 9}} \]

   if 2.80000000000000013e119 < x < 4.19999999999999996e150 or 1.69999999999999993e182 < x < 1.82e217 or 4.0000000000000001e266 < x

   1. Initial program 99.6%

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

      1. remove-double-neg 99.6%

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

      2. distribute-lft-neg-out 99.6%

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

      3. distribute-rgt-neg-in 99.6%

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

      4. +-commutative 99.6%

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

      5. associate--l+ 99.6%

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

      6. distribute-neg-in 99.6%

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

      7. distribute-frac-neg2 99.6%

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

      8. distribute-lft-neg-out 99.6%

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

      9. *-commutative 99.6%

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

      10. distribute-rgt-neg-in 99.6%

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

      11. metadata-eval 99.6%

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

   3. Simplified 99.6%

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

   5. Taylor expanded in y around 0 68.6%

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

      1. *-commutative 68.6%

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

      2. associate-*l* 68.6%

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

      3. sub-neg 68.6%

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

      4. associate-*r/ 68.6%

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

      5. metadata-eval 68.6%

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

      6. distribute-neg-frac 68.6%

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

      7. metadata-eval 68.6%

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

   7. Simplified 68.6%

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

   8. Taylor expanded in x around inf 68.6%

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

   if 1.82e217 < x < 4.0000000000000001e266

   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. associate-*l* 99.5%

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

      2. sub-neg 99.5%

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

      3. +-commutative 99.5%

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

      4. associate-+l+ 99.5%

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

      5. *-commutative 99.5%

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

      6. associate-/r* 99.5%

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

      7. metadata-eval 99.5%

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

      8. metadata-eval 99.5%

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

   3. Simplified 99.5%

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

   5. Taylor expanded in y around inf 70.2%

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

      1. *-commutative 70.2%

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

      2. associate-*r* 70.4%

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

   7. Simplified 70.4%

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

4. Final simplification 71.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 4.6 \cdot 10^{-18}:\\ \;\;\;\;\sqrt{0.1111111111111111 \cdot \frac{1}{x} - 2}\\ \mathbf{elif}\;x \leq 2.8 \cdot 10^{+119}:\\ \;\;\;\;y \cdot \sqrt{x \cdot 9}\\ \mathbf{elif}\;x \leq 4.2 \cdot 10^{+150}:\\ \;\;\;\;\sqrt{x} \cdot -3\\ \mathbf{elif}\;x \leq 1.7 \cdot 10^{+182}:\\ \;\;\;\;y \cdot \sqrt{x \cdot 9}\\ \mathbf{elif}\;x \leq 1.82 \cdot 10^{+217} \lor \neg \left(x \leq 4 \cdot 10^{+266}\right):\\ \;\;\;\;\sqrt{x} \cdot -3\\ \mathbf{else}:\\ \;\;\;\;\sqrt{x} \cdot \left(y \cdot 3\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 87.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 2 \cdot \left(y + -1\right)\\ \mathbf{if}\;x \leq 4 \cdot 10^{-46}:\\ \;\;\;\;\sqrt{\frac{0.1111111111111111}{x} + t\_0}\\ \mathbf{elif}\;x \leq 2.5 \cdot 10^{-31}:\\ \;\;\;\;3 \cdot \left(y \cdot \sqrt{x}\right)\\ \mathbf{elif}\;x \leq 7.2 \cdot 10^{-17}:\\ \;\;\;\;\sqrt{t\_0 + 0.1111111111111111 \cdot \frac{1}{x}}\\ \mathbf{else}:\\ \;\;\;\;\left(y + -1\right) \cdot {\left(\frac{0.1111111111111111}{x}\right)}^{-0.5}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (* 2.0 (+ y -1.0))))
   (if (<= x 4e-46)
     (sqrt (+ (/ 0.1111111111111111 x) t_0))
     (if (<= x 2.5e-31)
       (* 3.0 (* y (sqrt x)))
       (if (<= x 7.2e-17)
         (sqrt (+ t_0 (* 0.1111111111111111 (/ 1.0 x))))
         (* (+ y -1.0) (pow (/ 0.1111111111111111 x) -0.5)))))))

C

double code(double x, double y) {
	double t_0 = 2.0 * (y + -1.0);
	double tmp;
	if (x <= 4e-46) {
		tmp = sqrt(((0.1111111111111111 / x) + t_0));
	} else if (x <= 2.5e-31) {
		tmp = 3.0 * (y * sqrt(x));
	} else if (x <= 7.2e-17) {
		tmp = sqrt((t_0 + (0.1111111111111111 * (1.0 / x))));
	} else {
		tmp = (y + -1.0) * pow((0.1111111111111111 / x), -0.5);
	}
	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 = 2.0d0 * (y + (-1.0d0))
    if (x <= 4d-46) then
        tmp = sqrt(((0.1111111111111111d0 / x) + t_0))
    else if (x <= 2.5d-31) then
        tmp = 3.0d0 * (y * sqrt(x))
    else if (x <= 7.2d-17) then
        tmp = sqrt((t_0 + (0.1111111111111111d0 * (1.0d0 / x))))
    else
        tmp = (y + (-1.0d0)) * ((0.1111111111111111d0 / x) ** (-0.5d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double t_0 = 2.0 * (y + -1.0);
	double tmp;
	if (x <= 4e-46) {
		tmp = Math.sqrt(((0.1111111111111111 / x) + t_0));
	} else if (x <= 2.5e-31) {
		tmp = 3.0 * (y * Math.sqrt(x));
	} else if (x <= 7.2e-17) {
		tmp = Math.sqrt((t_0 + (0.1111111111111111 * (1.0 / x))));
	} else {
		tmp = (y + -1.0) * Math.pow((0.1111111111111111 / x), -0.5);
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = 2.0 * (y + -1.0)
	tmp = 0
	if x <= 4e-46:
		tmp = math.sqrt(((0.1111111111111111 / x) + t_0))
	elif x <= 2.5e-31:
		tmp = 3.0 * (y * math.sqrt(x))
	elif x <= 7.2e-17:
		tmp = math.sqrt((t_0 + (0.1111111111111111 * (1.0 / x))))
	else:
		tmp = (y + -1.0) * math.pow((0.1111111111111111 / x), -0.5)
	return tmp

Julia

function code(x, y)
	t_0 = Float64(2.0 * Float64(y + -1.0))
	tmp = 0.0
	if (x <= 4e-46)
		tmp = sqrt(Float64(Float64(0.1111111111111111 / x) + t_0));
	elseif (x <= 2.5e-31)
		tmp = Float64(3.0 * Float64(y * sqrt(x)));
	elseif (x <= 7.2e-17)
		tmp = sqrt(Float64(t_0 + Float64(0.1111111111111111 * Float64(1.0 / x))));
	else
		tmp = Float64(Float64(y + -1.0) * (Float64(0.1111111111111111 / x) ^ -0.5));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = 2.0 * (y + -1.0);
	tmp = 0.0;
	if (x <= 4e-46)
		tmp = sqrt(((0.1111111111111111 / x) + t_0));
	elseif (x <= 2.5e-31)
		tmp = 3.0 * (y * sqrt(x));
	elseif (x <= 7.2e-17)
		tmp = sqrt((t_0 + (0.1111111111111111 * (1.0 / x))));
	else
		tmp = (y + -1.0) * ((0.1111111111111111 / x) ^ -0.5);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(2.0 * N[(y + -1.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, 4e-46], N[Sqrt[N[(N[(0.1111111111111111 / x), $MachinePrecision] + t$95$0), $MachinePrecision]], $MachinePrecision], If[LessEqual[x, 2.5e-31], N[(3.0 * N[(y * N[Sqrt[x], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 7.2e-17], N[Sqrt[N[(t$95$0 + N[(0.1111111111111111 * N[(1.0 / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision], N[(N[(y + -1.0), $MachinePrecision] * N[Power[N[(0.1111111111111111 / x), $MachinePrecision], -0.5], $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 4 regimes

2. if x < 4.00000000000000009e-46

   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. associate-*l* 99.2%

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

      2. sub-neg 99.2%

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

      3. +-commutative 99.2%

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

      4. associate-+l+ 99.2%

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

      5. *-commutative 99.2%

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

      6. associate-/r* 99.2%

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

      7. metadata-eval 99.2%

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

      8. metadata-eval 99.2%

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

   3. Simplified 99.2%

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

   6. Applied egg-rr 31.2%

      \[\leadsto \color{blue}{\sqrt{9 \cdot \left(x \cdot {\left(\frac{0.1111111111111111}{x} + \left(y + -1\right)\right)}^{2}\right)}} \]
   7. Step-by-step derivation

      1. *-commutative 31.2%

         \[\leadsto \sqrt{\color{blue}{\left(x \cdot {\left(\frac{0.1111111111111111}{x} + \left(y + -1\right)\right)}^{2}\right) \cdot 9}} \]

      2. associate-*l* 31.2%

         \[\leadsto \sqrt{\color{blue}{x \cdot \left({\left(\frac{0.1111111111111111}{x} + \left(y + -1\right)\right)}^{2} \cdot 9\right)}} \]

      3. associate-+r+ 31.2%

         \[\leadsto \sqrt{x \cdot \left({\color{blue}{\left(\left(\frac{0.1111111111111111}{x} + y\right) + -1\right)}}^{2} \cdot 9\right)} \]

      4. +-commutative 31.2%

         \[\leadsto \sqrt{x \cdot \left({\left(\color{blue}{\left(y + \frac{0.1111111111111111}{x}\right)} + -1\right)}^{2} \cdot 9\right)} \]

      5. associate-+r+ 31.2%

         \[\leadsto \sqrt{x \cdot \left({\color{blue}{\left(y + \left(\frac{0.1111111111111111}{x} + -1\right)\right)}}^{2} \cdot 9\right)} \]

   8. Simplified 31.2%

      \[\leadsto \color{blue}{\sqrt{x \cdot \left({\left(y + \left(\frac{0.1111111111111111}{x} + -1\right)\right)}^{2} \cdot 9\right)}} \]

   9. Taylor expanded in x around 0 77.5%

      \[\leadsto \sqrt{\color{blue}{2 \cdot \left(y - 1\right) + 0.1111111111111111 \cdot \frac{1}{x}}} \]

   10. Taylor expanded in x around 0 77.6%

       \[\leadsto \sqrt{2 \cdot \left(y - 1\right) + \color{blue}{\frac{0.1111111111111111}{x}}} \]

   if 4.00000000000000009e-46 < x < 2.5e-31

   1. Initial program 99.0%

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

      1. associate-*l* 99.7%

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

      2. sub-neg 99.7%

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

      3. +-commutative 99.7%

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

      4. associate-+l+ 99.7%

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

      5. *-commutative 99.7%

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

      6. associate-/r* 99.5%

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

      7. metadata-eval 99.5%

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

      8. metadata-eval 99.5%

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

   3. Simplified 99.5%

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

   5. Taylor expanded in y around inf 83.6%

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

   if 2.5e-31 < x < 7.1999999999999999e-17

   1. Initial program 98.7%

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

      1. associate-*l* 98.7%

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

      2. sub-neg 98.7%

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

      3. +-commutative 98.7%

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

      4. associate-+l+ 98.7%

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

      5. *-commutative 98.7%

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

      6. associate-/r* 99.0%

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

      7. metadata-eval 99.0%

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

      8. metadata-eval 99.0%

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

   3. Simplified 99.0%

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

   6. Applied egg-rr 99.0%

      \[\leadsto \color{blue}{\sqrt{9 \cdot \left(x \cdot {\left(\frac{0.1111111111111111}{x} + \left(y + -1\right)\right)}^{2}\right)}} \]
   7. Step-by-step derivation

      1. *-commutative 99.0%

         \[\leadsto \sqrt{\color{blue}{\left(x \cdot {\left(\frac{0.1111111111111111}{x} + \left(y + -1\right)\right)}^{2}\right) \cdot 9}} \]

      2. associate-*l* 99.0%

         \[\leadsto \sqrt{\color{blue}{x \cdot \left({\left(\frac{0.1111111111111111}{x} + \left(y + -1\right)\right)}^{2} \cdot 9\right)}} \]

      3. associate-+r+ 99.0%

         \[\leadsto \sqrt{x \cdot \left({\color{blue}{\left(\left(\frac{0.1111111111111111}{x} + y\right) + -1\right)}}^{2} \cdot 9\right)} \]

      4. +-commutative 99.0%

         \[\leadsto \sqrt{x \cdot \left({\left(\color{blue}{\left(y + \frac{0.1111111111111111}{x}\right)} + -1\right)}^{2} \cdot 9\right)} \]

      5. associate-+r+ 99.0%

         \[\leadsto \sqrt{x \cdot \left({\color{blue}{\left(y + \left(\frac{0.1111111111111111}{x} + -1\right)\right)}}^{2} \cdot 9\right)} \]

   8. Simplified 99.0%

      \[\leadsto \color{blue}{\sqrt{x \cdot \left({\left(y + \left(\frac{0.1111111111111111}{x} + -1\right)\right)}^{2} \cdot 9\right)}} \]

   9. Taylor expanded in x around 0 99.7%

      \[\leadsto \sqrt{\color{blue}{2 \cdot \left(y - 1\right) + 0.1111111111111111 \cdot \frac{1}{x}}} \]

   if 7.1999999999999999e-17 < 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. add0 99.5%

         \[\leadsto \color{blue}{\left(3 \cdot \sqrt{x} + 0\right)} \cdot \left(\left(y + \frac{1}{x \cdot 9}\right) - 1\right) \]

      2. *-commutative 99.5%

         \[\leadsto \left(\color{blue}{\sqrt{x} \cdot 3} + 0\right) \cdot \left(\left(y + \frac{1}{x \cdot 9}\right) - 1\right) \]

      3. metadata-eval 99.5%

         \[\leadsto \left(\sqrt{x} \cdot \color{blue}{\sqrt{9}} + 0\right) \cdot \left(\left(y + \frac{1}{x \cdot 9}\right) - 1\right) \]

      4. sqrt-prod 99.1%

         \[\leadsto \left(\color{blue}{\sqrt{x \cdot 9}} + 0\right) \cdot \left(\left(y + \frac{1}{x \cdot 9}\right) - 1\right) \]

   4. Applied egg-rr 99.1%

      \[\leadsto \color{blue}{\left(\sqrt{x \cdot 9} + 0\right)} \cdot \left(\left(y + \frac{1}{x \cdot 9}\right) - 1\right) \]
   5. Step-by-step derivation

      1. add0 99.1%

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

   6. Simplified 99.1%

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

   7. Taylor expanded in y around inf 98.7%

      \[\leadsto \sqrt{x \cdot 9} \cdot \left(\color{blue}{y} - 1\right) \]
   8. Step-by-step derivation

      1. sqrt-prod 99.1%

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

      2. metadata-eval 99.1%

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

   9. Applied egg-rr 99.1%

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

       1. *-commutative 99.1%

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

       2. metadata-eval 99.1%

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

       3. associate-/r/ 99.0%

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

       4. metadata-eval 99.0%

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

       5. sqrt-div 99.1%

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

       6. pow1/2 99.1%

          \[\leadsto \frac{1}{\color{blue}{{\left(\frac{0.1111111111111111}{x}\right)}^{0.5}}} \cdot \left(y - 1\right) \]

       7. pow-flip 99.2%

          \[\leadsto \color{blue}{{\left(\frac{0.1111111111111111}{x}\right)}^{\left(-0.5\right)}} \cdot \left(y - 1\right) \]

       8. metadata-eval 99.2%

          \[\leadsto {\left(\frac{0.1111111111111111}{x}\right)}^{\color{blue}{-0.5}} \cdot \left(y - 1\right) \]

   11. Applied egg-rr 99.2%

       \[\leadsto \color{blue}{{\left(\frac{0.1111111111111111}{x}\right)}^{-0.5}} \cdot \left(y - 1\right) \]
3. Recombined 4 regimes into one program.

4. Final simplification 90.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 4 \cdot 10^{-46}:\\ \;\;\;\;\sqrt{\frac{0.1111111111111111}{x} + 2 \cdot \left(y + -1\right)}\\ \mathbf{elif}\;x \leq 2.5 \cdot 10^{-31}:\\ \;\;\;\;3 \cdot \left(y \cdot \sqrt{x}\right)\\ \mathbf{elif}\;x \leq 7.2 \cdot 10^{-17}:\\ \;\;\;\;\sqrt{2 \cdot \left(y + -1\right) + 0.1111111111111111 \cdot \frac{1}{x}}\\ \mathbf{else}:\\ \;\;\;\;\left(y + -1\right) \cdot {\left(\frac{0.1111111111111111}{x}\right)}^{-0.5}\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 87.2% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \sqrt{\frac{0.1111111111111111}{x} + 2 \cdot \left(y + -1\right)}\\ \mathbf{if}\;x \leq 5.6 \cdot 10^{-41}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 2.9 \cdot 10^{-31}:\\ \;\;\;\;3 \cdot \left(y \cdot \sqrt{x}\right)\\ \mathbf{elif}\;x \leq 8.5 \cdot 10^{-17}:\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;\left(y + -1\right) \cdot {\left(\frac{0.1111111111111111}{x}\right)}^{-0.5}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (sqrt (+ (/ 0.1111111111111111 x) (* 2.0 (+ y -1.0))))))
   (if (<= x 5.6e-41)
     t_0
     (if (<= x 2.9e-31)
       (* 3.0 (* y (sqrt x)))
       (if (<= x 8.5e-17)
         t_0
         (* (+ y -1.0) (pow (/ 0.1111111111111111 x) -0.5)))))))

C

double code(double x, double y) {
	double t_0 = sqrt(((0.1111111111111111 / x) + (2.0 * (y + -1.0))));
	double tmp;
	if (x <= 5.6e-41) {
		tmp = t_0;
	} else if (x <= 2.9e-31) {
		tmp = 3.0 * (y * sqrt(x));
	} else if (x <= 8.5e-17) {
		tmp = t_0;
	} else {
		tmp = (y + -1.0) * pow((0.1111111111111111 / x), -0.5);
	}
	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(((0.1111111111111111d0 / x) + (2.0d0 * (y + (-1.0d0)))))
    if (x <= 5.6d-41) then
        tmp = t_0
    else if (x <= 2.9d-31) then
        tmp = 3.0d0 * (y * sqrt(x))
    else if (x <= 8.5d-17) then
        tmp = t_0
    else
        tmp = (y + (-1.0d0)) * ((0.1111111111111111d0 / x) ** (-0.5d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double t_0 = Math.sqrt(((0.1111111111111111 / x) + (2.0 * (y + -1.0))));
	double tmp;
	if (x <= 5.6e-41) {
		tmp = t_0;
	} else if (x <= 2.9e-31) {
		tmp = 3.0 * (y * Math.sqrt(x));
	} else if (x <= 8.5e-17) {
		tmp = t_0;
	} else {
		tmp = (y + -1.0) * Math.pow((0.1111111111111111 / x), -0.5);
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = math.sqrt(((0.1111111111111111 / x) + (2.0 * (y + -1.0))))
	tmp = 0
	if x <= 5.6e-41:
		tmp = t_0
	elif x <= 2.9e-31:
		tmp = 3.0 * (y * math.sqrt(x))
	elif x <= 8.5e-17:
		tmp = t_0
	else:
		tmp = (y + -1.0) * math.pow((0.1111111111111111 / x), -0.5)
	return tmp

Julia

function code(x, y)
	t_0 = sqrt(Float64(Float64(0.1111111111111111 / x) + Float64(2.0 * Float64(y + -1.0))))
	tmp = 0.0
	if (x <= 5.6e-41)
		tmp = t_0;
	elseif (x <= 2.9e-31)
		tmp = Float64(3.0 * Float64(y * sqrt(x)));
	elseif (x <= 8.5e-17)
		tmp = t_0;
	else
		tmp = Float64(Float64(y + -1.0) * (Float64(0.1111111111111111 / x) ^ -0.5));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = sqrt(((0.1111111111111111 / x) + (2.0 * (y + -1.0))));
	tmp = 0.0;
	if (x <= 5.6e-41)
		tmp = t_0;
	elseif (x <= 2.9e-31)
		tmp = 3.0 * (y * sqrt(x));
	elseif (x <= 8.5e-17)
		tmp = t_0;
	else
		tmp = (y + -1.0) * ((0.1111111111111111 / x) ^ -0.5);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[Sqrt[N[(N[(0.1111111111111111 / x), $MachinePrecision] + N[(2.0 * N[(y + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]}, If[LessEqual[x, 5.6e-41], t$95$0, If[LessEqual[x, 2.9e-31], N[(3.0 * N[(y * N[Sqrt[x], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 8.5e-17], t$95$0, N[(N[(y + -1.0), $MachinePrecision] * N[Power[N[(0.1111111111111111 / x), $MachinePrecision], -0.5], $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if x < 5.6000000000000003e-41 or 2.9000000000000001e-31 < x < 8.5e-17

   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. associate-*l* 99.2%

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

      2. sub-neg 99.2%

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

      3. +-commutative 99.2%

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

      4. associate-+l+ 99.2%

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

      5. *-commutative 99.2%

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

      6. associate-/r* 99.2%

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

      7. metadata-eval 99.2%

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

      8. metadata-eval 99.2%

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

   3. Simplified 99.2%

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

   6. Applied egg-rr 34.9%

      \[\leadsto \color{blue}{\sqrt{9 \cdot \left(x \cdot {\left(\frac{0.1111111111111111}{x} + \left(y + -1\right)\right)}^{2}\right)}} \]
   7. Step-by-step derivation

      1. *-commutative 34.9%

         \[\leadsto \sqrt{\color{blue}{\left(x \cdot {\left(\frac{0.1111111111111111}{x} + \left(y + -1\right)\right)}^{2}\right) \cdot 9}} \]

      2. associate-*l* 34.9%

         \[\leadsto \sqrt{\color{blue}{x \cdot \left({\left(\frac{0.1111111111111111}{x} + \left(y + -1\right)\right)}^{2} \cdot 9\right)}} \]

      3. associate-+r+ 34.9%

         \[\leadsto \sqrt{x \cdot \left({\color{blue}{\left(\left(\frac{0.1111111111111111}{x} + y\right) + -1\right)}}^{2} \cdot 9\right)} \]

      4. +-commutative 34.9%

         \[\leadsto \sqrt{x \cdot \left({\left(\color{blue}{\left(y + \frac{0.1111111111111111}{x}\right)} + -1\right)}^{2} \cdot 9\right)} \]

      5. associate-+r+ 34.9%

         \[\leadsto \sqrt{x \cdot \left({\color{blue}{\left(y + \left(\frac{0.1111111111111111}{x} + -1\right)\right)}}^{2} \cdot 9\right)} \]

   8. Simplified 34.9%

      \[\leadsto \color{blue}{\sqrt{x \cdot \left({\left(y + \left(\frac{0.1111111111111111}{x} + -1\right)\right)}^{2} \cdot 9\right)}} \]

   9. Taylor expanded in x around 0 78.8%

      \[\leadsto \sqrt{\color{blue}{2 \cdot \left(y - 1\right) + 0.1111111111111111 \cdot \frac{1}{x}}} \]

   10. Taylor expanded in x around 0 78.8%

       \[\leadsto \sqrt{2 \cdot \left(y - 1\right) + \color{blue}{\frac{0.1111111111111111}{x}}} \]

   if 5.6000000000000003e-41 < x < 2.9000000000000001e-31

   1. Initial program 99.0%

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

      1. associate-*l* 99.7%

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

      2. sub-neg 99.7%

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

      3. +-commutative 99.7%

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

      4. associate-+l+ 99.7%

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

      5. *-commutative 99.7%

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

      6. associate-/r* 99.5%

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

      7. metadata-eval 99.5%

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

      8. metadata-eval 99.5%

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

   3. Simplified 99.5%

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

   5. Taylor expanded in y around inf 83.6%

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

   if 8.5e-17 < 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. add0 99.5%

         \[\leadsto \color{blue}{\left(3 \cdot \sqrt{x} + 0\right)} \cdot \left(\left(y + \frac{1}{x \cdot 9}\right) - 1\right) \]

      2. *-commutative 99.5%

         \[\leadsto \left(\color{blue}{\sqrt{x} \cdot 3} + 0\right) \cdot \left(\left(y + \frac{1}{x \cdot 9}\right) - 1\right) \]

      3. metadata-eval 99.5%

         \[\leadsto \left(\sqrt{x} \cdot \color{blue}{\sqrt{9}} + 0\right) \cdot \left(\left(y + \frac{1}{x \cdot 9}\right) - 1\right) \]

      4. sqrt-prod 99.1%

         \[\leadsto \left(\color{blue}{\sqrt{x \cdot 9}} + 0\right) \cdot \left(\left(y + \frac{1}{x \cdot 9}\right) - 1\right) \]

   4. Applied egg-rr 99.1%

      \[\leadsto \color{blue}{\left(\sqrt{x \cdot 9} + 0\right)} \cdot \left(\left(y + \frac{1}{x \cdot 9}\right) - 1\right) \]
   5. Step-by-step derivation

      1. add0 99.1%

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

   6. Simplified 99.1%

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

   7. Taylor expanded in y around inf 98.7%

      \[\leadsto \sqrt{x \cdot 9} \cdot \left(\color{blue}{y} - 1\right) \]
   8. Step-by-step derivation

      1. sqrt-prod 99.1%

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

      2. metadata-eval 99.1%

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

   9. Applied egg-rr 99.1%

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

       1. *-commutative 99.1%

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

       2. metadata-eval 99.1%

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

       3. associate-/r/ 99.0%

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

       4. metadata-eval 99.0%

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

       5. sqrt-div 99.1%

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

       6. pow1/2 99.1%

          \[\leadsto \frac{1}{\color{blue}{{\left(\frac{0.1111111111111111}{x}\right)}^{0.5}}} \cdot \left(y - 1\right) \]

       7. pow-flip 99.2%

          \[\leadsto \color{blue}{{\left(\frac{0.1111111111111111}{x}\right)}^{\left(-0.5\right)}} \cdot \left(y - 1\right) \]

       8. metadata-eval 99.2%

          \[\leadsto {\left(\frac{0.1111111111111111}{x}\right)}^{\color{blue}{-0.5}} \cdot \left(y - 1\right) \]

   11. Applied egg-rr 99.2%

       \[\leadsto \color{blue}{{\left(\frac{0.1111111111111111}{x}\right)}^{-0.5}} \cdot \left(y - 1\right) \]
3. Recombined 3 regimes into one program.

4. Final simplification 90.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 5.6 \cdot 10^{-41}:\\ \;\;\;\;\sqrt{\frac{0.1111111111111111}{x} + 2 \cdot \left(y + -1\right)}\\ \mathbf{elif}\;x \leq 2.9 \cdot 10^{-31}:\\ \;\;\;\;3 \cdot \left(y \cdot \sqrt{x}\right)\\ \mathbf{elif}\;x \leq 8.5 \cdot 10^{-17}:\\ \;\;\;\;\sqrt{\frac{0.1111111111111111}{x} + 2 \cdot \left(y + -1\right)}\\ \mathbf{else}:\\ \;\;\;\;\left(y + -1\right) \cdot {\left(\frac{0.1111111111111111}{x}\right)}^{-0.5}\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 86.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5.2 \cdot 10^{+25} \lor \neg \left(y \leq 26\right):\\ \;\;\;\;y \cdot \sqrt{x \cdot 9}\\ \mathbf{else}:\\ \;\;\;\;\sqrt{x} \cdot \left(-3 + \frac{0.3333333333333333}{x}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= y -5.2e+25) (not (<= y 26.0)))
   (* y (sqrt (* x 9.0)))
   (* (sqrt x) (+ -3.0 (/ 0.3333333333333333 x)))))

C

double code(double x, double y) {
	double tmp;
	if ((y <= -5.2e+25) || !(y <= 26.0)) {
		tmp = y * sqrt((x * 9.0));
	} else {
		tmp = sqrt(x) * (-3.0 + (0.3333333333333333 / x));
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if ((y <= (-5.2d+25)) .or. (.not. (y <= 26.0d0))) then
        tmp = y * sqrt((x * 9.0d0))
    else
        tmp = sqrt(x) * ((-3.0d0) + (0.3333333333333333d0 / x))
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((y <= -5.2e+25) || !(y <= 26.0)) {
		tmp = y * Math.sqrt((x * 9.0));
	} else {
		tmp = Math.sqrt(x) * (-3.0 + (0.3333333333333333 / x));
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (y <= -5.2e+25) or not (y <= 26.0):
		tmp = y * math.sqrt((x * 9.0))
	else:
		tmp = math.sqrt(x) * (-3.0 + (0.3333333333333333 / x))
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((y <= -5.2e+25) || !(y <= 26.0))
		tmp = Float64(y * sqrt(Float64(x * 9.0)));
	else
		tmp = Float64(sqrt(x) * Float64(-3.0 + Float64(0.3333333333333333 / x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((y <= -5.2e+25) || ~((y <= 26.0)))
		tmp = y * sqrt((x * 9.0));
	else
		tmp = sqrt(x) * (-3.0 + (0.3333333333333333 / x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[y, -5.2e+25], N[Not[LessEqual[y, 26.0]], $MachinePrecision]], N[(y * N[Sqrt[N[(x * 9.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], N[(N[Sqrt[x], $MachinePrecision] * N[(-3.0 + N[(0.3333333333333333 / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -5.1999999999999997e25 or 26 < y

   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. associate-*l* 99.5%

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

      2. sub-neg 99.5%

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

      3. +-commutative 99.5%

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

      4. associate-+l+ 99.5%

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

      5. *-commutative 99.5%

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

      6. associate-/r* 99.5%

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

      7. metadata-eval 99.5%

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

      8. metadata-eval 99.5%

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

   3. Simplified 99.5%

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

   5. Taylor expanded in y around inf 77.1%

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

      1. add0 77.1%

         \[\leadsto \color{blue}{3 \cdot \left(\sqrt{x} \cdot y\right) + 0} \]

      2. associate-*r* 77.2%

         \[\leadsto \color{blue}{\left(3 \cdot \sqrt{x}\right) \cdot y} + 0 \]

      3. *-commutative 77.2%

         \[\leadsto \color{blue}{\left(\sqrt{x} \cdot 3\right)} \cdot y + 0 \]

      4. metadata-eval 77.2%

         \[\leadsto \left(\sqrt{x} \cdot \color{blue}{\sqrt{9}}\right) \cdot y + 0 \]

      5. sqrt-prod 77.3%

         \[\leadsto \color{blue}{\sqrt{x \cdot 9}} \cdot y + 0 \]

   7. Applied egg-rr 77.3%

      \[\leadsto \color{blue}{\sqrt{x \cdot 9} \cdot y + 0} \]
   8. Step-by-step derivation

      1. add0 77.3%

         \[\leadsto \color{blue}{\sqrt{x \cdot 9} \cdot y} \]

      2. *-commutative 77.3%

         \[\leadsto \color{blue}{y \cdot \sqrt{x \cdot 9}} \]

   9. Simplified 77.3%

      \[\leadsto \color{blue}{y \cdot \sqrt{x \cdot 9}} \]

   if -5.1999999999999997e25 < y < 26

   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. remove-double-neg 99.3%

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

      2. distribute-lft-neg-out 99.3%

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

      3. distribute-rgt-neg-in 99.3%

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

      4. +-commutative 99.3%

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

      5. associate--l+ 99.3%

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

      6. distribute-neg-in 99.3%

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

      7. distribute-frac-neg2 99.3%

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

      8. distribute-lft-neg-out 99.3%

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

      9. *-commutative 99.3%

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

      10. distribute-rgt-neg-in 99.3%

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

      11. metadata-eval 99.3%

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

   3. Simplified 99.3%

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

   5. Taylor expanded in y around 0 96.8%

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

      1. *-commutative 96.8%

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

      2. associate-*l* 96.9%

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

      3. sub-neg 96.9%

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

      4. associate-*r/ 96.9%

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

      5. metadata-eval 96.9%

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

      6. distribute-neg-frac 96.9%

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

      7. metadata-eval 96.9%

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

   7. Simplified 96.9%

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

   8. Taylor expanded in x around 0 96.9%

      \[\leadsto \sqrt{x} \cdot \color{blue}{\left(0.3333333333333333 \cdot \frac{1}{x} - 3\right)} \]
   9. Step-by-step derivation

      1. sub-neg 96.9%

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

      2. associate-*r/ 96.9%

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

      3. metadata-eval 96.9%

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

      4. metadata-eval 96.9%

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

   10. Simplified 96.9%

       \[\leadsto \sqrt{x} \cdot \color{blue}{\left(\frac{0.3333333333333333}{x} + -3\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 86.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.2 \cdot 10^{+25} \lor \neg \left(y \leq 26\right):\\ \;\;\;\;y \cdot \sqrt{x \cdot 9}\\ \mathbf{else}:\\ \;\;\;\;\sqrt{x} \cdot \left(-3 + \frac{0.3333333333333333}{x}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 87.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 2.8 \cdot 10^{-17}:\\ \;\;\;\;\sqrt{0.1111111111111111 \cdot \frac{1}{x} - 2}\\ \mathbf{else}:\\ \;\;\;\;\left(y + -1\right) \cdot {\left(\frac{0.1111111111111111}{x}\right)}^{-0.5}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x 2.8e-17)
   (sqrt (- (* 0.1111111111111111 (/ 1.0 x)) 2.0))
   (* (+ y -1.0) (pow (/ 0.1111111111111111 x) -0.5))))

C

double code(double x, double y) {
	double tmp;
	if (x <= 2.8e-17) {
		tmp = sqrt(((0.1111111111111111 * (1.0 / x)) - 2.0));
	} else {
		tmp = (y + -1.0) * pow((0.1111111111111111 / x), -0.5);
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (x <= 2.8d-17) then
        tmp = sqrt(((0.1111111111111111d0 * (1.0d0 / x)) - 2.0d0))
    else
        tmp = (y + (-1.0d0)) * ((0.1111111111111111d0 / x) ** (-0.5d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= 2.8e-17) {
		tmp = Math.sqrt(((0.1111111111111111 * (1.0 / x)) - 2.0));
	} else {
		tmp = (y + -1.0) * Math.pow((0.1111111111111111 / x), -0.5);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= 2.8e-17:
		tmp = math.sqrt(((0.1111111111111111 * (1.0 / x)) - 2.0))
	else:
		tmp = (y + -1.0) * math.pow((0.1111111111111111 / x), -0.5)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= 2.8e-17)
		tmp = sqrt(Float64(Float64(0.1111111111111111 * Float64(1.0 / x)) - 2.0));
	else
		tmp = Float64(Float64(y + -1.0) * (Float64(0.1111111111111111 / x) ^ -0.5));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= 2.8e-17)
		tmp = sqrt(((0.1111111111111111 * (1.0 / x)) - 2.0));
	else
		tmp = (y + -1.0) * ((0.1111111111111111 / x) ^ -0.5);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, 2.8e-17], N[Sqrt[N[(N[(0.1111111111111111 * N[(1.0 / x), $MachinePrecision]), $MachinePrecision] - 2.0), $MachinePrecision]], $MachinePrecision], N[(N[(y + -1.0), $MachinePrecision] * N[Power[N[(0.1111111111111111 / x), $MachinePrecision], -0.5], $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < 2.7999999999999999e-17

   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. associate-*l* 99.2%

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

      2. sub-neg 99.2%

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

      3. +-commutative 99.2%

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

      4. associate-+l+ 99.2%

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

      5. *-commutative 99.2%

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

      6. associate-/r* 99.2%

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

      7. metadata-eval 99.2%

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

      8. metadata-eval 99.2%

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

   3. Simplified 99.2%

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

   6. Applied egg-rr 34.0%

      \[\leadsto \color{blue}{\sqrt{9 \cdot \left(x \cdot {\left(\frac{0.1111111111111111}{x} + \left(y + -1\right)\right)}^{2}\right)}} \]
   7. Step-by-step derivation

      1. *-commutative 34.0%

         \[\leadsto \sqrt{\color{blue}{\left(x \cdot {\left(\frac{0.1111111111111111}{x} + \left(y + -1\right)\right)}^{2}\right) \cdot 9}} \]

      2. associate-*l* 33.9%

         \[\leadsto \sqrt{\color{blue}{x \cdot \left({\left(\frac{0.1111111111111111}{x} + \left(y + -1\right)\right)}^{2} \cdot 9\right)}} \]

      3. associate-+r+ 33.9%

         \[\leadsto \sqrt{x \cdot \left({\color{blue}{\left(\left(\frac{0.1111111111111111}{x} + y\right) + -1\right)}}^{2} \cdot 9\right)} \]

      4. +-commutative 33.9%

         \[\leadsto \sqrt{x \cdot \left({\left(\color{blue}{\left(y + \frac{0.1111111111111111}{x}\right)} + -1\right)}^{2} \cdot 9\right)} \]

      5. associate-+r+ 33.9%

         \[\leadsto \sqrt{x \cdot \left({\color{blue}{\left(y + \left(\frac{0.1111111111111111}{x} + -1\right)\right)}}^{2} \cdot 9\right)} \]

   8. Simplified 33.9%

      \[\leadsto \color{blue}{\sqrt{x \cdot \left({\left(y + \left(\frac{0.1111111111111111}{x} + -1\right)\right)}^{2} \cdot 9\right)}} \]

   9. Taylor expanded in x around 0 75.5%

      \[\leadsto \sqrt{\color{blue}{2 \cdot \left(y - 1\right) + 0.1111111111111111 \cdot \frac{1}{x}}} \]

   10. Taylor expanded in y around 0 75.4%

       \[\leadsto \color{blue}{\sqrt{0.1111111111111111 \cdot \frac{1}{x} - 2}} \]

   if 2.7999999999999999e-17 < 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. add0 99.5%

         \[\leadsto \color{blue}{\left(3 \cdot \sqrt{x} + 0\right)} \cdot \left(\left(y + \frac{1}{x \cdot 9}\right) - 1\right) \]

      2. *-commutative 99.5%

         \[\leadsto \left(\color{blue}{\sqrt{x} \cdot 3} + 0\right) \cdot \left(\left(y + \frac{1}{x \cdot 9}\right) - 1\right) \]

      3. metadata-eval 99.5%

         \[\leadsto \left(\sqrt{x} \cdot \color{blue}{\sqrt{9}} + 0\right) \cdot \left(\left(y + \frac{1}{x \cdot 9}\right) - 1\right) \]

      4. sqrt-prod 99.1%

         \[\leadsto \left(\color{blue}{\sqrt{x \cdot 9}} + 0\right) \cdot \left(\left(y + \frac{1}{x \cdot 9}\right) - 1\right) \]

   4. Applied egg-rr 99.1%

      \[\leadsto \color{blue}{\left(\sqrt{x \cdot 9} + 0\right)} \cdot \left(\left(y + \frac{1}{x \cdot 9}\right) - 1\right) \]
   5. Step-by-step derivation

      1. add0 99.1%

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

   6. Simplified 99.1%

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

   7. Taylor expanded in y around inf 98.7%

      \[\leadsto \sqrt{x \cdot 9} \cdot \left(\color{blue}{y} - 1\right) \]
   8. Step-by-step derivation

      1. sqrt-prod 99.1%

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

      2. metadata-eval 99.1%

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

   9. Applied egg-rr 99.1%

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

       1. *-commutative 99.1%

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

       2. metadata-eval 99.1%

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

       3. associate-/r/ 99.0%

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

       4. metadata-eval 99.0%

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

       5. sqrt-div 99.1%

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

       6. pow1/2 99.1%

          \[\leadsto \frac{1}{\color{blue}{{\left(\frac{0.1111111111111111}{x}\right)}^{0.5}}} \cdot \left(y - 1\right) \]

       7. pow-flip 99.2%

          \[\leadsto \color{blue}{{\left(\frac{0.1111111111111111}{x}\right)}^{\left(-0.5\right)}} \cdot \left(y - 1\right) \]

       8. metadata-eval 99.2%

          \[\leadsto {\left(\frac{0.1111111111111111}{x}\right)}^{\color{blue}{-0.5}} \cdot \left(y - 1\right) \]

   11. Applied egg-rr 99.2%

       \[\leadsto \color{blue}{{\left(\frac{0.1111111111111111}{x}\right)}^{-0.5}} \cdot \left(y - 1\right) \]
3. Recombined 2 regimes into one program.

4. Final simplification 88.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 2.8 \cdot 10^{-17}:\\ \;\;\;\;\sqrt{0.1111111111111111 \cdot \frac{1}{x} - 2}\\ \mathbf{else}:\\ \;\;\;\;\left(y + -1\right) \cdot {\left(\frac{0.1111111111111111}{x}\right)}^{-0.5}\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 87.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 1.55 \cdot 10^{-18}:\\ \;\;\;\;\sqrt{0.1111111111111111 \cdot \frac{1}{x} - 2}\\ \mathbf{else}:\\ \;\;\;\;\left(y + -1\right) \cdot \sqrt{x \cdot 9}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x 1.55e-18)
   (sqrt (- (* 0.1111111111111111 (/ 1.0 x)) 2.0))
   (* (+ y -1.0) (sqrt (* x 9.0)))))

C

double code(double x, double y) {
	double tmp;
	if (x <= 1.55e-18) {
		tmp = sqrt(((0.1111111111111111 * (1.0 / x)) - 2.0));
	} else {
		tmp = (y + -1.0) * sqrt((x * 9.0));
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (x <= 1.55d-18) then
        tmp = sqrt(((0.1111111111111111d0 * (1.0d0 / x)) - 2.0d0))
    else
        tmp = (y + (-1.0d0)) * sqrt((x * 9.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= 1.55e-18) {
		tmp = Math.sqrt(((0.1111111111111111 * (1.0 / x)) - 2.0));
	} else {
		tmp = (y + -1.0) * Math.sqrt((x * 9.0));
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= 1.55e-18:
		tmp = math.sqrt(((0.1111111111111111 * (1.0 / x)) - 2.0))
	else:
		tmp = (y + -1.0) * math.sqrt((x * 9.0))
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= 1.55e-18)
		tmp = sqrt(Float64(Float64(0.1111111111111111 * Float64(1.0 / x)) - 2.0));
	else
		tmp = Float64(Float64(y + -1.0) * sqrt(Float64(x * 9.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= 1.55e-18)
		tmp = sqrt(((0.1111111111111111 * (1.0 / x)) - 2.0));
	else
		tmp = (y + -1.0) * sqrt((x * 9.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, 1.55e-18], N[Sqrt[N[(N[(0.1111111111111111 * N[(1.0 / x), $MachinePrecision]), $MachinePrecision] - 2.0), $MachinePrecision]], $MachinePrecision], N[(N[(y + -1.0), $MachinePrecision] * N[Sqrt[N[(x * 9.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < 1.55000000000000003e-18

   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. associate-*l* 99.2%

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

      2. sub-neg 99.2%

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

      3. +-commutative 99.2%

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

      4. associate-+l+ 99.2%

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

      5. *-commutative 99.2%

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

      6. associate-/r* 99.2%

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

      7. metadata-eval 99.2%

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

      8. metadata-eval 99.2%

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

   3. Simplified 99.2%

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

   6. Applied egg-rr 34.0%

      \[\leadsto \color{blue}{\sqrt{9 \cdot \left(x \cdot {\left(\frac{0.1111111111111111}{x} + \left(y + -1\right)\right)}^{2}\right)}} \]
   7. Step-by-step derivation

      1. *-commutative 34.0%

         \[\leadsto \sqrt{\color{blue}{\left(x \cdot {\left(\frac{0.1111111111111111}{x} + \left(y + -1\right)\right)}^{2}\right) \cdot 9}} \]

      2. associate-*l* 33.9%

         \[\leadsto \sqrt{\color{blue}{x \cdot \left({\left(\frac{0.1111111111111111}{x} + \left(y + -1\right)\right)}^{2} \cdot 9\right)}} \]

      3. associate-+r+ 33.9%

         \[\leadsto \sqrt{x \cdot \left({\color{blue}{\left(\left(\frac{0.1111111111111111}{x} + y\right) + -1\right)}}^{2} \cdot 9\right)} \]

      4. +-commutative 33.9%

         \[\leadsto \sqrt{x \cdot \left({\left(\color{blue}{\left(y + \frac{0.1111111111111111}{x}\right)} + -1\right)}^{2} \cdot 9\right)} \]

      5. associate-+r+ 33.9%

         \[\leadsto \sqrt{x \cdot \left({\color{blue}{\left(y + \left(\frac{0.1111111111111111}{x} + -1\right)\right)}}^{2} \cdot 9\right)} \]

   8. Simplified 33.9%

      \[\leadsto \color{blue}{\sqrt{x \cdot \left({\left(y + \left(\frac{0.1111111111111111}{x} + -1\right)\right)}^{2} \cdot 9\right)}} \]

   9. Taylor expanded in x around 0 75.5%

      \[\leadsto \sqrt{\color{blue}{2 \cdot \left(y - 1\right) + 0.1111111111111111 \cdot \frac{1}{x}}} \]

   10. Taylor expanded in y around 0 75.4%

       \[\leadsto \color{blue}{\sqrt{0.1111111111111111 \cdot \frac{1}{x} - 2}} \]

   if 1.55000000000000003e-18 < 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. add0 99.5%

         \[\leadsto \color{blue}{\left(3 \cdot \sqrt{x} + 0\right)} \cdot \left(\left(y + \frac{1}{x \cdot 9}\right) - 1\right) \]

      2. *-commutative 99.5%

         \[\leadsto \left(\color{blue}{\sqrt{x} \cdot 3} + 0\right) \cdot \left(\left(y + \frac{1}{x \cdot 9}\right) - 1\right) \]

      3. metadata-eval 99.5%

         \[\leadsto \left(\sqrt{x} \cdot \color{blue}{\sqrt{9}} + 0\right) \cdot \left(\left(y + \frac{1}{x \cdot 9}\right) - 1\right) \]

      4. sqrt-prod 99.1%

         \[\leadsto \left(\color{blue}{\sqrt{x \cdot 9}} + 0\right) \cdot \left(\left(y + \frac{1}{x \cdot 9}\right) - 1\right) \]

   4. Applied egg-rr 99.1%

      \[\leadsto \color{blue}{\left(\sqrt{x \cdot 9} + 0\right)} \cdot \left(\left(y + \frac{1}{x \cdot 9}\right) - 1\right) \]
   5. Step-by-step derivation

      1. add0 99.1%

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

   6. Simplified 99.1%

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

   7. Taylor expanded in y around inf 98.7%

      \[\leadsto \sqrt{x \cdot 9} \cdot \left(\color{blue}{y} - 1\right) \]
3. Recombined 2 regimes into one program.

4. Final simplification 88.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 1.55 \cdot 10^{-18}:\\ \;\;\;\;\sqrt{0.1111111111111111 \cdot \frac{1}{x} - 2}\\ \mathbf{else}:\\ \;\;\;\;\left(y + -1\right) \cdot \sqrt{x \cdot 9}\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 87.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 4.2 \cdot 10^{-17}:\\ \;\;\;\;\sqrt{0.1111111111111111 \cdot \frac{1}{x} - 2}\\ \mathbf{else}:\\ \;\;\;\;\left(y + -1\right) \cdot \left(\sqrt{x} \cdot 3\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x 4.2e-17)
   (sqrt (- (* 0.1111111111111111 (/ 1.0 x)) 2.0))
   (* (+ y -1.0) (* (sqrt x) 3.0))))

C

double code(double x, double y) {
	double tmp;
	if (x <= 4.2e-17) {
		tmp = sqrt(((0.1111111111111111 * (1.0 / x)) - 2.0));
	} else {
		tmp = (y + -1.0) * (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 <= 4.2d-17) then
        tmp = sqrt(((0.1111111111111111d0 * (1.0d0 / x)) - 2.0d0))
    else
        tmp = (y + (-1.0d0)) * (sqrt(x) * 3.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= 4.2e-17) {
		tmp = Math.sqrt(((0.1111111111111111 * (1.0 / x)) - 2.0));
	} else {
		tmp = (y + -1.0) * (Math.sqrt(x) * 3.0);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= 4.2e-17:
		tmp = math.sqrt(((0.1111111111111111 * (1.0 / x)) - 2.0))
	else:
		tmp = (y + -1.0) * (math.sqrt(x) * 3.0)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= 4.2e-17)
		tmp = sqrt(Float64(Float64(0.1111111111111111 * Float64(1.0 / x)) - 2.0));
	else
		tmp = Float64(Float64(y + -1.0) * Float64(sqrt(x) * 3.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= 4.2e-17)
		tmp = sqrt(((0.1111111111111111 * (1.0 / x)) - 2.0));
	else
		tmp = (y + -1.0) * (sqrt(x) * 3.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, 4.2e-17], N[Sqrt[N[(N[(0.1111111111111111 * N[(1.0 / x), $MachinePrecision]), $MachinePrecision] - 2.0), $MachinePrecision]], $MachinePrecision], N[(N[(y + -1.0), $MachinePrecision] * N[(N[Sqrt[x], $MachinePrecision] * 3.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < 4.19999999999999984e-17

   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. associate-*l* 99.2%

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

      2. sub-neg 99.2%

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

      3. +-commutative 99.2%

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

      4. associate-+l+ 99.2%

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

      5. *-commutative 99.2%

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

      6. associate-/r* 99.2%

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

      7. metadata-eval 99.2%

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

      8. metadata-eval 99.2%

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

   3. Simplified 99.2%

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

   6. Applied egg-rr 34.0%

      \[\leadsto \color{blue}{\sqrt{9 \cdot \left(x \cdot {\left(\frac{0.1111111111111111}{x} + \left(y + -1\right)\right)}^{2}\right)}} \]
   7. Step-by-step derivation

      1. *-commutative 34.0%

         \[\leadsto \sqrt{\color{blue}{\left(x \cdot {\left(\frac{0.1111111111111111}{x} + \left(y + -1\right)\right)}^{2}\right) \cdot 9}} \]

      2. associate-*l* 33.9%

         \[\leadsto \sqrt{\color{blue}{x \cdot \left({\left(\frac{0.1111111111111111}{x} + \left(y + -1\right)\right)}^{2} \cdot 9\right)}} \]

      3. associate-+r+ 33.9%

         \[\leadsto \sqrt{x \cdot \left({\color{blue}{\left(\left(\frac{0.1111111111111111}{x} + y\right) + -1\right)}}^{2} \cdot 9\right)} \]

      4. +-commutative 33.9%

         \[\leadsto \sqrt{x \cdot \left({\left(\color{blue}{\left(y + \frac{0.1111111111111111}{x}\right)} + -1\right)}^{2} \cdot 9\right)} \]

      5. associate-+r+ 33.9%

         \[\leadsto \sqrt{x \cdot \left({\color{blue}{\left(y + \left(\frac{0.1111111111111111}{x} + -1\right)\right)}}^{2} \cdot 9\right)} \]

   8. Simplified 33.9%

      \[\leadsto \color{blue}{\sqrt{x \cdot \left({\left(y + \left(\frac{0.1111111111111111}{x} + -1\right)\right)}^{2} \cdot 9\right)}} \]

   9. Taylor expanded in x around 0 75.5%

      \[\leadsto \sqrt{\color{blue}{2 \cdot \left(y - 1\right) + 0.1111111111111111 \cdot \frac{1}{x}}} \]

   10. Taylor expanded in y around 0 75.4%

       \[\leadsto \color{blue}{\sqrt{0.1111111111111111 \cdot \frac{1}{x} - 2}} \]

   if 4.19999999999999984e-17 < 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. Taylor expanded in y around inf 99.1%

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

4. Final simplification 88.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 4.2 \cdot 10^{-17}:\\ \;\;\;\;\sqrt{0.1111111111111111 \cdot \frac{1}{x} - 2}\\ \mathbf{else}:\\ \;\;\;\;\left(y + -1\right) \cdot \left(\sqrt{x} \cdot 3\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 12: 99.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ 3 \cdot \left(\sqrt{x} \cdot \left(\frac{0.1111111111111111}{x} + \left(y + -1\right)\right)\right) \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (* 3.0 (* (sqrt x) (+ (/ 0.1111111111111111 x) (+ y -1.0)))))

C

double code(double x, double y) {
	return 3.0 * (sqrt(x) * ((0.1111111111111111 / x) + (y + -1.0)));
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = 3.0d0 * (sqrt(x) * ((0.1111111111111111d0 / x) + (y + (-1.0d0))))
end function

Java

public static double code(double x, double y) {
	return 3.0 * (Math.sqrt(x) * ((0.1111111111111111 / x) + (y + -1.0)));
}

Python

def code(x, y):
	return 3.0 * (math.sqrt(x) * ((0.1111111111111111 / x) + (y + -1.0)))

Julia

function code(x, y)
	return Float64(3.0 * Float64(sqrt(x) * Float64(Float64(0.1111111111111111 / x) + Float64(y + -1.0))))
end

MATLAB

function tmp = code(x, y)
	tmp = 3.0 * (sqrt(x) * ((0.1111111111111111 / x) + (y + -1.0)));
end

Wolfram

code[x_, y_] := N[(3.0 * N[(N[Sqrt[x], $MachinePrecision] * N[(N[(0.1111111111111111 / x), $MachinePrecision] + N[(y + -1.0), $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. associate-*l* 99.4%

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

   2. sub-neg 99.4%

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

   3. +-commutative 99.4%

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

   4. associate-+l+ 99.4%

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

   5. *-commutative 99.4%

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

   6. associate-/r* 99.4%

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

   7. metadata-eval 99.4%

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

   8. metadata-eval 99.4%

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

3. Simplified 99.4%

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

5. Final simplification 99.4%

   \[\leadsto 3 \cdot \left(\sqrt{x} \cdot \left(\frac{0.1111111111111111}{x} + \left(y + -1\right)\right)\right) \]
6. Add Preprocessing

Alternative 13: 99.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \left(\sqrt{x} \cdot -3\right) \cdot \left(\frac{-0.1111111111111111}{x} + \left(1 - y\right)\right) \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (* (* (sqrt x) -3.0) (+ (/ -0.1111111111111111 x) (- 1.0 y))))

C

double code(double x, double y) {
	return (sqrt(x) * -3.0) * ((-0.1111111111111111 / x) + (1.0 - y));
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = (sqrt(x) * (-3.0d0)) * (((-0.1111111111111111d0) / x) + (1.0d0 - y))
end function

Java

public static double code(double x, double y) {
	return (Math.sqrt(x) * -3.0) * ((-0.1111111111111111 / x) + (1.0 - y));
}

Python

def code(x, y):
	return (math.sqrt(x) * -3.0) * ((-0.1111111111111111 / x) + (1.0 - y))

Julia

function code(x, y)
	return Float64(Float64(sqrt(x) * -3.0) * Float64(Float64(-0.1111111111111111 / x) + Float64(1.0 - y)))
end

MATLAB

function tmp = code(x, y)
	tmp = (sqrt(x) * -3.0) * ((-0.1111111111111111 / x) + (1.0 - y));
end

Wolfram

code[x_, y_] := N[(N[(N[Sqrt[x], $MachinePrecision] * -3.0), $MachinePrecision] * N[(N[(-0.1111111111111111 / x), $MachinePrecision] + N[(1.0 - y), $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. remove-double-neg 99.4%

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

   2. distribute-lft-neg-out 99.4%

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

   3. distribute-rgt-neg-in 99.4%

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

   4. +-commutative 99.4%

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

   5. associate--l+ 99.4%

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

   6. distribute-neg-in 99.4%

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

   7. distribute-frac-neg2 99.4%

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

   8. distribute-lft-neg-out 99.4%

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

   9. *-commutative 99.4%

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

   10. distribute-rgt-neg-in 99.4%

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

   11. metadata-eval 99.4%

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

3. Simplified 99.4%

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

5. Final simplification 99.4%

   \[\leadsto \left(\sqrt{x} \cdot -3\right) \cdot \left(\frac{-0.1111111111111111}{x} + \left(1 - y\right)\right) \]
6. Add Preprocessing

Alternative 14: 61.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 2.1 \cdot 10^{-9}:\\ \;\;\;\;\sqrt{\frac{0.1111111111111111}{x} + -2}\\ \mathbf{else}:\\ \;\;\;\;\sqrt{x} \cdot -3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x 2.1e-9) (sqrt (+ (/ 0.1111111111111111 x) -2.0)) (* (sqrt x) -3.0)))

C

double code(double x, double y) {
	double tmp;
	if (x <= 2.1e-9) {
		tmp = sqrt(((0.1111111111111111 / x) + -2.0));
	} 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 <= 2.1d-9) then
        tmp = sqrt(((0.1111111111111111d0 / x) + (-2.0d0)))
    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 <= 2.1e-9) {
		tmp = Math.sqrt(((0.1111111111111111 / x) + -2.0));
	} else {
		tmp = Math.sqrt(x) * -3.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= 2.1e-9:
		tmp = math.sqrt(((0.1111111111111111 / x) + -2.0))
	else:
		tmp = math.sqrt(x) * -3.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= 2.1e-9)
		tmp = sqrt(Float64(Float64(0.1111111111111111 / x) + -2.0));
	else
		tmp = Float64(sqrt(x) * -3.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= 2.1e-9)
		tmp = sqrt(((0.1111111111111111 / x) + -2.0));
	else
		tmp = sqrt(x) * -3.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, 2.1e-9], N[Sqrt[N[(N[(0.1111111111111111 / x), $MachinePrecision] + -2.0), $MachinePrecision]], $MachinePrecision], N[(N[Sqrt[x], $MachinePrecision] * -3.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < 2.10000000000000019e-9

   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. associate-*l* 99.2%

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

      2. sub-neg 99.2%

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

      3. +-commutative 99.2%

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

      4. associate-+l+ 99.2%

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

      5. *-commutative 99.2%

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

      6. associate-/r* 99.2%

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

      7. metadata-eval 99.2%

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

      8. metadata-eval 99.2%

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

   3. Simplified 99.2%

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

   6. Applied egg-rr 33.5%

      \[\leadsto \color{blue}{\sqrt{9 \cdot \left(x \cdot {\left(\frac{0.1111111111111111}{x} + \left(y + -1\right)\right)}^{2}\right)}} \]
   7. Step-by-step derivation

      1. *-commutative 33.5%

         \[\leadsto \sqrt{\color{blue}{\left(x \cdot {\left(\frac{0.1111111111111111}{x} + \left(y + -1\right)\right)}^{2}\right) \cdot 9}} \]

      2. associate-*l* 33.4%

         \[\leadsto \sqrt{\color{blue}{x \cdot \left({\left(\frac{0.1111111111111111}{x} + \left(y + -1\right)\right)}^{2} \cdot 9\right)}} \]

      3. associate-+r+ 33.4%

         \[\leadsto \sqrt{x \cdot \left({\color{blue}{\left(\left(\frac{0.1111111111111111}{x} + y\right) + -1\right)}}^{2} \cdot 9\right)} \]

      4. +-commutative 33.4%

         \[\leadsto \sqrt{x \cdot \left({\left(\color{blue}{\left(y + \frac{0.1111111111111111}{x}\right)} + -1\right)}^{2} \cdot 9\right)} \]

      5. associate-+r+ 33.4%

         \[\leadsto \sqrt{x \cdot \left({\color{blue}{\left(y + \left(\frac{0.1111111111111111}{x} + -1\right)\right)}}^{2} \cdot 9\right)} \]

   8. Simplified 33.4%

      \[\leadsto \color{blue}{\sqrt{x \cdot \left({\left(y + \left(\frac{0.1111111111111111}{x} + -1\right)\right)}^{2} \cdot 9\right)}} \]

   9. Taylor expanded in x around 0 74.4%

      \[\leadsto \sqrt{\color{blue}{2 \cdot \left(y - 1\right) + 0.1111111111111111 \cdot \frac{1}{x}}} \]

   10. Taylor expanded in y around 0 74.2%

       \[\leadsto \color{blue}{\sqrt{0.1111111111111111 \cdot \frac{1}{x} - 2}} \]
   11. Step-by-step derivation

       1. sub-neg 74.2%

          \[\leadsto \sqrt{\color{blue}{0.1111111111111111 \cdot \frac{1}{x} + \left(-2\right)}} \]

       2. associate-*r/ 74.2%

          \[\leadsto \sqrt{\color{blue}{\frac{0.1111111111111111 \cdot 1}{x}} + \left(-2\right)} \]

       3. metadata-eval 74.2%

          \[\leadsto \sqrt{\frac{\color{blue}{0.1111111111111111}}{x} + \left(-2\right)} \]

       4. metadata-eval 74.2%

          \[\leadsto \sqrt{\frac{0.1111111111111111}{x} + \color{blue}{-2}} \]

   12. Simplified 74.2%

       \[\leadsto \color{blue}{\sqrt{\frac{0.1111111111111111}{x} + -2}} \]

   if 2.10000000000000019e-9 < 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. remove-double-neg 99.5%

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

      2. distribute-lft-neg-out 99.5%

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

      3. distribute-rgt-neg-in 99.5%

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

      4. +-commutative 99.5%

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

      5. associate--l+ 99.5%

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

      6. distribute-neg-in 99.5%

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

      7. distribute-frac-neg2 99.5%

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

      8. distribute-lft-neg-out 99.5%

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

      9. *-commutative 99.5%

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

      10. distribute-rgt-neg-in 99.5%

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

      11. metadata-eval 99.5%

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

   3. Simplified 99.5%

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

   5. Taylor expanded in y around 0 45.9%

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

      1. *-commutative 45.9%

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

      2. associate-*l* 45.9%

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

      3. sub-neg 45.9%

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

      4. associate-*r/ 45.9%

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

      5. metadata-eval 45.9%

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

      6. distribute-neg-frac 45.9%

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

      7. metadata-eval 45.9%

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

   7. Simplified 45.9%

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

   8. Taylor expanded in x around inf 45.4%

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

4. Final simplification 58.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 2.1 \cdot 10^{-9}:\\ \;\;\;\;\sqrt{\frac{0.1111111111111111}{x} + -2}\\ \mathbf{else}:\\ \;\;\;\;\sqrt{x} \cdot -3\\ \end{array} \]
5. Add Preprocessing

Alternative 15: 3.3% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \sqrt{x \cdot 9} \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (sqrt (* x 9.0)))

C

double code(double x, double y) {
	return sqrt((x * 9.0));
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = sqrt((x * 9.0d0))
end function

Java

public static double code(double x, double y) {
	return Math.sqrt((x * 9.0));
}

Python

def code(x, y):
	return math.sqrt((x * 9.0))

Julia

function code(x, y)
	return sqrt(Float64(x * 9.0))
end

MATLAB

function tmp = code(x, y)
	tmp = sqrt((x * 9.0));
end

Wolfram

code[x_, y_] := N[Sqrt[N[(x * 9.0), $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. Step-by-step derivation

   1. remove-double-neg 99.4%

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

   2. distribute-lft-neg-out 99.4%

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

   3. distribute-rgt-neg-in 99.4%

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

   4. +-commutative 99.4%

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

   5. associate--l+ 99.4%

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

   6. distribute-neg-in 99.4%

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

   7. distribute-frac-neg2 99.4%

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

   8. distribute-lft-neg-out 99.4%

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

   9. *-commutative 99.4%

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

   10. distribute-rgt-neg-in 99.4%

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

   11. metadata-eval 99.4%

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

3. Simplified 99.4%

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

5. Taylor expanded in y around 0 58.7%

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

   1. *-commutative 58.7%

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

   2. associate-*l* 58.8%

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

   3. sub-neg 58.8%

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

   4. associate-*r/ 58.8%

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

   5. metadata-eval 58.8%

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

   6. distribute-neg-frac 58.8%

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

   7. metadata-eval 58.8%

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

7. Simplified 58.8%

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

8. Taylor expanded in x around inf 25.4%

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

   1. add-sqr-sqrt 0.0%

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

   2. sqrt-unprod 3.0%

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

   3. swap-sqr 3.0%

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

   4. add-sqr-sqrt 3.0%

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

   5. metadata-eval 3.0%

      \[\leadsto \sqrt{x \cdot \color{blue}{9}} \]

   6. pow1/2 3.0%

      \[\leadsto \color{blue}{{\left(x \cdot 9\right)}^{0.5}} \]

10. Applied egg-rr 3.0%

    \[\leadsto \color{blue}{{\left(x \cdot 9\right)}^{0.5}} \]
11. Step-by-step derivation

    1. unpow1/2 3.0%

       \[\leadsto \color{blue}{\sqrt{x \cdot 9}} \]

12. Simplified 3.0%

    \[\leadsto \color{blue}{\sqrt{x \cdot 9}} \]

13. Final simplification 3.0%

    \[\leadsto \sqrt{x \cdot 9} \]
14. Add Preprocessing

Alternative 16: 26.1% 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. remove-double-neg 99.4%

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

   2. distribute-lft-neg-out 99.4%

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

   3. distribute-rgt-neg-in 99.4%

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

   4. +-commutative 99.4%

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

   5. associate--l+ 99.4%

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

   6. distribute-neg-in 99.4%

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

   7. distribute-frac-neg2 99.4%

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

   8. distribute-lft-neg-out 99.4%

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

   9. *-commutative 99.4%

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

   10. distribute-rgt-neg-in 99.4%

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

   11. metadata-eval 99.4%

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

3. Simplified 99.4%

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

5. Taylor expanded in y around 0 58.7%

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

   1. *-commutative 58.7%

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

   2. associate-*l* 58.8%

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

   3. sub-neg 58.8%

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

   4. associate-*r/ 58.8%

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

   5. metadata-eval 58.8%

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

   6. distribute-neg-frac 58.8%

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

   7. metadata-eval 58.8%

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

7. Simplified 58.8%

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

8. Taylor expanded in x around inf 25.4%

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

9. Final simplification 25.4%

   \[\leadsto \sqrt{x} \cdot -3 \]
10. Add Preprocessing

Developer target: 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 2024046 
(FPCore (x y)
  :name "Numeric.SpecFunctions:incompleteGamma from math-functions-0.1.5.2, B"
  :precision binary64

  :alt
  (* 3.0 (+ (* y (sqrt x)) (* (- (/ 1.0 (* x 9.0)) 1.0) (sqrt x))))

  (* (* 3.0 (sqrt x)) (- (+ y (/ 1.0 (* x 9.0))) 1.0)))