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

Percentage Accurate: 99.4% → 99.5%

Time: 13.1s

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

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

FPCore

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

C

double code(double x, double y) {
	return sqrt((x * 9.0)) * ((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 = sqrt((x * 9.0d0)) * ((y + (1.0d0 / (x * 9.0d0))) + (-1.0d0))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.3%

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

   1. *-commutative 99.3%

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

   2. metadata-eval 99.3%

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

   3. sqrt-prod 99.5%

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

   4. pow1/2 99.5%

      \[\leadsto \color{blue}{{\left(x \cdot 9\right)}^{0.5}} \cdot \left(\left(y + \frac{1}{x \cdot 9}\right) - 1\right) \]

4. Applied egg-rr 99.5%

   \[\leadsto \color{blue}{{\left(x \cdot 9\right)}^{0.5}} \cdot \left(\left(y + \frac{1}{x \cdot 9}\right) - 1\right) \]
5. Step-by-step derivation

   1. unpow1/2 99.5%

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

6. Simplified 99.5%

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

7. Final simplification 99.5%

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

Alternative 2: 61.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 2.5 \cdot 10^{-50}:\\ \;\;\;\;0.3333333333333333 \cdot \sqrt{\frac{1}{x}}\\ \mathbf{elif}\;x \leq 2350000000000 \lor \neg \left(x \leq 1.18 \cdot 10^{+76}\right) \land \left(x \leq 9 \cdot 10^{+106} \lor \neg \left(x \leq 9.2 \cdot 10^{+144}\right) \land x \leq 1.3 \cdot 10^{+206}\right):\\ \;\;\;\;3 \cdot \left(y \cdot \sqrt{x}\right)\\ \mathbf{else}:\\ \;\;\;\;\sqrt{x} \cdot -3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x 2.5e-50)
   (* 0.3333333333333333 (sqrt (/ 1.0 x)))
   (if (or (<= x 2350000000000.0)
           (and (not (<= x 1.18e+76))
                (or (<= x 9e+106)
                    (and (not (<= x 9.2e+144)) (<= x 1.3e+206)))))
     (* 3.0 (* y (sqrt x)))
     (* (sqrt x) -3.0))))

C

double code(double x, double y) {
	double tmp;
	if (x <= 2.5e-50) {
		tmp = 0.3333333333333333 * sqrt((1.0 / x));
	} else if ((x <= 2350000000000.0) || (!(x <= 1.18e+76) && ((x <= 9e+106) || (!(x <= 9.2e+144) && (x <= 1.3e+206))))) {
		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 <= 2.5d-50) then
        tmp = 0.3333333333333333d0 * sqrt((1.0d0 / x))
    else if ((x <= 2350000000000.0d0) .or. (.not. (x <= 1.18d+76)) .and. (x <= 9d+106) .or. (.not. (x <= 9.2d+144)) .and. (x <= 1.3d+206)) 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 <= 2.5e-50) {
		tmp = 0.3333333333333333 * Math.sqrt((1.0 / x));
	} else if ((x <= 2350000000000.0) || (!(x <= 1.18e+76) && ((x <= 9e+106) || (!(x <= 9.2e+144) && (x <= 1.3e+206))))) {
		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 <= 2.5e-50:
		tmp = 0.3333333333333333 * math.sqrt((1.0 / x))
	elif (x <= 2350000000000.0) or (not (x <= 1.18e+76) and ((x <= 9e+106) or (not (x <= 9.2e+144) and (x <= 1.3e+206)))):
		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 <= 2.5e-50)
		tmp = Float64(0.3333333333333333 * sqrt(Float64(1.0 / x)));
	elseif ((x <= 2350000000000.0) || (!(x <= 1.18e+76) && ((x <= 9e+106) || (!(x <= 9.2e+144) && (x <= 1.3e+206)))))
		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 <= 2.5e-50)
		tmp = 0.3333333333333333 * sqrt((1.0 / x));
	elseif ((x <= 2350000000000.0) || (~((x <= 1.18e+76)) && ((x <= 9e+106) || (~((x <= 9.2e+144)) && (x <= 1.3e+206)))))
		tmp = 3.0 * (y * sqrt(x));
	else
		tmp = sqrt(x) * -3.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, 2.5e-50], N[(0.3333333333333333 * N[Sqrt[N[(1.0 / x), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[x, 2350000000000.0], And[N[Not[LessEqual[x, 1.18e+76]], $MachinePrecision], Or[LessEqual[x, 9e+106], And[N[Not[LessEqual[x, 9.2e+144]], $MachinePrecision], LessEqual[x, 1.3e+206]]]]], 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 < 2.49999999999999984e-50

   1. Initial program 99.2%

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

      1. 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* 99.3%

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

      7. metadata-eval 99.3%

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

      8. metadata-eval 99.3%

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

   3. Simplified 99.3%

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

   5. Taylor expanded in y around 0 99.2%

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

      1. associate-*r* 99.1%

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

      2. associate-*r* 99.2%

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

      3. sub-neg 99.2%

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

      4. associate-*r/ 99.3%

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

      5. metadata-eval 99.3%

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

      6. metadata-eval 99.3%

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

      7. distribute-lft-out 99.4%

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

      8. *-commutative 99.4%

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

      9. associate-+r+ 99.4%

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

      10. +-commutative 99.4%

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

      11. associate-+r+ 99.4%

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

      12. associate-*r* 99.3%

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

      13. distribute-lft-in 99.2%

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

      14. associate-*r/ 99.3%

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

      15. metadata-eval 99.3%

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

      16. +-commutative 99.3%

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

      17. distribute-lft-in 99.3%

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

      18. metadata-eval 99.3%

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

   7. Simplified 99.3%

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

   8. Taylor expanded in y around inf 99.3%

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

   9. Taylor expanded in y around 0 77.8%

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

   if 2.49999999999999984e-50 < x < 2.35e12 or 1.17999999999999997e76 < x < 8.9999999999999994e106 or 9.2000000000000006e144 < x < 1.29999999999999994e206

   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. Taylor expanded in y around inf 61.1%

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

   if 2.35e12 < x < 1.17999999999999997e76 or 8.9999999999999994e106 < x < 9.2000000000000006e144 or 1.29999999999999994e206 < x

   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. Taylor expanded in y around 0 70.3%

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

      1. sub-neg 70.3%

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

      2. associate-*r/ 70.3%

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

      3. metadata-eval 70.3%

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

      4. metadata-eval 70.3%

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

   7. Simplified 70.3%

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

   8. Taylor expanded in x around inf 70.1%

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

      1. add0 70.1%

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

      2. associate-*r* 70.1%

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

      3. fma-define 70.1%

         \[\leadsto \color{blue}{\mathsf{fma}\left(3 \cdot \sqrt{x}, -1, 0\right)} \]

      4. /-rgt-identity 70.1%

         \[\leadsto \mathsf{fma}\left(3 \cdot \sqrt{\color{blue}{\frac{x}{1}}}, -1, 0\right) \]

      5. div-inv 70.1%

         \[\leadsto \mathsf{fma}\left(3 \cdot \sqrt{\color{blue}{x \cdot \frac{1}{1}}}, -1, 0\right) \]

      6. add-sqr-sqrt 70.1%

         \[\leadsto \mathsf{fma}\left(3 \cdot \sqrt{\color{blue}{\left(\sqrt{x} \cdot \sqrt{x}\right)} \cdot \frac{1}{1}}, -1, 0\right) \]

      7. metadata-eval 70.1%

         \[\leadsto \mathsf{fma}\left(3 \cdot \sqrt{\left(\sqrt{x} \cdot \sqrt{x}\right) \cdot \color{blue}{1}}, -1, 0\right) \]

      8. metadata-eval 70.1%

         \[\leadsto \mathsf{fma}\left(3 \cdot \sqrt{\left(\sqrt{x} \cdot \sqrt{x}\right) \cdot \color{blue}{\left(-1 \cdot -1\right)}}, -1, 0\right) \]

      9. swap-sqr 70.1%

         \[\leadsto \mathsf{fma}\left(3 \cdot \sqrt{\color{blue}{\left(\sqrt{x} \cdot -1\right) \cdot \left(\sqrt{x} \cdot -1\right)}}, -1, 0\right) \]

      10. sqrt-unprod 0.0%

          \[\leadsto \mathsf{fma}\left(3 \cdot \color{blue}{\left(\sqrt{\sqrt{x} \cdot -1} \cdot \sqrt{\sqrt{x} \cdot -1}\right)}, -1, 0\right) \]

      11. add-sqr-sqrt 1.8%

          \[\leadsto \mathsf{fma}\left(3 \cdot \color{blue}{\left(\sqrt{x} \cdot -1\right)}, -1, 0\right) \]

      12. *-commutative 1.8%

          \[\leadsto \mathsf{fma}\left(\color{blue}{\left(\sqrt{x} \cdot -1\right) \cdot 3}, -1, 0\right) \]

      13. add-sqr-sqrt 0.0%

          \[\leadsto \mathsf{fma}\left(\color{blue}{\left(\sqrt{\sqrt{x} \cdot -1} \cdot \sqrt{\sqrt{x} \cdot -1}\right)} \cdot 3, -1, 0\right) \]

      14. sqrt-unprod 70.1%

          \[\leadsto \mathsf{fma}\left(\color{blue}{\sqrt{\left(\sqrt{x} \cdot -1\right) \cdot \left(\sqrt{x} \cdot -1\right)}} \cdot 3, -1, 0\right) \]

      15. swap-sqr 70.1%

          \[\leadsto \mathsf{fma}\left(\sqrt{\color{blue}{\left(\sqrt{x} \cdot \sqrt{x}\right) \cdot \left(-1 \cdot -1\right)}} \cdot 3, -1, 0\right) \]

      16. add-sqr-sqrt 70.1%

          \[\leadsto \mathsf{fma}\left(\sqrt{\color{blue}{x} \cdot \left(-1 \cdot -1\right)} \cdot 3, -1, 0\right) \]

      17. metadata-eval 70.1%

          \[\leadsto \mathsf{fma}\left(\sqrt{x \cdot \color{blue}{1}} \cdot 3, -1, 0\right) \]

      18. metadata-eval 70.1%

          \[\leadsto \mathsf{fma}\left(\sqrt{x \cdot \color{blue}{\frac{1}{1}}} \cdot 3, -1, 0\right) \]

      19. div-inv 70.1%

          \[\leadsto \mathsf{fma}\left(\sqrt{\color{blue}{\frac{x}{1}}} \cdot 3, -1, 0\right) \]

      20. /-rgt-identity 70.1%

          \[\leadsto \mathsf{fma}\left(\sqrt{\color{blue}{x}} \cdot 3, -1, 0\right) \]

   10. Applied egg-rr 70.1%

       \[\leadsto \color{blue}{\mathsf{fma}\left(\sqrt{x} \cdot 3, -1, 0\right)} \]
   11. Step-by-step derivation

       1. fma-undefine 70.1%

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

       2. *-commutative 70.1%

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

       3. add0 70.1%

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

       4. mul-1-neg 70.1%

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

       5. distribute-rgt-neg-in 70.1%

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

       6. metadata-eval 70.1%

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

   12. Simplified 70.1%

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

4. Final simplification 70.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 2.5 \cdot 10^{-50}:\\ \;\;\;\;0.3333333333333333 \cdot \sqrt{\frac{1}{x}}\\ \mathbf{elif}\;x \leq 2350000000000 \lor \neg \left(x \leq 1.18 \cdot 10^{+76}\right) \land \left(x \leq 9 \cdot 10^{+106} \lor \neg \left(x \leq 9.2 \cdot 10^{+144}\right) \land x \leq 1.3 \cdot 10^{+206}\right):\\ \;\;\;\;3 \cdot \left(y \cdot \sqrt{x}\right)\\ \mathbf{else}:\\ \;\;\;\;\sqrt{x} \cdot -3\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 61.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \sqrt{x} \cdot -3\\ t_1 := 3 \cdot \left(y \cdot \sqrt{x}\right)\\ \mathbf{if}\;x \leq 1.5 \cdot 10^{-50}:\\ \;\;\;\;0.3333333333333333 \cdot \sqrt{\frac{1}{x}}\\ \mathbf{elif}\;x \leq 2350000000000:\\ \;\;\;\;t\_1\\ \mathbf{elif}\;x \leq 1.3 \cdot 10^{+76}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 1.9 \cdot 10^{+111}:\\ \;\;\;\;\sqrt{x \cdot 9} \cdot y\\ \mathbf{elif}\;x \leq 4 \cdot 10^{+144} \lor \neg \left(x \leq 9.5 \cdot 10^{+206}\right):\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;t\_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (* (sqrt x) -3.0)) (t_1 (* 3.0 (* y (sqrt x)))))
   (if (<= x 1.5e-50)
     (* 0.3333333333333333 (sqrt (/ 1.0 x)))
     (if (<= x 2350000000000.0)
       t_1
       (if (<= x 1.3e+76)
         t_0
         (if (<= x 1.9e+111)
           (* (sqrt (* x 9.0)) y)
           (if (or (<= x 4e+144) (not (<= x 9.5e+206))) t_0 t_1)))))))

C

double code(double x, double y) {
	double t_0 = sqrt(x) * -3.0;
	double t_1 = 3.0 * (y * sqrt(x));
	double tmp;
	if (x <= 1.5e-50) {
		tmp = 0.3333333333333333 * sqrt((1.0 / x));
	} else if (x <= 2350000000000.0) {
		tmp = t_1;
	} else if (x <= 1.3e+76) {
		tmp = t_0;
	} else if (x <= 1.9e+111) {
		tmp = sqrt((x * 9.0)) * y;
	} else if ((x <= 4e+144) || !(x <= 9.5e+206)) {
		tmp = t_0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = sqrt(x) * (-3.0d0)
    t_1 = 3.0d0 * (y * sqrt(x))
    if (x <= 1.5d-50) then
        tmp = 0.3333333333333333d0 * sqrt((1.0d0 / x))
    else if (x <= 2350000000000.0d0) then
        tmp = t_1
    else if (x <= 1.3d+76) then
        tmp = t_0
    else if (x <= 1.9d+111) then
        tmp = sqrt((x * 9.0d0)) * y
    else if ((x <= 4d+144) .or. (.not. (x <= 9.5d+206))) then
        tmp = t_0
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double t_0 = Math.sqrt(x) * -3.0;
	double t_1 = 3.0 * (y * Math.sqrt(x));
	double tmp;
	if (x <= 1.5e-50) {
		tmp = 0.3333333333333333 * Math.sqrt((1.0 / x));
	} else if (x <= 2350000000000.0) {
		tmp = t_1;
	} else if (x <= 1.3e+76) {
		tmp = t_0;
	} else if (x <= 1.9e+111) {
		tmp = Math.sqrt((x * 9.0)) * y;
	} else if ((x <= 4e+144) || !(x <= 9.5e+206)) {
		tmp = t_0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = math.sqrt(x) * -3.0
	t_1 = 3.0 * (y * math.sqrt(x))
	tmp = 0
	if x <= 1.5e-50:
		tmp = 0.3333333333333333 * math.sqrt((1.0 / x))
	elif x <= 2350000000000.0:
		tmp = t_1
	elif x <= 1.3e+76:
		tmp = t_0
	elif x <= 1.9e+111:
		tmp = math.sqrt((x * 9.0)) * y
	elif (x <= 4e+144) or not (x <= 9.5e+206):
		tmp = t_0
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y)
	t_0 = Float64(sqrt(x) * -3.0)
	t_1 = Float64(3.0 * Float64(y * sqrt(x)))
	tmp = 0.0
	if (x <= 1.5e-50)
		tmp = Float64(0.3333333333333333 * sqrt(Float64(1.0 / x)));
	elseif (x <= 2350000000000.0)
		tmp = t_1;
	elseif (x <= 1.3e+76)
		tmp = t_0;
	elseif (x <= 1.9e+111)
		tmp = Float64(sqrt(Float64(x * 9.0)) * y);
	elseif ((x <= 4e+144) || !(x <= 9.5e+206))
		tmp = t_0;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = sqrt(x) * -3.0;
	t_1 = 3.0 * (y * sqrt(x));
	tmp = 0.0;
	if (x <= 1.5e-50)
		tmp = 0.3333333333333333 * sqrt((1.0 / x));
	elseif (x <= 2350000000000.0)
		tmp = t_1;
	elseif (x <= 1.3e+76)
		tmp = t_0;
	elseif (x <= 1.9e+111)
		tmp = sqrt((x * 9.0)) * y;
	elseif ((x <= 4e+144) || ~((x <= 9.5e+206)))
		tmp = t_0;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(N[Sqrt[x], $MachinePrecision] * -3.0), $MachinePrecision]}, Block[{t$95$1 = N[(3.0 * N[(y * N[Sqrt[x], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, 1.5e-50], N[(0.3333333333333333 * N[Sqrt[N[(1.0 / x), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2350000000000.0], t$95$1, If[LessEqual[x, 1.3e+76], t$95$0, If[LessEqual[x, 1.9e+111], N[(N[Sqrt[N[(x * 9.0), $MachinePrecision]], $MachinePrecision] * y), $MachinePrecision], If[Or[LessEqual[x, 4e+144], N[Not[LessEqual[x, 9.5e+206]], $MachinePrecision]], t$95$0, t$95$1]]]]]]]

Derivation

1. Split input into 4 regimes

2. if x < 1.49999999999999995e-50

   1. Initial program 99.2%

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

      1. 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* 99.3%

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

      7. metadata-eval 99.3%

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

      8. metadata-eval 99.3%

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

   3. Simplified 99.3%

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

   5. Taylor expanded in y around 0 99.2%

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

      1. associate-*r* 99.1%

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

      2. associate-*r* 99.2%

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

      3. sub-neg 99.2%

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

      4. associate-*r/ 99.3%

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

      5. metadata-eval 99.3%

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

      6. metadata-eval 99.3%

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

      7. distribute-lft-out 99.4%

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

      8. *-commutative 99.4%

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

      9. associate-+r+ 99.4%

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

      10. +-commutative 99.4%

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

      11. associate-+r+ 99.4%

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

      12. associate-*r* 99.3%

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

      13. distribute-lft-in 99.2%

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

      14. associate-*r/ 99.3%

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

      15. metadata-eval 99.3%

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

      16. +-commutative 99.3%

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

      17. distribute-lft-in 99.3%

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

      18. metadata-eval 99.3%

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

   7. Simplified 99.3%

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

   8. Taylor expanded in y around inf 99.3%

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

   9. Taylor expanded in y around 0 77.8%

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

   if 1.49999999999999995e-50 < x < 2.35e12 or 4.00000000000000009e144 < x < 9.49999999999999966e206

   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. Taylor expanded in y around inf 56.8%

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

   if 2.35e12 < x < 1.3e76 or 1.89999999999999988e111 < x < 4.00000000000000009e144 or 9.49999999999999966e206 < x

   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. Taylor expanded in y around 0 70.8%

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

      1. sub-neg 70.8%

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

      2. associate-*r/ 70.8%

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

      3. metadata-eval 70.8%

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

      4. metadata-eval 70.8%

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

   7. Simplified 70.8%

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

   8. Taylor expanded in x around inf 70.7%

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

      1. add0 70.7%

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

      2. associate-*r* 70.7%

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

      3. fma-define 70.7%

         \[\leadsto \color{blue}{\mathsf{fma}\left(3 \cdot \sqrt{x}, -1, 0\right)} \]

      4. /-rgt-identity 70.7%

         \[\leadsto \mathsf{fma}\left(3 \cdot \sqrt{\color{blue}{\frac{x}{1}}}, -1, 0\right) \]

      5. div-inv 70.7%

         \[\leadsto \mathsf{fma}\left(3 \cdot \sqrt{\color{blue}{x \cdot \frac{1}{1}}}, -1, 0\right) \]

      6. add-sqr-sqrt 70.7%

         \[\leadsto \mathsf{fma}\left(3 \cdot \sqrt{\color{blue}{\left(\sqrt{x} \cdot \sqrt{x}\right)} \cdot \frac{1}{1}}, -1, 0\right) \]

      7. metadata-eval 70.7%

         \[\leadsto \mathsf{fma}\left(3 \cdot \sqrt{\left(\sqrt{x} \cdot \sqrt{x}\right) \cdot \color{blue}{1}}, -1, 0\right) \]

      8. metadata-eval 70.7%

         \[\leadsto \mathsf{fma}\left(3 \cdot \sqrt{\left(\sqrt{x} \cdot \sqrt{x}\right) \cdot \color{blue}{\left(-1 \cdot -1\right)}}, -1, 0\right) \]

      9. swap-sqr 70.7%

         \[\leadsto \mathsf{fma}\left(3 \cdot \sqrt{\color{blue}{\left(\sqrt{x} \cdot -1\right) \cdot \left(\sqrt{x} \cdot -1\right)}}, -1, 0\right) \]

      10. sqrt-unprod 0.0%

          \[\leadsto \mathsf{fma}\left(3 \cdot \color{blue}{\left(\sqrt{\sqrt{x} \cdot -1} \cdot \sqrt{\sqrt{x} \cdot -1}\right)}, -1, 0\right) \]

      11. add-sqr-sqrt 1.8%

          \[\leadsto \mathsf{fma}\left(3 \cdot \color{blue}{\left(\sqrt{x} \cdot -1\right)}, -1, 0\right) \]

      12. *-commutative 1.8%

          \[\leadsto \mathsf{fma}\left(\color{blue}{\left(\sqrt{x} \cdot -1\right) \cdot 3}, -1, 0\right) \]

      13. add-sqr-sqrt 0.0%

          \[\leadsto \mathsf{fma}\left(\color{blue}{\left(\sqrt{\sqrt{x} \cdot -1} \cdot \sqrt{\sqrt{x} \cdot -1}\right)} \cdot 3, -1, 0\right) \]

      14. sqrt-unprod 70.7%

          \[\leadsto \mathsf{fma}\left(\color{blue}{\sqrt{\left(\sqrt{x} \cdot -1\right) \cdot \left(\sqrt{x} \cdot -1\right)}} \cdot 3, -1, 0\right) \]

      15. swap-sqr 70.7%

          \[\leadsto \mathsf{fma}\left(\sqrt{\color{blue}{\left(\sqrt{x} \cdot \sqrt{x}\right) \cdot \left(-1 \cdot -1\right)}} \cdot 3, -1, 0\right) \]

      16. add-sqr-sqrt 70.7%

          \[\leadsto \mathsf{fma}\left(\sqrt{\color{blue}{x} \cdot \left(-1 \cdot -1\right)} \cdot 3, -1, 0\right) \]

      17. metadata-eval 70.7%

          \[\leadsto \mathsf{fma}\left(\sqrt{x \cdot \color{blue}{1}} \cdot 3, -1, 0\right) \]

      18. metadata-eval 70.7%

          \[\leadsto \mathsf{fma}\left(\sqrt{x \cdot \color{blue}{\frac{1}{1}}} \cdot 3, -1, 0\right) \]

      19. div-inv 70.7%

          \[\leadsto \mathsf{fma}\left(\sqrt{\color{blue}{\frac{x}{1}}} \cdot 3, -1, 0\right) \]

      20. /-rgt-identity 70.7%

          \[\leadsto \mathsf{fma}\left(\sqrt{\color{blue}{x}} \cdot 3, -1, 0\right) \]

   10. Applied egg-rr 70.7%

       \[\leadsto \color{blue}{\mathsf{fma}\left(\sqrt{x} \cdot 3, -1, 0\right)} \]
   11. Step-by-step derivation

       1. fma-undefine 70.7%

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

       2. *-commutative 70.7%

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

       3. add0 70.7%

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

       4. mul-1-neg 70.7%

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

       5. distribute-rgt-neg-in 70.7%

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

       6. metadata-eval 70.7%

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

   12. Simplified 70.7%

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

   if 1.3e76 < x < 1.89999999999999988e111

   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* 99.3%

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

      2. sub-neg 99.3%

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

      3. +-commutative 99.3%

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

      4. associate-+l+ 99.3%

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

      5. *-commutative 99.3%

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

      6. associate-/r* 99.3%

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

      7. metadata-eval 99.3%

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

      8. metadata-eval 99.3%

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

   3. Simplified 99.3%

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

   5. Taylor expanded in y around inf 78.3%

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

      1. add0 78.3%

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

      2. *-commutative 78.3%

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

      3. *-commutative 78.3%

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

      4. associate-*l* 78.5%

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

      5. metadata-eval 78.5%

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

      6. sqrt-prod 78.5%

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

   7. Applied egg-rr 78.5%

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

      1. add0 78.5%

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

   9. Simplified 78.5%

      \[\leadsto \color{blue}{y \cdot \sqrt{x \cdot 9}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 70.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 1.5 \cdot 10^{-50}:\\ \;\;\;\;0.3333333333333333 \cdot \sqrt{\frac{1}{x}}\\ \mathbf{elif}\;x \leq 2350000000000:\\ \;\;\;\;3 \cdot \left(y \cdot \sqrt{x}\right)\\ \mathbf{elif}\;x \leq 1.3 \cdot 10^{+76}:\\ \;\;\;\;\sqrt{x} \cdot -3\\ \mathbf{elif}\;x \leq 1.9 \cdot 10^{+111}:\\ \;\;\;\;\sqrt{x \cdot 9} \cdot y\\ \mathbf{elif}\;x \leq 4 \cdot 10^{+144} \lor \neg \left(x \leq 9.5 \cdot 10^{+206}\right):\\ \;\;\;\;\sqrt{x} \cdot -3\\ \mathbf{else}:\\ \;\;\;\;3 \cdot \left(y \cdot \sqrt{x}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 61.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \sqrt{x} \cdot -3\\ \mathbf{if}\;x \leq 7.2 \cdot 10^{-51}:\\ \;\;\;\;0.3333333333333333 \cdot \sqrt{\frac{1}{x}}\\ \mathbf{elif}\;x \leq 2350000000000:\\ \;\;\;\;3 \cdot \left(y \cdot \sqrt{x}\right)\\ \mathbf{elif}\;x \leq 1.12 \cdot 10^{+77}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 1.9 \cdot 10^{+111}:\\ \;\;\;\;\sqrt{x \cdot 9} \cdot y\\ \mathbf{elif}\;x \leq 4.4 \cdot 10^{+143} \lor \neg \left(x \leq 1.65 \cdot 10^{+206}\right):\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;\sqrt{x} \cdot \left(y \cdot 3\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (* (sqrt x) -3.0)))
   (if (<= x 7.2e-51)
     (* 0.3333333333333333 (sqrt (/ 1.0 x)))
     (if (<= x 2350000000000.0)
       (* 3.0 (* y (sqrt x)))
       (if (<= x 1.12e+77)
         t_0
         (if (<= x 1.9e+111)
           (* (sqrt (* x 9.0)) y)
           (if (or (<= x 4.4e+143) (not (<= x 1.65e+206)))
             t_0
             (* (sqrt x) (* y 3.0)))))))))

C

double code(double x, double y) {
	double t_0 = sqrt(x) * -3.0;
	double tmp;
	if (x <= 7.2e-51) {
		tmp = 0.3333333333333333 * sqrt((1.0 / x));
	} else if (x <= 2350000000000.0) {
		tmp = 3.0 * (y * sqrt(x));
	} else if (x <= 1.12e+77) {
		tmp = t_0;
	} else if (x <= 1.9e+111) {
		tmp = sqrt((x * 9.0)) * y;
	} else if ((x <= 4.4e+143) || !(x <= 1.65e+206)) {
		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) :: tmp
    t_0 = sqrt(x) * (-3.0d0)
    if (x <= 7.2d-51) then
        tmp = 0.3333333333333333d0 * sqrt((1.0d0 / x))
    else if (x <= 2350000000000.0d0) then
        tmp = 3.0d0 * (y * sqrt(x))
    else if (x <= 1.12d+77) then
        tmp = t_0
    else if (x <= 1.9d+111) then
        tmp = sqrt((x * 9.0d0)) * y
    else if ((x <= 4.4d+143) .or. (.not. (x <= 1.65d+206))) 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 tmp;
	if (x <= 7.2e-51) {
		tmp = 0.3333333333333333 * Math.sqrt((1.0 / x));
	} else if (x <= 2350000000000.0) {
		tmp = 3.0 * (y * Math.sqrt(x));
	} else if (x <= 1.12e+77) {
		tmp = t_0;
	} else if (x <= 1.9e+111) {
		tmp = Math.sqrt((x * 9.0)) * y;
	} else if ((x <= 4.4e+143) || !(x <= 1.65e+206)) {
		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
	tmp = 0
	if x <= 7.2e-51:
		tmp = 0.3333333333333333 * math.sqrt((1.0 / x))
	elif x <= 2350000000000.0:
		tmp = 3.0 * (y * math.sqrt(x))
	elif x <= 1.12e+77:
		tmp = t_0
	elif x <= 1.9e+111:
		tmp = math.sqrt((x * 9.0)) * y
	elif (x <= 4.4e+143) or not (x <= 1.65e+206):
		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)
	tmp = 0.0
	if (x <= 7.2e-51)
		tmp = Float64(0.3333333333333333 * sqrt(Float64(1.0 / x)));
	elseif (x <= 2350000000000.0)
		tmp = Float64(3.0 * Float64(y * sqrt(x)));
	elseif (x <= 1.12e+77)
		tmp = t_0;
	elseif (x <= 1.9e+111)
		tmp = Float64(sqrt(Float64(x * 9.0)) * y);
	elseif ((x <= 4.4e+143) || !(x <= 1.65e+206))
		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;
	tmp = 0.0;
	if (x <= 7.2e-51)
		tmp = 0.3333333333333333 * sqrt((1.0 / x));
	elseif (x <= 2350000000000.0)
		tmp = 3.0 * (y * sqrt(x));
	elseif (x <= 1.12e+77)
		tmp = t_0;
	elseif (x <= 1.9e+111)
		tmp = sqrt((x * 9.0)) * y;
	elseif ((x <= 4.4e+143) || ~((x <= 1.65e+206)))
		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]}, If[LessEqual[x, 7.2e-51], N[(0.3333333333333333 * N[Sqrt[N[(1.0 / x), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2350000000000.0], N[(3.0 * N[(y * N[Sqrt[x], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.12e+77], t$95$0, If[LessEqual[x, 1.9e+111], N[(N[Sqrt[N[(x * 9.0), $MachinePrecision]], $MachinePrecision] * y), $MachinePrecision], If[Or[LessEqual[x, 4.4e+143], N[Not[LessEqual[x, 1.65e+206]], $MachinePrecision]], t$95$0, N[(N[Sqrt[x], $MachinePrecision] * N[(y * 3.0), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

2. if x < 7.2000000000000001e-51

   1. Initial program 99.2%

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

      1. 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* 99.3%

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

      7. metadata-eval 99.3%

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

      8. metadata-eval 99.3%

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

   3. Simplified 99.3%

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

   5. Taylor expanded in y around 0 99.2%

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

      1. associate-*r* 99.1%

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

      2. associate-*r* 99.2%

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

      3. sub-neg 99.2%

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

      4. associate-*r/ 99.3%

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

      5. metadata-eval 99.3%

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

      6. metadata-eval 99.3%

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

      7. distribute-lft-out 99.4%

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

      8. *-commutative 99.4%

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

      9. associate-+r+ 99.4%

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

      10. +-commutative 99.4%

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

      11. associate-+r+ 99.4%

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

      12. associate-*r* 99.3%

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

      13. distribute-lft-in 99.2%

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

      14. associate-*r/ 99.3%

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

      15. metadata-eval 99.3%

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

      16. +-commutative 99.3%

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

      17. distribute-lft-in 99.3%

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

      18. metadata-eval 99.3%

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

   7. Simplified 99.3%

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

   8. Taylor expanded in y around inf 99.3%

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

   9. Taylor expanded in y around 0 77.8%

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

   if 7.2000000000000001e-51 < x < 2.35e12

   1. Initial program 99.2%

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

      1. associate-*l* 99.3%

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

      2. sub-neg 99.3%

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

      3. +-commutative 99.3%

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

      4. associate-+l+ 99.3%

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

      5. *-commutative 99.3%

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

      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

   5. Taylor expanded in y around inf 53.2%

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

   if 2.35e12 < x < 1.1199999999999999e77 or 1.89999999999999988e111 < x < 4.40000000000000028e143 or 1.64999999999999992e206 < x

   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. Taylor expanded in y around 0 70.8%

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

      1. sub-neg 70.8%

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

      2. associate-*r/ 70.8%

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

      3. metadata-eval 70.8%

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

      4. metadata-eval 70.8%

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

   7. Simplified 70.8%

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

   8. Taylor expanded in x around inf 70.7%

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

      1. add0 70.7%

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

      2. associate-*r* 70.7%

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

      3. fma-define 70.7%

         \[\leadsto \color{blue}{\mathsf{fma}\left(3 \cdot \sqrt{x}, -1, 0\right)} \]

      4. /-rgt-identity 70.7%

         \[\leadsto \mathsf{fma}\left(3 \cdot \sqrt{\color{blue}{\frac{x}{1}}}, -1, 0\right) \]

      5. div-inv 70.7%

         \[\leadsto \mathsf{fma}\left(3 \cdot \sqrt{\color{blue}{x \cdot \frac{1}{1}}}, -1, 0\right) \]

      6. add-sqr-sqrt 70.7%

         \[\leadsto \mathsf{fma}\left(3 \cdot \sqrt{\color{blue}{\left(\sqrt{x} \cdot \sqrt{x}\right)} \cdot \frac{1}{1}}, -1, 0\right) \]

      7. metadata-eval 70.7%

         \[\leadsto \mathsf{fma}\left(3 \cdot \sqrt{\left(\sqrt{x} \cdot \sqrt{x}\right) \cdot \color{blue}{1}}, -1, 0\right) \]

      8. metadata-eval 70.7%

         \[\leadsto \mathsf{fma}\left(3 \cdot \sqrt{\left(\sqrt{x} \cdot \sqrt{x}\right) \cdot \color{blue}{\left(-1 \cdot -1\right)}}, -1, 0\right) \]

      9. swap-sqr 70.7%

         \[\leadsto \mathsf{fma}\left(3 \cdot \sqrt{\color{blue}{\left(\sqrt{x} \cdot -1\right) \cdot \left(\sqrt{x} \cdot -1\right)}}, -1, 0\right) \]

      10. sqrt-unprod 0.0%

          \[\leadsto \mathsf{fma}\left(3 \cdot \color{blue}{\left(\sqrt{\sqrt{x} \cdot -1} \cdot \sqrt{\sqrt{x} \cdot -1}\right)}, -1, 0\right) \]

      11. add-sqr-sqrt 1.8%

          \[\leadsto \mathsf{fma}\left(3 \cdot \color{blue}{\left(\sqrt{x} \cdot -1\right)}, -1, 0\right) \]

      12. *-commutative 1.8%

          \[\leadsto \mathsf{fma}\left(\color{blue}{\left(\sqrt{x} \cdot -1\right) \cdot 3}, -1, 0\right) \]

      13. add-sqr-sqrt 0.0%

          \[\leadsto \mathsf{fma}\left(\color{blue}{\left(\sqrt{\sqrt{x} \cdot -1} \cdot \sqrt{\sqrt{x} \cdot -1}\right)} \cdot 3, -1, 0\right) \]

      14. sqrt-unprod 70.7%

          \[\leadsto \mathsf{fma}\left(\color{blue}{\sqrt{\left(\sqrt{x} \cdot -1\right) \cdot \left(\sqrt{x} \cdot -1\right)}} \cdot 3, -1, 0\right) \]

      15. swap-sqr 70.7%

          \[\leadsto \mathsf{fma}\left(\sqrt{\color{blue}{\left(\sqrt{x} \cdot \sqrt{x}\right) \cdot \left(-1 \cdot -1\right)}} \cdot 3, -1, 0\right) \]

      16. add-sqr-sqrt 70.7%

          \[\leadsto \mathsf{fma}\left(\sqrt{\color{blue}{x} \cdot \left(-1 \cdot -1\right)} \cdot 3, -1, 0\right) \]

      17. metadata-eval 70.7%

          \[\leadsto \mathsf{fma}\left(\sqrt{x \cdot \color{blue}{1}} \cdot 3, -1, 0\right) \]

      18. metadata-eval 70.7%

          \[\leadsto \mathsf{fma}\left(\sqrt{x \cdot \color{blue}{\frac{1}{1}}} \cdot 3, -1, 0\right) \]

      19. div-inv 70.7%

          \[\leadsto \mathsf{fma}\left(\sqrt{\color{blue}{\frac{x}{1}}} \cdot 3, -1, 0\right) \]

      20. /-rgt-identity 70.7%

          \[\leadsto \mathsf{fma}\left(\sqrt{\color{blue}{x}} \cdot 3, -1, 0\right) \]

   10. Applied egg-rr 70.7%

       \[\leadsto \color{blue}{\mathsf{fma}\left(\sqrt{x} \cdot 3, -1, 0\right)} \]
   11. Step-by-step derivation

       1. fma-undefine 70.7%

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

       2. *-commutative 70.7%

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

       3. add0 70.7%

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

       4. mul-1-neg 70.7%

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

       5. distribute-rgt-neg-in 70.7%

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

       6. metadata-eval 70.7%

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

   12. Simplified 70.7%

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

   if 1.1199999999999999e77 < x < 1.89999999999999988e111

   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* 99.3%

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

      2. sub-neg 99.3%

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

      3. +-commutative 99.3%

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

      4. associate-+l+ 99.3%

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

      5. *-commutative 99.3%

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

      6. associate-/r* 99.3%

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

      7. metadata-eval 99.3%

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

      8. metadata-eval 99.3%

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

   3. Simplified 99.3%

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

   5. Taylor expanded in y around inf 78.3%

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

      1. add0 78.3%

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

      2. *-commutative 78.3%

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

      3. *-commutative 78.3%

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

      4. associate-*l* 78.5%

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

      5. metadata-eval 78.5%

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

      6. sqrt-prod 78.5%

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

   7. Applied egg-rr 78.5%

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

      1. add0 78.5%

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

   9. Simplified 78.5%

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

   if 4.40000000000000028e143 < x < 1.64999999999999992e206

   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* 99.6%

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

      2. sub-neg 99.6%

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

      3. +-commutative 99.6%

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

      4. associate-+l+ 99.6%

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

      5. *-commutative 99.6%

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

      6. associate-/r* 99.6%

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

      7. metadata-eval 99.6%

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

      8. metadata-eval 99.6%

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

   3. Simplified 99.6%

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

   5. Taylor expanded in y around 0 99.6%

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

      1. associate-*r* 99.6%

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

      2. associate-*r* 99.6%

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

      3. sub-neg 99.6%

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

      4. associate-*r/ 99.6%

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

      5. metadata-eval 99.6%

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

      6. metadata-eval 99.6%

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

      7. distribute-lft-out 99.6%

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

      8. *-commutative 99.6%

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

      9. associate-+r+ 99.6%

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

      10. +-commutative 99.6%

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

      11. associate-+r+ 99.6%

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

      12. associate-*r* 99.7%

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

      13. distribute-lft-in 99.7%

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

      14. associate-*r/ 99.7%

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

      15. metadata-eval 99.7%

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

      16. +-commutative 99.7%

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

      17. distribute-lft-in 99.7%

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

      18. metadata-eval 99.7%

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

   7. Simplified 99.7%

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

   8. Taylor expanded in y around inf 60.7%

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

      1. *-commutative 60.7%

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

      2. associate-*l* 60.7%

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

      3. *-commutative 60.7%

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

   10. Simplified 60.7%

       \[\leadsto \color{blue}{\sqrt{x} \cdot \left(3 \cdot y\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 70.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 7.2 \cdot 10^{-51}:\\ \;\;\;\;0.3333333333333333 \cdot \sqrt{\frac{1}{x}}\\ \mathbf{elif}\;x \leq 2350000000000:\\ \;\;\;\;3 \cdot \left(y \cdot \sqrt{x}\right)\\ \mathbf{elif}\;x \leq 1.12 \cdot 10^{+77}:\\ \;\;\;\;\sqrt{x} \cdot -3\\ \mathbf{elif}\;x \leq 1.9 \cdot 10^{+111}:\\ \;\;\;\;\sqrt{x \cdot 9} \cdot y\\ \mathbf{elif}\;x \leq 4.4 \cdot 10^{+143} \lor \neg \left(x \leq 1.65 \cdot 10^{+206}\right):\\ \;\;\;\;\sqrt{x} \cdot -3\\ \mathbf{else}:\\ \;\;\;\;\sqrt{x} \cdot \left(y \cdot 3\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 61.4% accurate, 0.8× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \sqrt{x} \cdot -3\\ \mathbf{if}\;x \leq 6.5 \cdot 10^{-51}:\\ \;\;\;\;3 \cdot \left(\sqrt{x} \cdot \frac{0.1111111111111111}{x}\right)\\ \mathbf{elif}\;x \leq 2350000000000:\\ \;\;\;\;3 \cdot \left(y \cdot \sqrt{x}\right)\\ \mathbf{elif}\;x \leq 6 \cdot 10^{+75}:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;x \leq 2.05 \cdot 10^{+111}:\\ \;\;\;\;\sqrt{x \cdot 9} \cdot y\\ \mathbf{elif}\;x \leq 4.1 \cdot 10^{+144} \lor \neg \left(x \leq 3.2 \cdot 10^{+206}\right):\\ \;\;\;\;t\_0\\ \mathbf{else}:\\ \;\;\;\;\sqrt{x} \cdot \left(y \cdot 3\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (* (sqrt x) -3.0)))
   (if (<= x 6.5e-51)
     (* 3.0 (* (sqrt x) (/ 0.1111111111111111 x)))
     (if (<= x 2350000000000.0)
       (* 3.0 (* y (sqrt x)))
       (if (<= x 6e+75)
         t_0
         (if (<= x 2.05e+111)
           (* (sqrt (* x 9.0)) y)
           (if (or (<= x 4.1e+144) (not (<= x 3.2e+206)))
             t_0
             (* (sqrt x) (* y 3.0)))))))))

C

double code(double x, double y) {
	double t_0 = sqrt(x) * -3.0;
	double tmp;
	if (x <= 6.5e-51) {
		tmp = 3.0 * (sqrt(x) * (0.1111111111111111 / x));
	} else if (x <= 2350000000000.0) {
		tmp = 3.0 * (y * sqrt(x));
	} else if (x <= 6e+75) {
		tmp = t_0;
	} else if (x <= 2.05e+111) {
		tmp = sqrt((x * 9.0)) * y;
	} else if ((x <= 4.1e+144) || !(x <= 3.2e+206)) {
		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) :: tmp
    t_0 = sqrt(x) * (-3.0d0)
    if (x <= 6.5d-51) then
        tmp = 3.0d0 * (sqrt(x) * (0.1111111111111111d0 / x))
    else if (x <= 2350000000000.0d0) then
        tmp = 3.0d0 * (y * sqrt(x))
    else if (x <= 6d+75) then
        tmp = t_0
    else if (x <= 2.05d+111) then
        tmp = sqrt((x * 9.0d0)) * y
    else if ((x <= 4.1d+144) .or. (.not. (x <= 3.2d+206))) 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 tmp;
	if (x <= 6.5e-51) {
		tmp = 3.0 * (Math.sqrt(x) * (0.1111111111111111 / x));
	} else if (x <= 2350000000000.0) {
		tmp = 3.0 * (y * Math.sqrt(x));
	} else if (x <= 6e+75) {
		tmp = t_0;
	} else if (x <= 2.05e+111) {
		tmp = Math.sqrt((x * 9.0)) * y;
	} else if ((x <= 4.1e+144) || !(x <= 3.2e+206)) {
		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
	tmp = 0
	if x <= 6.5e-51:
		tmp = 3.0 * (math.sqrt(x) * (0.1111111111111111 / x))
	elif x <= 2350000000000.0:
		tmp = 3.0 * (y * math.sqrt(x))
	elif x <= 6e+75:
		tmp = t_0
	elif x <= 2.05e+111:
		tmp = math.sqrt((x * 9.0)) * y
	elif (x <= 4.1e+144) or not (x <= 3.2e+206):
		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)
	tmp = 0.0
	if (x <= 6.5e-51)
		tmp = Float64(3.0 * Float64(sqrt(x) * Float64(0.1111111111111111 / x)));
	elseif (x <= 2350000000000.0)
		tmp = Float64(3.0 * Float64(y * sqrt(x)));
	elseif (x <= 6e+75)
		tmp = t_0;
	elseif (x <= 2.05e+111)
		tmp = Float64(sqrt(Float64(x * 9.0)) * y);
	elseif ((x <= 4.1e+144) || !(x <= 3.2e+206))
		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;
	tmp = 0.0;
	if (x <= 6.5e-51)
		tmp = 3.0 * (sqrt(x) * (0.1111111111111111 / x));
	elseif (x <= 2350000000000.0)
		tmp = 3.0 * (y * sqrt(x));
	elseif (x <= 6e+75)
		tmp = t_0;
	elseif (x <= 2.05e+111)
		tmp = sqrt((x * 9.0)) * y;
	elseif ((x <= 4.1e+144) || ~((x <= 3.2e+206)))
		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]}, If[LessEqual[x, 6.5e-51], N[(3.0 * N[(N[Sqrt[x], $MachinePrecision] * N[(0.1111111111111111 / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2350000000000.0], N[(3.0 * N[(y * N[Sqrt[x], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 6e+75], t$95$0, If[LessEqual[x, 2.05e+111], N[(N[Sqrt[N[(x * 9.0), $MachinePrecision]], $MachinePrecision] * y), $MachinePrecision], If[Or[LessEqual[x, 4.1e+144], N[Not[LessEqual[x, 3.2e+206]], $MachinePrecision]], t$95$0, N[(N[Sqrt[x], $MachinePrecision] * N[(y * 3.0), $MachinePrecision]), $MachinePrecision]]]]]]]

Derivation

1. Split input into 5 regimes

2. if x < 6.5000000000000003e-51

   1. Initial program 99.2%

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

      1. 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* 99.3%

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

      7. metadata-eval 99.3%

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

      8. metadata-eval 99.3%

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

   3. Simplified 99.3%

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

   5. Taylor expanded in y around 0 77.8%

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

      1. sub-neg 77.8%

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

      2. associate-*r/ 77.9%

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

      3. metadata-eval 77.9%

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

      4. metadata-eval 77.9%

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

   7. Simplified 77.9%

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

   8. Taylor expanded in x around 0 77.9%

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

   if 6.5000000000000003e-51 < x < 2.35e12

   1. Initial program 99.2%

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

      1. associate-*l* 99.3%

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

      2. sub-neg 99.3%

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

      3. +-commutative 99.3%

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

      4. associate-+l+ 99.3%

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

      5. *-commutative 99.3%

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

      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

   5. Taylor expanded in y around inf 53.2%

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

   if 2.35e12 < x < 6e75 or 2.04999999999999993e111 < x < 4.10000000000000001e144 or 3.20000000000000005e206 < x

   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. Taylor expanded in y around 0 70.8%

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

      1. sub-neg 70.8%

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

      2. associate-*r/ 70.8%

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

      3. metadata-eval 70.8%

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

      4. metadata-eval 70.8%

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

   7. Simplified 70.8%

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

   8. Taylor expanded in x around inf 70.7%

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

      1. add0 70.7%

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

      2. associate-*r* 70.7%

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

      3. fma-define 70.7%

         \[\leadsto \color{blue}{\mathsf{fma}\left(3 \cdot \sqrt{x}, -1, 0\right)} \]

      4. /-rgt-identity 70.7%

         \[\leadsto \mathsf{fma}\left(3 \cdot \sqrt{\color{blue}{\frac{x}{1}}}, -1, 0\right) \]

      5. div-inv 70.7%

         \[\leadsto \mathsf{fma}\left(3 \cdot \sqrt{\color{blue}{x \cdot \frac{1}{1}}}, -1, 0\right) \]

      6. add-sqr-sqrt 70.7%

         \[\leadsto \mathsf{fma}\left(3 \cdot \sqrt{\color{blue}{\left(\sqrt{x} \cdot \sqrt{x}\right)} \cdot \frac{1}{1}}, -1, 0\right) \]

      7. metadata-eval 70.7%

         \[\leadsto \mathsf{fma}\left(3 \cdot \sqrt{\left(\sqrt{x} \cdot \sqrt{x}\right) \cdot \color{blue}{1}}, -1, 0\right) \]

      8. metadata-eval 70.7%

         \[\leadsto \mathsf{fma}\left(3 \cdot \sqrt{\left(\sqrt{x} \cdot \sqrt{x}\right) \cdot \color{blue}{\left(-1 \cdot -1\right)}}, -1, 0\right) \]

      9. swap-sqr 70.7%

         \[\leadsto \mathsf{fma}\left(3 \cdot \sqrt{\color{blue}{\left(\sqrt{x} \cdot -1\right) \cdot \left(\sqrt{x} \cdot -1\right)}}, -1, 0\right) \]

      10. sqrt-unprod 0.0%

          \[\leadsto \mathsf{fma}\left(3 \cdot \color{blue}{\left(\sqrt{\sqrt{x} \cdot -1} \cdot \sqrt{\sqrt{x} \cdot -1}\right)}, -1, 0\right) \]

      11. add-sqr-sqrt 1.8%

          \[\leadsto \mathsf{fma}\left(3 \cdot \color{blue}{\left(\sqrt{x} \cdot -1\right)}, -1, 0\right) \]

      12. *-commutative 1.8%

          \[\leadsto \mathsf{fma}\left(\color{blue}{\left(\sqrt{x} \cdot -1\right) \cdot 3}, -1, 0\right) \]

      13. add-sqr-sqrt 0.0%

          \[\leadsto \mathsf{fma}\left(\color{blue}{\left(\sqrt{\sqrt{x} \cdot -1} \cdot \sqrt{\sqrt{x} \cdot -1}\right)} \cdot 3, -1, 0\right) \]

      14. sqrt-unprod 70.7%

          \[\leadsto \mathsf{fma}\left(\color{blue}{\sqrt{\left(\sqrt{x} \cdot -1\right) \cdot \left(\sqrt{x} \cdot -1\right)}} \cdot 3, -1, 0\right) \]

      15. swap-sqr 70.7%

          \[\leadsto \mathsf{fma}\left(\sqrt{\color{blue}{\left(\sqrt{x} \cdot \sqrt{x}\right) \cdot \left(-1 \cdot -1\right)}} \cdot 3, -1, 0\right) \]

      16. add-sqr-sqrt 70.7%

          \[\leadsto \mathsf{fma}\left(\sqrt{\color{blue}{x} \cdot \left(-1 \cdot -1\right)} \cdot 3, -1, 0\right) \]

      17. metadata-eval 70.7%

          \[\leadsto \mathsf{fma}\left(\sqrt{x \cdot \color{blue}{1}} \cdot 3, -1, 0\right) \]

      18. metadata-eval 70.7%

          \[\leadsto \mathsf{fma}\left(\sqrt{x \cdot \color{blue}{\frac{1}{1}}} \cdot 3, -1, 0\right) \]

      19. div-inv 70.7%

          \[\leadsto \mathsf{fma}\left(\sqrt{\color{blue}{\frac{x}{1}}} \cdot 3, -1, 0\right) \]

      20. /-rgt-identity 70.7%

          \[\leadsto \mathsf{fma}\left(\sqrt{\color{blue}{x}} \cdot 3, -1, 0\right) \]

   10. Applied egg-rr 70.7%

       \[\leadsto \color{blue}{\mathsf{fma}\left(\sqrt{x} \cdot 3, -1, 0\right)} \]
   11. Step-by-step derivation

       1. fma-undefine 70.7%

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

       2. *-commutative 70.7%

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

       3. add0 70.7%

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

       4. mul-1-neg 70.7%

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

       5. distribute-rgt-neg-in 70.7%

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

       6. metadata-eval 70.7%

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

   12. Simplified 70.7%

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

   if 6e75 < x < 2.04999999999999993e111

   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* 99.3%

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

      2. sub-neg 99.3%

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

      3. +-commutative 99.3%

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

      4. associate-+l+ 99.3%

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

      5. *-commutative 99.3%

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

      6. associate-/r* 99.3%

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

      7. metadata-eval 99.3%

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

      8. metadata-eval 99.3%

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

   3. Simplified 99.3%

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

   5. Taylor expanded in y around inf 78.3%

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

      1. add0 78.3%

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

      2. *-commutative 78.3%

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

      3. *-commutative 78.3%

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

      4. associate-*l* 78.5%

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

      5. metadata-eval 78.5%

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

      6. sqrt-prod 78.5%

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

   7. Applied egg-rr 78.5%

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

      1. add0 78.5%

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

   9. Simplified 78.5%

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

   if 4.10000000000000001e144 < x < 3.20000000000000005e206

   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* 99.6%

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

      2. sub-neg 99.6%

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

      3. +-commutative 99.6%

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

      4. associate-+l+ 99.6%

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

      5. *-commutative 99.6%

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

      6. associate-/r* 99.6%

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

      7. metadata-eval 99.6%

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

      8. metadata-eval 99.6%

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

   3. Simplified 99.6%

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

   5. Taylor expanded in y around 0 99.6%

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

      1. associate-*r* 99.6%

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

      2. associate-*r* 99.6%

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

      3. sub-neg 99.6%

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

      4. associate-*r/ 99.6%

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

      5. metadata-eval 99.6%

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

      6. metadata-eval 99.6%

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

      7. distribute-lft-out 99.6%

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

      8. *-commutative 99.6%

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

      9. associate-+r+ 99.6%

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

      10. +-commutative 99.6%

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

      11. associate-+r+ 99.6%

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

      12. associate-*r* 99.7%

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

      13. distribute-lft-in 99.7%

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

      14. associate-*r/ 99.7%

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

      15. metadata-eval 99.7%

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

      16. +-commutative 99.7%

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

      17. distribute-lft-in 99.7%

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

      18. metadata-eval 99.7%

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

   7. Simplified 99.7%

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

   8. Taylor expanded in y around inf 60.7%

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

      1. *-commutative 60.7%

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

      2. associate-*l* 60.7%

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

      3. *-commutative 60.7%

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

   10. Simplified 60.7%

       \[\leadsto \color{blue}{\sqrt{x} \cdot \left(3 \cdot y\right)} \]
3. Recombined 5 regimes into one program.

4. Final simplification 70.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 6.5 \cdot 10^{-51}:\\ \;\;\;\;3 \cdot \left(\sqrt{x} \cdot \frac{0.1111111111111111}{x}\right)\\ \mathbf{elif}\;x \leq 2350000000000:\\ \;\;\;\;3 \cdot \left(y \cdot \sqrt{x}\right)\\ \mathbf{elif}\;x \leq 6 \cdot 10^{+75}:\\ \;\;\;\;\sqrt{x} \cdot -3\\ \mathbf{elif}\;x \leq 2.05 \cdot 10^{+111}:\\ \;\;\;\;\sqrt{x \cdot 9} \cdot y\\ \mathbf{elif}\;x \leq 4.1 \cdot 10^{+144} \lor \neg \left(x \leq 3.2 \cdot 10^{+206}\right):\\ \;\;\;\;\sqrt{x} \cdot -3\\ \mathbf{else}:\\ \;\;\;\;\sqrt{x} \cdot \left(y \cdot 3\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 97.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.3 \cdot 10^{-33} \lor \neg \left(y \leq 10^{-10}\right):\\ \;\;\;\;\sqrt{x} \cdot \left(\frac{0.3333333333333333}{x} + y \cdot 3\right)\\ \mathbf{else}:\\ \;\;\;\;\sqrt{x} \cdot \left(0.3333333333333333 \cdot \frac{1}{x} - 3\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= y -1.3e-33) (not (<= y 1e-10)))
   (* (sqrt x) (+ (/ 0.3333333333333333 x) (* y 3.0)))
   (* (sqrt x) (- (* 0.3333333333333333 (/ 1.0 x)) 3.0))))

C

double code(double x, double y) {
	double tmp;
	if ((y <= -1.3e-33) || !(y <= 1e-10)) {
		tmp = sqrt(x) * ((0.3333333333333333 / x) + (y * 3.0));
	} else {
		tmp = sqrt(x) * ((0.3333333333333333 * (1.0 / 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 ((y <= (-1.3d-33)) .or. (.not. (y <= 1d-10))) then
        tmp = sqrt(x) * ((0.3333333333333333d0 / x) + (y * 3.0d0))
    else
        tmp = sqrt(x) * ((0.3333333333333333d0 * (1.0d0 / x)) - 3.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((y <= -1.3e-33) || !(y <= 1e-10)) {
		tmp = Math.sqrt(x) * ((0.3333333333333333 / x) + (y * 3.0));
	} else {
		tmp = Math.sqrt(x) * ((0.3333333333333333 * (1.0 / x)) - 3.0);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (y <= -1.3e-33) or not (y <= 1e-10):
		tmp = math.sqrt(x) * ((0.3333333333333333 / x) + (y * 3.0))
	else:
		tmp = math.sqrt(x) * ((0.3333333333333333 * (1.0 / x)) - 3.0)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((y <= -1.3e-33) || !(y <= 1e-10))
		tmp = Float64(sqrt(x) * Float64(Float64(0.3333333333333333 / x) + Float64(y * 3.0)));
	else
		tmp = Float64(sqrt(x) * Float64(Float64(0.3333333333333333 * Float64(1.0 / x)) - 3.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((y <= -1.3e-33) || ~((y <= 1e-10)))
		tmp = sqrt(x) * ((0.3333333333333333 / x) + (y * 3.0));
	else
		tmp = sqrt(x) * ((0.3333333333333333 * (1.0 / x)) - 3.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[y, -1.3e-33], N[Not[LessEqual[y, 1e-10]], $MachinePrecision]], N[(N[Sqrt[x], $MachinePrecision] * N[(N[(0.3333333333333333 / x), $MachinePrecision] + N[(y * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[Sqrt[x], $MachinePrecision] * N[(N[(0.3333333333333333 * N[(1.0 / x), $MachinePrecision]), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.29999999999999997e-33 or 1.00000000000000004e-10 < y

   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* 99.4%

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

      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. Taylor expanded in y around 0 99.4%

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

      1. associate-*r* 99.3%

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

      2. associate-*r* 99.3%

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

      3. sub-neg 99.3%

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

      4. associate-*r/ 99.3%

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

      5. metadata-eval 99.3%

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

      6. metadata-eval 99.3%

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

      7. distribute-lft-out 99.4%

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

      8. *-commutative 99.4%

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

      9. associate-+r+ 99.4%

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

      10. +-commutative 99.4%

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

      11. associate-+r+ 99.4%

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

      12. associate-*r* 99.4%

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

      13. distribute-lft-in 99.3%

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

      14. associate-*r/ 99.4%

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

      15. metadata-eval 99.4%

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

      16. +-commutative 99.4%

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

      17. distribute-lft-in 99.4%

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

      18. metadata-eval 99.4%

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

   7. Simplified 99.4%

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

   8. Taylor expanded in y around inf 99.4%

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

   if -1.29999999999999997e-33 < y < 1.00000000000000004e-10

   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* 99.3%

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

      2. sub-neg 99.3%

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

      3. +-commutative 99.3%

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

      4. associate-+l+ 99.3%

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

      5. *-commutative 99.3%

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

      6. associate-/r* 99.3%

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

      7. metadata-eval 99.3%

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

      8. metadata-eval 99.3%

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

   3. Simplified 99.3%

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

   5. Taylor expanded in y around 0 99.3%

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

      1. associate-*r* 99.3%

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

      2. associate-*r* 99.3%

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

      3. sub-neg 99.3%

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

      4. associate-*r/ 99.4%

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

      5. metadata-eval 99.4%

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

      6. metadata-eval 99.4%

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

      7. distribute-lft-out 99.4%

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

      8. *-commutative 99.4%

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

      9. associate-+r+ 99.4%

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

      10. +-commutative 99.4%

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

      11. associate-+r+ 99.4%

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

      12. associate-*r* 99.4%

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

      13. distribute-lft-in 99.4%

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

      14. associate-*r/ 99.4%

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

      15. metadata-eval 99.4%

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

      16. +-commutative 99.4%

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

      17. distribute-lft-in 99.4%

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

      18. metadata-eval 99.4%

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

   7. Simplified 99.4%

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

   8. Taylor expanded in y around 0 99.5%

      \[\leadsto \color{blue}{\sqrt{x} \cdot \left(0.3333333333333333 \cdot \frac{1}{x} - 3\right)} \]
3. Recombined 2 regimes into one program.

4. Final simplification 99.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.3 \cdot 10^{-33} \lor \neg \left(y \leq 10^{-10}\right):\\ \;\;\;\;\sqrt{x} \cdot \left(\frac{0.3333333333333333}{x} + y \cdot 3\right)\\ \mathbf{else}:\\ \;\;\;\;\sqrt{x} \cdot \left(0.3333333333333333 \cdot \frac{1}{x} - 3\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 97.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.3 \cdot 10^{-33} \lor \neg \left(y \leq 1\right):\\ \;\;\;\;\sqrt{x} \cdot \left(\frac{0.3333333333333333}{x} + y \cdot 3\right)\\ \mathbf{else}:\\ \;\;\;\;\sqrt{x \cdot 9} \cdot \left(\frac{0.1111111111111111}{x} + -1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= y -1.3e-33) (not (<= y 1.0)))
   (* (sqrt x) (+ (/ 0.3333333333333333 x) (* y 3.0)))
   (* (sqrt (* x 9.0)) (+ (/ 0.1111111111111111 x) -1.0))))

C

double code(double x, double y) {
	double tmp;
	if ((y <= -1.3e-33) || !(y <= 1.0)) {
		tmp = sqrt(x) * ((0.3333333333333333 / x) + (y * 3.0));
	} else {
		tmp = sqrt((x * 9.0)) * ((0.1111111111111111 / x) + -1.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if ((y <= (-1.3d-33)) .or. (.not. (y <= 1.0d0))) then
        tmp = sqrt(x) * ((0.3333333333333333d0 / x) + (y * 3.0d0))
    else
        tmp = sqrt((x * 9.0d0)) * ((0.1111111111111111d0 / x) + (-1.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((y <= -1.3e-33) || !(y <= 1.0)) {
		tmp = Math.sqrt(x) * ((0.3333333333333333 / x) + (y * 3.0));
	} else {
		tmp = Math.sqrt((x * 9.0)) * ((0.1111111111111111 / x) + -1.0);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (y <= -1.3e-33) or not (y <= 1.0):
		tmp = math.sqrt(x) * ((0.3333333333333333 / x) + (y * 3.0))
	else:
		tmp = math.sqrt((x * 9.0)) * ((0.1111111111111111 / x) + -1.0)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((y <= -1.3e-33) || !(y <= 1.0))
		tmp = Float64(sqrt(x) * Float64(Float64(0.3333333333333333 / x) + Float64(y * 3.0)));
	else
		tmp = Float64(sqrt(Float64(x * 9.0)) * Float64(Float64(0.1111111111111111 / x) + -1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((y <= -1.3e-33) || ~((y <= 1.0)))
		tmp = sqrt(x) * ((0.3333333333333333 / x) + (y * 3.0));
	else
		tmp = sqrt((x * 9.0)) * ((0.1111111111111111 / x) + -1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[y, -1.3e-33], N[Not[LessEqual[y, 1.0]], $MachinePrecision]], N[(N[Sqrt[x], $MachinePrecision] * N[(N[(0.3333333333333333 / x), $MachinePrecision] + N[(y * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[Sqrt[N[(x * 9.0), $MachinePrecision]], $MachinePrecision] * N[(N[(0.1111111111111111 / x), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -1.29999999999999997e-33 or 1 < y

   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* 99.4%

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

      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. Taylor expanded in y around 0 99.4%

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

      1. associate-*r* 99.3%

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

      2. associate-*r* 99.3%

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

      3. sub-neg 99.3%

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

      4. associate-*r/ 99.3%

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

      5. metadata-eval 99.3%

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

      6. metadata-eval 99.3%

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

      7. distribute-lft-out 99.4%

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

      8. *-commutative 99.4%

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

      9. associate-+r+ 99.4%

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

      10. +-commutative 99.4%

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

      11. associate-+r+ 99.4%

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

      12. associate-*r* 99.4%

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

      13. distribute-lft-in 99.3%

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

      14. associate-*r/ 99.4%

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

      15. metadata-eval 99.4%

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

      16. +-commutative 99.4%

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

      17. distribute-lft-in 99.4%

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

      18. metadata-eval 99.4%

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

   7. Simplified 99.4%

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

   8. Taylor expanded in y around inf 99.4%

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

   if -1.29999999999999997e-33 < y < 1

   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* 99.3%

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

      2. sub-neg 99.3%

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

      3. +-commutative 99.3%

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

      4. associate-+l+ 99.3%

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

      5. *-commutative 99.3%

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

      6. associate-/r* 99.3%

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

      7. metadata-eval 99.3%

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

      8. metadata-eval 99.3%

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

   3. Simplified 99.3%

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

   5. Taylor expanded in y around 0 99.3%

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

      1. sub-neg 99.3%

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

      2. associate-*r/ 99.3%

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

      3. metadata-eval 99.3%

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

      4. metadata-eval 99.3%

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

   7. Simplified 99.3%

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

      1. add0 99.3%

         \[\leadsto \color{blue}{3 \cdot \left(\sqrt{x} \cdot \left(\frac{0.1111111111111111}{x} + -1\right)\right) + 0} \]

      2. *-commutative 99.3%

         \[\leadsto \color{blue}{\left(\sqrt{x} \cdot \left(\frac{0.1111111111111111}{x} + -1\right)\right) \cdot 3} + 0 \]

      3. *-commutative 99.3%

         \[\leadsto \color{blue}{\left(\left(\frac{0.1111111111111111}{x} + -1\right) \cdot \sqrt{x}\right)} \cdot 3 + 0 \]

      4. associate-*l* 99.4%

         \[\leadsto \color{blue}{\left(\frac{0.1111111111111111}{x} + -1\right) \cdot \left(\sqrt{x} \cdot 3\right)} + 0 \]

      5. metadata-eval 99.4%

         \[\leadsto \left(\frac{0.1111111111111111}{x} + -1\right) \cdot \left(\sqrt{x} \cdot \color{blue}{\sqrt{9}}\right) + 0 \]

      6. sqrt-prod 99.6%

         \[\leadsto \left(\frac{0.1111111111111111}{x} + -1\right) \cdot \color{blue}{\sqrt{x \cdot 9}} + 0 \]

   9. Applied egg-rr 99.6%

      \[\leadsto \color{blue}{\left(\frac{0.1111111111111111}{x} + -1\right) \cdot \sqrt{x \cdot 9} + 0} \]
   10. Step-by-step derivation

       1. add0 99.6%

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

   11. Simplified 99.6%

       \[\leadsto \color{blue}{\left(\frac{0.1111111111111111}{x} + -1\right) \cdot \sqrt{x \cdot 9}} \]
3. Recombined 2 regimes into one program.

4. Final simplification 99.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.3 \cdot 10^{-33} \lor \neg \left(y \leq 1\right):\\ \;\;\;\;\sqrt{x} \cdot \left(\frac{0.3333333333333333}{x} + y \cdot 3\right)\\ \mathbf{else}:\\ \;\;\;\;\sqrt{x \cdot 9} \cdot \left(\frac{0.1111111111111111}{x} + -1\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 85.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.8 \cdot 10^{+48}:\\ \;\;\;\;3 \cdot \left(y \cdot \sqrt{x}\right)\\ \mathbf{elif}\;y \leq 3.2 \cdot 10^{+74}:\\ \;\;\;\;\sqrt{x} \cdot \left(\frac{0.3333333333333333}{x} + -3\right)\\ \mathbf{else}:\\ \;\;\;\;\sqrt{x} \cdot \left(y \cdot 3\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -1.8e+48)
   (* 3.0 (* y (sqrt x)))
   (if (<= y 3.2e+74)
     (* (sqrt x) (+ (/ 0.3333333333333333 x) -3.0))
     (* (sqrt x) (* y 3.0)))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -1.8e+48) {
		tmp = 3.0 * (y * sqrt(x));
	} else if (y <= 3.2e+74) {
		tmp = sqrt(x) * ((0.3333333333333333 / x) + -3.0);
	} 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) :: tmp
    if (y <= (-1.8d+48)) then
        tmp = 3.0d0 * (y * sqrt(x))
    else if (y <= 3.2d+74) then
        tmp = sqrt(x) * ((0.3333333333333333d0 / x) + (-3.0d0))
    else
        tmp = sqrt(x) * (y * 3.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (y <= -1.8e+48) {
		tmp = 3.0 * (y * Math.sqrt(x));
	} else if (y <= 3.2e+74) {
		tmp = Math.sqrt(x) * ((0.3333333333333333 / x) + -3.0);
	} else {
		tmp = Math.sqrt(x) * (y * 3.0);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -1.8e+48:
		tmp = 3.0 * (y * math.sqrt(x))
	elif y <= 3.2e+74:
		tmp = math.sqrt(x) * ((0.3333333333333333 / x) + -3.0)
	else:
		tmp = math.sqrt(x) * (y * 3.0)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -1.8e+48)
		tmp = Float64(3.0 * Float64(y * sqrt(x)));
	elseif (y <= 3.2e+74)
		tmp = Float64(sqrt(x) * Float64(Float64(0.3333333333333333 / x) + -3.0));
	else
		tmp = Float64(sqrt(x) * Float64(y * 3.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -1.8e+48)
		tmp = 3.0 * (y * sqrt(x));
	elseif (y <= 3.2e+74)
		tmp = sqrt(x) * ((0.3333333333333333 / x) + -3.0);
	else
		tmp = sqrt(x) * (y * 3.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -1.8e+48], N[(3.0 * N[(y * N[Sqrt[x], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 3.2e+74], N[(N[Sqrt[x], $MachinePrecision] * N[(N[(0.3333333333333333 / x), $MachinePrecision] + -3.0), $MachinePrecision]), $MachinePrecision], N[(N[Sqrt[x], $MachinePrecision] * N[(y * 3.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.79999999999999992e48

   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* 99.6%

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

      2. sub-neg 99.6%

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

      3. +-commutative 99.6%

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

      4. associate-+l+ 99.6%

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

      5. *-commutative 99.6%

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

      6. associate-/r* 99.6%

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

      7. metadata-eval 99.6%

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

      8. metadata-eval 99.6%

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

   3. Simplified 99.6%

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

   5. Taylor expanded in y around inf 83.8%

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

   if -1.79999999999999992e48 < y < 3.19999999999999995e74

   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* 99.3%

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

      7. metadata-eval 99.3%

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

      8. metadata-eval 99.3%

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

   3. Simplified 99.3%

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

   5. Taylor expanded in y around 0 93.6%

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

      1. associate-*r* 93.7%

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

      2. sub-neg 93.7%

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

      3. associate-*r/ 93.8%

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

      4. metadata-eval 93.8%

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

      5. metadata-eval 93.8%

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

      6. distribute-rgt-in 93.8%

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

      7. *-commutative 93.8%

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

      8. associate-*l* 93.7%

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

      9. *-commutative 93.7%

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

      10. associate-*r* 93.7%

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

      11. associate-*r* 93.7%

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

      12. distribute-rgt-out 93.7%

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

      13. associate-*r/ 93.7%

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

      14. metadata-eval 93.7%

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

      15. metadata-eval 93.7%

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

   7. Simplified 93.7%

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

   if 3.19999999999999995e74 < y

   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* 99.5%

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

      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 0 99.4%

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

      1. associate-*r* 99.4%

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

      2. associate-*r* 99.4%

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

      3. sub-neg 99.4%

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

      4. associate-*r/ 99.4%

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

      5. metadata-eval 99.4%

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

      6. metadata-eval 99.4%

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

      7. distribute-lft-out 99.4%

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

      8. *-commutative 99.4%

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

      9. associate-+r+ 99.4%

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

      10. +-commutative 99.4%

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

      11. associate-+r+ 99.4%

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

      12. associate-*r* 99.4%

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

      13. distribute-lft-in 99.4%

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

      14. associate-*r/ 99.5%

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

      15. metadata-eval 99.5%

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

      16. +-commutative 99.5%

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

      17. distribute-lft-in 99.5%

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

      18. metadata-eval 99.5%

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

   7. Simplified 99.5%

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

   8. Taylor expanded in y around inf 84.6%

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

      1. *-commutative 84.6%

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

      2. associate-*l* 84.6%

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

      3. *-commutative 84.6%

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

   10. Simplified 84.6%

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

4. Final simplification 90.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.8 \cdot 10^{+48}:\\ \;\;\;\;3 \cdot \left(y \cdot \sqrt{x}\right)\\ \mathbf{elif}\;y \leq 3.2 \cdot 10^{+74}:\\ \;\;\;\;\sqrt{x} \cdot \left(\frac{0.3333333333333333}{x} + -3\right)\\ \mathbf{else}:\\ \;\;\;\;\sqrt{x} \cdot \left(y \cdot 3\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 98.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 0.11:\\ \;\;\;\;\sqrt{x} \cdot \left(\frac{0.3333333333333333}{x} + y \cdot 3\right)\\ \mathbf{else}:\\ \;\;\;\;\sqrt{x \cdot 9} \cdot \left(y + -1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x 0.11)
   (* (sqrt x) (+ (/ 0.3333333333333333 x) (* y 3.0)))
   (* (sqrt (* x 9.0)) (+ y -1.0))))

C

double code(double x, double y) {
	double tmp;
	if (x <= 0.11) {
		tmp = sqrt(x) * ((0.3333333333333333 / x) + (y * 3.0));
	} else {
		tmp = sqrt((x * 9.0)) * (y + -1.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (x <= 0.11d0) then
        tmp = sqrt(x) * ((0.3333333333333333d0 / x) + (y * 3.0d0))
    else
        tmp = sqrt((x * 9.0d0)) * (y + (-1.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= 0.11) {
		tmp = Math.sqrt(x) * ((0.3333333333333333 / x) + (y * 3.0));
	} else {
		tmp = Math.sqrt((x * 9.0)) * (y + -1.0);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= 0.11:
		tmp = math.sqrt(x) * ((0.3333333333333333 / x) + (y * 3.0))
	else:
		tmp = math.sqrt((x * 9.0)) * (y + -1.0)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= 0.11)
		tmp = Float64(sqrt(x) * Float64(Float64(0.3333333333333333 / x) + Float64(y * 3.0)));
	else
		tmp = Float64(sqrt(Float64(x * 9.0)) * Float64(y + -1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= 0.11)
		tmp = sqrt(x) * ((0.3333333333333333 / x) + (y * 3.0));
	else
		tmp = sqrt((x * 9.0)) * (y + -1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, 0.11], N[(N[Sqrt[x], $MachinePrecision] * N[(N[(0.3333333333333333 / x), $MachinePrecision] + N[(y * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[Sqrt[N[(x * 9.0), $MachinePrecision]], $MachinePrecision] * N[(y + -1.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < 0.110000000000000001

   1. Initial program 99.2%

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

      1. associate-*l* 99.3%

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

      2. sub-neg 99.3%

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

      3. +-commutative 99.3%

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

      4. associate-+l+ 99.3%

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

      5. *-commutative 99.3%

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

      6. associate-/r* 99.3%

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

      7. metadata-eval 99.3%

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

      8. metadata-eval 99.3%

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

   3. Simplified 99.3%

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

   5. Taylor expanded in y around 0 99.2%

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

      1. associate-*r* 99.2%

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

      2. associate-*r* 99.2%

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

      3. sub-neg 99.2%

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

      4. associate-*r/ 99.3%

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

      5. metadata-eval 99.3%

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

      6. metadata-eval 99.3%

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

      7. distribute-lft-out 99.3%

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

      8. *-commutative 99.3%

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

      9. associate-+r+ 99.3%

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

      10. +-commutative 99.3%

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

      11. associate-+r+ 99.3%

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

      12. associate-*r* 99.2%

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

      13. distribute-lft-in 99.2%

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

      14. associate-*r/ 99.3%

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

      15. metadata-eval 99.3%

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

      16. +-commutative 99.3%

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

      17. distribute-lft-in 99.3%

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

      18. metadata-eval 99.3%

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

   7. Simplified 99.3%

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

   8. Taylor expanded in y around inf 97.2%

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

   if 0.110000000000000001 < x

   1. Initial program 99.5%

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

      1. *-commutative 99.5%

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

      2. metadata-eval 99.5%

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

      3. sqrt-prod 99.7%

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

      4. pow1/2 99.7%

         \[\leadsto \color{blue}{{\left(x \cdot 9\right)}^{0.5}} \cdot \left(\left(y + \frac{1}{x \cdot 9}\right) - 1\right) \]

   4. Applied egg-rr 99.7%

      \[\leadsto \color{blue}{{\left(x \cdot 9\right)}^{0.5}} \cdot \left(\left(y + \frac{1}{x \cdot 9}\right) - 1\right) \]
   5. Step-by-step derivation

      1. unpow1/2 99.7%

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

   6. Simplified 99.7%

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

   7. Taylor expanded in y around inf 98.5%

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

4. Final simplification 97.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 0.11:\\ \;\;\;\;\sqrt{x} \cdot \left(\frac{0.3333333333333333}{x} + y \cdot 3\right)\\ \mathbf{else}:\\ \;\;\;\;\sqrt{x \cdot 9} \cdot \left(y + -1\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 85.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 6.5 \cdot 10^{-51}:\\ \;\;\;\;3 \cdot \left(\sqrt{x} \cdot \frac{0.1111111111111111}{x}\right)\\ \mathbf{else}:\\ \;\;\;\;\sqrt{x} \cdot \left(-3 + y \cdot 3\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x 6.5e-51)
   (* 3.0 (* (sqrt x) (/ 0.1111111111111111 x)))
   (* (sqrt x) (+ -3.0 (* y 3.0)))))

C

double code(double x, double y) {
	double tmp;
	if (x <= 6.5e-51) {
		tmp = 3.0 * (sqrt(x) * (0.1111111111111111 / x));
	} else {
		tmp = sqrt(x) * (-3.0 + (y * 3.0));
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (x <= 6.5d-51) then
        tmp = 3.0d0 * (sqrt(x) * (0.1111111111111111d0 / x))
    else
        tmp = sqrt(x) * ((-3.0d0) + (y * 3.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= 6.5e-51) {
		tmp = 3.0 * (Math.sqrt(x) * (0.1111111111111111 / x));
	} else {
		tmp = Math.sqrt(x) * (-3.0 + (y * 3.0));
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= 6.5e-51:
		tmp = 3.0 * (math.sqrt(x) * (0.1111111111111111 / x))
	else:
		tmp = math.sqrt(x) * (-3.0 + (y * 3.0))
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= 6.5e-51)
		tmp = Float64(3.0 * Float64(sqrt(x) * Float64(0.1111111111111111 / x)));
	else
		tmp = Float64(sqrt(x) * Float64(-3.0 + Float64(y * 3.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= 6.5e-51)
		tmp = 3.0 * (sqrt(x) * (0.1111111111111111 / x));
	else
		tmp = sqrt(x) * (-3.0 + (y * 3.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, 6.5e-51], N[(3.0 * N[(N[Sqrt[x], $MachinePrecision] * N[(0.1111111111111111 / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[Sqrt[x], $MachinePrecision] * N[(-3.0 + N[(y * 3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < 6.5000000000000003e-51

   1. Initial program 99.2%

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

      1. 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* 99.3%

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

      7. metadata-eval 99.3%

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

      8. metadata-eval 99.3%

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

   3. Simplified 99.3%

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

   5. Taylor expanded in y around 0 77.8%

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

      1. sub-neg 77.8%

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

      2. associate-*r/ 77.9%

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

      3. metadata-eval 77.9%

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

      4. metadata-eval 77.9%

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

   7. Simplified 77.9%

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

   8. Taylor expanded in x around 0 77.9%

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

   if 6.5000000000000003e-51 < x

   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%

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

      2. metadata-eval 99.4%

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

      3. sqrt-prod 99.6%

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

      4. pow1/2 99.6%

         \[\leadsto \color{blue}{{\left(x \cdot 9\right)}^{0.5}} \cdot \left(\left(y + \frac{1}{x \cdot 9}\right) - 1\right) \]

   4. Applied egg-rr 99.6%

      \[\leadsto \color{blue}{{\left(x \cdot 9\right)}^{0.5}} \cdot \left(\left(y + \frac{1}{x \cdot 9}\right) - 1\right) \]
   5. Step-by-step derivation

      1. unpow1/2 99.6%

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

   6. Simplified 99.6%

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

      1. sqrt-prod 99.4%

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

      2. metadata-eval 99.4%

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

      3. *-commutative 99.4%

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

      4. *-commutative 99.4%

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

      5. pow1/2 99.4%

         \[\leadsto \left(\left(y + \frac{1}{x \cdot 9}\right) - 1\right) \cdot \left(3 \cdot \color{blue}{{x}^{0.5}}\right) \]

      6. metadata-eval 99.4%

         \[\leadsto \left(\left(y + \frac{1}{x \cdot 9}\right) - 1\right) \cdot \left(3 \cdot {x}^{\color{blue}{\left(1 - 0.5\right)}}\right) \]

      7. pow-div 99.3%

         \[\leadsto \left(\left(y + \frac{1}{x \cdot 9}\right) - 1\right) \cdot \left(3 \cdot \color{blue}{\frac{{x}^{1}}{{x}^{0.5}}}\right) \]

      8. pow1 99.3%

         \[\leadsto \left(\left(y + \frac{1}{x \cdot 9}\right) - 1\right) \cdot \left(3 \cdot \frac{\color{blue}{x}}{{x}^{0.5}}\right) \]

      9. pow1/2 99.3%

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

      10. associate-*r/ 99.4%

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

      11. associate-*r/ 93.1%

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

      12. associate--l+ 93.1%

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

      13. *-commutative 93.1%

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

      14. associate-/r* 93.1%

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

      15. metadata-eval 93.1%

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

      16. associate--l+ 93.1%

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

      17. sub-neg 93.1%

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

      18. metadata-eval 93.1%

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

      19. associate-+l+ 93.1%

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

   8. Applied egg-rr 93.1%

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

      1. associate-/l* 99.3%

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

   10. Simplified 99.3%

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

   11. Taylor expanded in x around inf 89.4%

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

   12. Taylor expanded in y around 0 89.6%

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

       1. associate-*r* 89.5%

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

       2. *-commutative 89.5%

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

       3. associate-*r* 89.6%

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

       4. distribute-rgt-out 89.6%

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

       5. *-commutative 89.6%

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

   14. Simplified 89.6%

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

4. Final simplification 84.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 6.5 \cdot 10^{-51}:\\ \;\;\;\;3 \cdot \left(\sqrt{x} \cdot \frac{0.1111111111111111}{x}\right)\\ \mathbf{else}:\\ \;\;\;\;\sqrt{x} \cdot \left(-3 + y \cdot 3\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 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 99.3%

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

   1. associate-*l* 99.3%

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

   2. sub-neg 99.3%

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

   3. +-commutative 99.3%

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

   4. associate-+l+ 99.3%

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

   5. *-commutative 99.3%

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

   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 12: 99.4% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

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* 99.3%

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

   2. sub-neg 99.3%

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

   3. +-commutative 99.3%

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

   4. associate-+l+ 99.3%

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

   5. *-commutative 99.3%

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

   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. Taylor expanded in y around 0 99.3%

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

   1. associate-*r* 99.3%

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

   2. associate-*r* 99.3%

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

   3. sub-neg 99.3%

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

   4. associate-*r/ 99.4%

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

   5. metadata-eval 99.4%

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

   6. metadata-eval 99.4%

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

   7. distribute-lft-out 99.4%

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

   8. *-commutative 99.4%

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

   9. associate-+r+ 99.4%

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

   10. +-commutative 99.4%

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

   11. associate-+r+ 99.4%

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

   12. associate-*r* 99.4%

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

   13. distribute-lft-in 99.4%

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

   14. associate-*r/ 99.4%

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

   15. metadata-eval 99.4%

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

   16. +-commutative 99.4%

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

   17. distribute-lft-in 99.4%

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

   18. metadata-eval 99.4%

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

7. Simplified 99.4%

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

8. Final simplification 99.4%

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

Alternative 13: 99.4% accurate, 1.0× speedup

Math

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

FPCore

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

C

double code(double x, double y) {
	return (3.0 * sqrt(x)) * ((y + (0.1111111111111111 / x)) + -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 + (0.1111111111111111d0 / x)) + (-1.0d0))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.3%

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

3. Taylor expanded in x around 0 99.4%

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

4. Final simplification 99.4%

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

Alternative 14: 61.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 7.8:\\ \;\;\;\;0.3333333333333333 \cdot \sqrt{\frac{1}{x}}\\ \mathbf{else}:\\ \;\;\;\;\sqrt{x} \cdot -3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x 7.8) (* 0.3333333333333333 (sqrt (/ 1.0 x))) (* (sqrt x) -3.0)))

C

double code(double x, double y) {
	double tmp;
	if (x <= 7.8) {
		tmp = 0.3333333333333333 * sqrt((1.0 / 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 <= 7.8d0) then
        tmp = 0.3333333333333333d0 * sqrt((1.0d0 / 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 <= 7.8) {
		tmp = 0.3333333333333333 * Math.sqrt((1.0 / x));
	} else {
		tmp = Math.sqrt(x) * -3.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= 7.8:
		tmp = 0.3333333333333333 * math.sqrt((1.0 / x))
	else:
		tmp = math.sqrt(x) * -3.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= 7.8)
		tmp = Float64(0.3333333333333333 * sqrt(Float64(1.0 / x)));
	else
		tmp = Float64(sqrt(x) * -3.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= 7.8)
		tmp = 0.3333333333333333 * sqrt((1.0 / x));
	else
		tmp = sqrt(x) * -3.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, 7.8], N[(0.3333333333333333 * N[Sqrt[N[(1.0 / x), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], N[(N[Sqrt[x], $MachinePrecision] * -3.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < 7.79999999999999982

   1. Initial program 99.2%

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

      1. associate-*l* 99.3%

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

      2. sub-neg 99.3%

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

      3. +-commutative 99.3%

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

      4. associate-+l+ 99.3%

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

      5. *-commutative 99.3%

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

      6. associate-/r* 99.3%

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

      7. metadata-eval 99.3%

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

      8. metadata-eval 99.3%

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

   3. Simplified 99.3%

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

   5. Taylor expanded in y around 0 99.2%

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

      1. associate-*r* 99.2%

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

      2. associate-*r* 99.2%

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

      3. sub-neg 99.2%

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

      4. associate-*r/ 99.3%

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

      5. metadata-eval 99.3%

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

      6. metadata-eval 99.3%

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

      7. distribute-lft-out 99.3%

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

      8. *-commutative 99.3%

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

      9. associate-+r+ 99.3%

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

      10. +-commutative 99.3%

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

      11. associate-+r+ 99.3%

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

      12. associate-*r* 99.2%

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

      13. distribute-lft-in 99.2%

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

      14. associate-*r/ 99.3%

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

      15. metadata-eval 99.3%

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

      16. +-commutative 99.3%

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

      17. distribute-lft-in 99.3%

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

      18. metadata-eval 99.3%

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

   7. Simplified 99.3%

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

   8. Taylor expanded in y around inf 97.3%

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

   9. Taylor expanded in y around 0 69.8%

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

   if 7.79999999999999982 < 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. 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. Taylor expanded in y around 0 57.4%

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

      1. sub-neg 57.4%

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

      2. associate-*r/ 57.4%

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

      3. metadata-eval 57.4%

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

      4. metadata-eval 57.4%

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

   7. Simplified 57.4%

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

   8. Taylor expanded in x around inf 56.2%

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

      1. add0 56.2%

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

      2. associate-*r* 56.2%

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

      3. fma-define 56.2%

         \[\leadsto \color{blue}{\mathsf{fma}\left(3 \cdot \sqrt{x}, -1, 0\right)} \]

      4. /-rgt-identity 56.2%

         \[\leadsto \mathsf{fma}\left(3 \cdot \sqrt{\color{blue}{\frac{x}{1}}}, -1, 0\right) \]

      5. div-inv 56.2%

         \[\leadsto \mathsf{fma}\left(3 \cdot \sqrt{\color{blue}{x \cdot \frac{1}{1}}}, -1, 0\right) \]

      6. add-sqr-sqrt 56.2%

         \[\leadsto \mathsf{fma}\left(3 \cdot \sqrt{\color{blue}{\left(\sqrt{x} \cdot \sqrt{x}\right)} \cdot \frac{1}{1}}, -1, 0\right) \]

      7. metadata-eval 56.2%

         \[\leadsto \mathsf{fma}\left(3 \cdot \sqrt{\left(\sqrt{x} \cdot \sqrt{x}\right) \cdot \color{blue}{1}}, -1, 0\right) \]

      8. metadata-eval 56.2%

         \[\leadsto \mathsf{fma}\left(3 \cdot \sqrt{\left(\sqrt{x} \cdot \sqrt{x}\right) \cdot \color{blue}{\left(-1 \cdot -1\right)}}, -1, 0\right) \]

      9. swap-sqr 56.2%

         \[\leadsto \mathsf{fma}\left(3 \cdot \sqrt{\color{blue}{\left(\sqrt{x} \cdot -1\right) \cdot \left(\sqrt{x} \cdot -1\right)}}, -1, 0\right) \]

      10. sqrt-unprod 0.0%

          \[\leadsto \mathsf{fma}\left(3 \cdot \color{blue}{\left(\sqrt{\sqrt{x} \cdot -1} \cdot \sqrt{\sqrt{x} \cdot -1}\right)}, -1, 0\right) \]

      11. add-sqr-sqrt 1.8%

          \[\leadsto \mathsf{fma}\left(3 \cdot \color{blue}{\left(\sqrt{x} \cdot -1\right)}, -1, 0\right) \]

      12. *-commutative 1.8%

          \[\leadsto \mathsf{fma}\left(\color{blue}{\left(\sqrt{x} \cdot -1\right) \cdot 3}, -1, 0\right) \]

      13. add-sqr-sqrt 0.0%

          \[\leadsto \mathsf{fma}\left(\color{blue}{\left(\sqrt{\sqrt{x} \cdot -1} \cdot \sqrt{\sqrt{x} \cdot -1}\right)} \cdot 3, -1, 0\right) \]

      14. sqrt-unprod 56.2%

          \[\leadsto \mathsf{fma}\left(\color{blue}{\sqrt{\left(\sqrt{x} \cdot -1\right) \cdot \left(\sqrt{x} \cdot -1\right)}} \cdot 3, -1, 0\right) \]

      15. swap-sqr 56.2%

          \[\leadsto \mathsf{fma}\left(\sqrt{\color{blue}{\left(\sqrt{x} \cdot \sqrt{x}\right) \cdot \left(-1 \cdot -1\right)}} \cdot 3, -1, 0\right) \]

      16. add-sqr-sqrt 56.2%

          \[\leadsto \mathsf{fma}\left(\sqrt{\color{blue}{x} \cdot \left(-1 \cdot -1\right)} \cdot 3, -1, 0\right) \]

      17. metadata-eval 56.2%

          \[\leadsto \mathsf{fma}\left(\sqrt{x \cdot \color{blue}{1}} \cdot 3, -1, 0\right) \]

      18. metadata-eval 56.2%

          \[\leadsto \mathsf{fma}\left(\sqrt{x \cdot \color{blue}{\frac{1}{1}}} \cdot 3, -1, 0\right) \]

      19. div-inv 56.2%

          \[\leadsto \mathsf{fma}\left(\sqrt{\color{blue}{\frac{x}{1}}} \cdot 3, -1, 0\right) \]

      20. /-rgt-identity 56.2%

          \[\leadsto \mathsf{fma}\left(\sqrt{\color{blue}{x}} \cdot 3, -1, 0\right) \]

   10. Applied egg-rr 56.2%

       \[\leadsto \color{blue}{\mathsf{fma}\left(\sqrt{x} \cdot 3, -1, 0\right)} \]
   11. Step-by-step derivation

       1. fma-undefine 56.2%

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

       2. *-commutative 56.2%

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

       3. add0 56.2%

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

       4. mul-1-neg 56.2%

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

       5. distribute-rgt-neg-in 56.2%

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

       6. metadata-eval 56.2%

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

   12. Simplified 56.2%

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

4. Final simplification 63.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 7.8:\\ \;\;\;\;0.3333333333333333 \cdot \sqrt{\frac{1}{x}}\\ \mathbf{else}:\\ \;\;\;\;\sqrt{x} \cdot -3\\ \end{array} \]
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 99.3%

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

   1. associate-*l* 99.3%

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

   2. sub-neg 99.3%

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

   3. +-commutative 99.3%

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

   4. associate-+l+ 99.3%

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

   5. *-commutative 99.3%

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

   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. Taylor expanded in y around 0 65.0%

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

   1. sub-neg 65.0%

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

   2. associate-*r/ 65.1%

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

   3. metadata-eval 65.1%

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

   4. metadata-eval 65.1%

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

7. Simplified 65.1%

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

8. Taylor expanded in x around inf 27.1%

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

   1. add-sqr-sqrt 0.0%

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

   2. sqrt-unprod 3.4%

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

   3. *-commutative 3.4%

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

   4. *-commutative 3.4%

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

   5. swap-sqr 3.4%

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

   6. swap-sqr 3.4%

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

   7. add-sqr-sqrt 3.4%

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

   8. metadata-eval 3.4%

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

   9. metadata-eval 3.4%

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

   10. div-inv 3.4%

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

   11. /-rgt-identity 3.4%

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

   12. metadata-eval 3.4%

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

10. Applied egg-rr 3.4%

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

11. Final simplification 3.4%

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

Alternative 16: 25.3% 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 99.3%

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

   1. associate-*l* 99.3%

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

   2. sub-neg 99.3%

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

   3. +-commutative 99.3%

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

   4. associate-+l+ 99.3%

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

   5. *-commutative 99.3%

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

   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. Taylor expanded in y around 0 65.0%

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

   1. sub-neg 65.0%

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

   2. associate-*r/ 65.1%

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

   3. metadata-eval 65.1%

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

   4. metadata-eval 65.1%

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

7. Simplified 65.1%

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

8. Taylor expanded in x around inf 27.1%

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

   1. add0 27.1%

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

   2. associate-*r* 27.1%

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

   3. fma-define 27.1%

      \[\leadsto \color{blue}{\mathsf{fma}\left(3 \cdot \sqrt{x}, -1, 0\right)} \]

   4. /-rgt-identity 27.1%

      \[\leadsto \mathsf{fma}\left(3 \cdot \sqrt{\color{blue}{\frac{x}{1}}}, -1, 0\right) \]

   5. div-inv 27.1%

      \[\leadsto \mathsf{fma}\left(3 \cdot \sqrt{\color{blue}{x \cdot \frac{1}{1}}}, -1, 0\right) \]

   6. add-sqr-sqrt 27.1%

      \[\leadsto \mathsf{fma}\left(3 \cdot \sqrt{\color{blue}{\left(\sqrt{x} \cdot \sqrt{x}\right)} \cdot \frac{1}{1}}, -1, 0\right) \]

   7. metadata-eval 27.1%

      \[\leadsto \mathsf{fma}\left(3 \cdot \sqrt{\left(\sqrt{x} \cdot \sqrt{x}\right) \cdot \color{blue}{1}}, -1, 0\right) \]

   8. metadata-eval 27.1%

      \[\leadsto \mathsf{fma}\left(3 \cdot \sqrt{\left(\sqrt{x} \cdot \sqrt{x}\right) \cdot \color{blue}{\left(-1 \cdot -1\right)}}, -1, 0\right) \]

   9. swap-sqr 27.1%

      \[\leadsto \mathsf{fma}\left(3 \cdot \sqrt{\color{blue}{\left(\sqrt{x} \cdot -1\right) \cdot \left(\sqrt{x} \cdot -1\right)}}, -1, 0\right) \]

   10. sqrt-unprod 0.0%

       \[\leadsto \mathsf{fma}\left(3 \cdot \color{blue}{\left(\sqrt{\sqrt{x} \cdot -1} \cdot \sqrt{\sqrt{x} \cdot -1}\right)}, -1, 0\right) \]

   11. add-sqr-sqrt 3.4%

       \[\leadsto \mathsf{fma}\left(3 \cdot \color{blue}{\left(\sqrt{x} \cdot -1\right)}, -1, 0\right) \]

   12. *-commutative 3.4%

       \[\leadsto \mathsf{fma}\left(\color{blue}{\left(\sqrt{x} \cdot -1\right) \cdot 3}, -1, 0\right) \]

   13. add-sqr-sqrt 0.0%

       \[\leadsto \mathsf{fma}\left(\color{blue}{\left(\sqrt{\sqrt{x} \cdot -1} \cdot \sqrt{\sqrt{x} \cdot -1}\right)} \cdot 3, -1, 0\right) \]

   14. sqrt-unprod 27.1%

       \[\leadsto \mathsf{fma}\left(\color{blue}{\sqrt{\left(\sqrt{x} \cdot -1\right) \cdot \left(\sqrt{x} \cdot -1\right)}} \cdot 3, -1, 0\right) \]

   15. swap-sqr 27.1%

       \[\leadsto \mathsf{fma}\left(\sqrt{\color{blue}{\left(\sqrt{x} \cdot \sqrt{x}\right) \cdot \left(-1 \cdot -1\right)}} \cdot 3, -1, 0\right) \]

   16. add-sqr-sqrt 27.1%

       \[\leadsto \mathsf{fma}\left(\sqrt{\color{blue}{x} \cdot \left(-1 \cdot -1\right)} \cdot 3, -1, 0\right) \]

   17. metadata-eval 27.1%

       \[\leadsto \mathsf{fma}\left(\sqrt{x \cdot \color{blue}{1}} \cdot 3, -1, 0\right) \]

   18. metadata-eval 27.1%

       \[\leadsto \mathsf{fma}\left(\sqrt{x \cdot \color{blue}{\frac{1}{1}}} \cdot 3, -1, 0\right) \]

   19. div-inv 27.1%

       \[\leadsto \mathsf{fma}\left(\sqrt{\color{blue}{\frac{x}{1}}} \cdot 3, -1, 0\right) \]

   20. /-rgt-identity 27.1%

       \[\leadsto \mathsf{fma}\left(\sqrt{\color{blue}{x}} \cdot 3, -1, 0\right) \]

10. Applied egg-rr 27.1%

    \[\leadsto \color{blue}{\mathsf{fma}\left(\sqrt{x} \cdot 3, -1, 0\right)} \]
11. Step-by-step derivation

    1. fma-undefine 27.1%

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

    2. *-commutative 27.1%

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

    3. add0 27.1%

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

    4. mul-1-neg 27.1%

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

    5. distribute-rgt-neg-in 27.1%

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

    6. metadata-eval 27.1%

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

12. Simplified 27.1%

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

13. Final simplification 27.1%

    \[\leadsto \sqrt{x} \cdot -3 \]
14. 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 2024034 
(FPCore (x y)
  :name "Numeric.SpecFunctions:incompleteGamma from math-functions-0.1.5.2, B"
  :precision binary64

  :herbie-target
  (* 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)))