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

Percentage Accurate: 99.4% → 99.4%

Time: 8.9s

Alternatives: 12

Speedup: N/A×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 99.4% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \sqrt{x \cdot 9} \cdot \left(\left(y + \frac{0.1111111111111111}{x}\right) + -1\right) \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (* (sqrt (* x 9.0)) (+ (+ y (/ 0.1111111111111111 x)) -1.0)))

C

double code(double x, double y) {
	return sqrt((x * 9.0)) * ((y + (0.1111111111111111 / x)) + -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 + (0.1111111111111111d0 / x)) + (-1.0d0))
end function

Java

public static double code(double x, double y) {
	return Math.sqrt((x * 9.0)) * ((y + (0.1111111111111111 / x)) + -1.0);
}

Python

def code(x, y):
	return math.sqrt((x * 9.0)) * ((y + (0.1111111111111111 / x)) + -1.0)

Julia

function code(x, y)
	return Float64(sqrt(Float64(x * 9.0)) * Float64(Float64(y + Float64(0.1111111111111111 / x)) + -1.0))
end

MATLAB

function tmp = code(x, y)
	tmp = sqrt((x * 9.0)) * ((y + (0.1111111111111111 / x)) + -1.0);
end

Wolfram

code[x_, y_] := N[(N[Sqrt[N[(x * 9.0), $MachinePrecision]], $MachinePrecision] * N[(N[(y + N[(0.1111111111111111 / x), $MachinePrecision]), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 99.4%

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

   1. associate-+r+ 99.4%

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

   2. distribute-rgt-in 99.4%

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

   3. div-inv 99.3%

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

   4. div-inv 99.4%

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

   5. clear-num 99.3%

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

   6. div-inv 99.3%

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

   7. metadata-eval 99.3%

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

   8. +-commutative 99.3%

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

   9. distribute-rgt-in 99.3%

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

   10. metadata-eval 99.3%

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

   11. sub-neg 99.3%

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

   12. associate-*r* 99.4%

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

   13. associate--l+ 99.4%

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

5. Applied egg-rr 99.5%

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

   1. distribute-lft-out 99.5%

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

   2. associate-+r+ 99.5%

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

7. Simplified 99.5%

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

8. Final simplification 99.5%

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

Alternative 2: 61.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 4.5 \cdot 10^{-69}:\\ \;\;\;\;\sqrt{\frac{0.1111111111111111}{x}}\\ \mathbf{elif}\;x \leq 1.2 \cdot 10^{+39} \lor \neg \left(x \leq 1.55 \cdot 10^{+50}\right) \land x \leq 2 \cdot 10^{+170}:\\ \;\;\;\;3 \cdot \left(y \cdot \sqrt{x}\right)\\ \mathbf{else}:\\ \;\;\;\;\sqrt{x} \cdot -3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x 4.5e-69)
   (sqrt (/ 0.1111111111111111 x))
   (if (or (<= x 1.2e+39) (and (not (<= x 1.55e+50)) (<= x 2e+170)))
     (* 3.0 (* y (sqrt x)))
     (* (sqrt x) -3.0))))

C

double code(double x, double y) {
	double tmp;
	if (x <= 4.5e-69) {
		tmp = sqrt((0.1111111111111111 / x));
	} else if ((x <= 1.2e+39) || (!(x <= 1.55e+50) && (x <= 2e+170))) {
		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 <= 4.5d-69) then
        tmp = sqrt((0.1111111111111111d0 / x))
    else if ((x <= 1.2d+39) .or. (.not. (x <= 1.55d+50)) .and. (x <= 2d+170)) 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 <= 4.5e-69) {
		tmp = Math.sqrt((0.1111111111111111 / x));
	} else if ((x <= 1.2e+39) || (!(x <= 1.55e+50) && (x <= 2e+170))) {
		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 <= 4.5e-69:
		tmp = math.sqrt((0.1111111111111111 / x))
	elif (x <= 1.2e+39) or (not (x <= 1.55e+50) and (x <= 2e+170)):
		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 <= 4.5e-69)
		tmp = sqrt(Float64(0.1111111111111111 / x));
	elseif ((x <= 1.2e+39) || (!(x <= 1.55e+50) && (x <= 2e+170)))
		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 <= 4.5e-69)
		tmp = sqrt((0.1111111111111111 / x));
	elseif ((x <= 1.2e+39) || (~((x <= 1.55e+50)) && (x <= 2e+170)))
		tmp = 3.0 * (y * sqrt(x));
	else
		tmp = sqrt(x) * -3.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, 4.5e-69], N[Sqrt[N[(0.1111111111111111 / x), $MachinePrecision]], $MachinePrecision], If[Or[LessEqual[x, 1.2e+39], And[N[Not[LessEqual[x, 1.55e+50]], $MachinePrecision], LessEqual[x, 2e+170]]], 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 < 4.50000000000000009e-69

   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* 99.1%

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

      2. sub-neg 99.1%

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

      3. +-commutative 99.1%

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

      4. associate-+l+ 99.1%

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

      5. *-commutative 99.1%

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

      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. Step-by-step derivation

      1. associate-+r+ 99.3%

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

      2. distribute-rgt-in 99.3%

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

      3. div-inv 99.1%

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

      4. div-inv 99.3%

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

      5. clear-num 99.1%

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

      6. div-inv 99.1%

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

      7. metadata-eval 99.1%

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

      8. +-commutative 99.1%

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

      9. distribute-rgt-in 99.1%

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

      10. metadata-eval 99.1%

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

      11. sub-neg 99.1%

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

      12. associate-*r* 99.3%

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

      13. associate--l+ 99.3%

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

   5. Applied egg-rr 99.4%

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

      1. distribute-lft-out 99.4%

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

      2. associate-+r+ 99.4%

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

   7. Simplified 99.4%

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

   8. Taylor expanded in y around 0 79.0%

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

      1. associate-*r* 79.1%

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

      2. sub-neg 79.1%

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

      3. associate-*r/ 79.2%

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

      4. metadata-eval 79.2%

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

      5. metadata-eval 79.2%

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

      6. *-commutative 79.2%

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

      7. associate-*r* 79.1%

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

   10. Simplified 79.1%

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

   11. Taylor expanded in x around 0 79.2%

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

       1. add-sqr-sqrt 78.8%

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

       2. sqrt-unprod 79.2%

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

       3. *-commutative 79.2%

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

       4. *-commutative 79.2%

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

       5. swap-sqr 23.3%

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

       6. add-sqr-sqrt 23.3%

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

       7. frac-times 23.4%

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

       8. metadata-eval 23.4%

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

       9. pow2 23.4%

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

   13. Applied egg-rr 23.4%

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

       1. associate-*r/ 23.7%

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

       2. unpow2 23.7%

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

       3. times-frac 79.5%

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

       4. *-inverses 79.5%

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

   15. Simplified 79.5%

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

   if 4.50000000000000009e-69 < x < 1.2e39 or 1.55000000000000001e50 < x < 2.00000000000000007e170

   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. distribute-lft-out-- 99.5%

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

      2. *-rgt-identity 99.5%

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

      3. associate-*l* 99.4%

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

      4. *-commutative 99.4%

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

      5. associate-*r* 99.4%

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

      6. distribute-rgt-out-- 99.4%

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

      7. +-commutative 99.4%

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

      8. distribute-lft-in 99.4%

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

      9. associate--l+ 99.4%

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

      10. *-commutative 99.4%

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

      11. associate-/r* 99.4%

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

      12. associate-*r/ 99.4%

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

      13. metadata-eval 99.4%

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

      14. metadata-eval 99.4%

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

      15. sub-neg 99.4%

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

      16. metadata-eval 99.4%

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

      17. metadata-eval 99.4%

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

      18. metadata-eval 99.4%

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

      19. fma-def 99.4%

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

   3. Simplified 99.4%

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

   4. Taylor expanded in y around inf 63.4%

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

   if 1.2e39 < x < 1.55000000000000001e50 or 2.00000000000000007e170 < 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. distribute-lft-out-- 99.5%

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

      2. *-rgt-identity 99.5%

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

      3. associate-*l* 99.5%

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

      4. *-commutative 99.5%

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

      5. associate-*r* 99.6%

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

      6. distribute-rgt-out-- 99.6%

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

      7. +-commutative 99.6%

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

      8. distribute-lft-in 99.6%

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

      9. associate--l+ 99.6%

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

      10. *-commutative 99.6%

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

      11. associate-/r* 99.6%

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

      12. associate-*r/ 99.6%

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

      13. metadata-eval 99.6%

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

      14. metadata-eval 99.6%

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

      15. sub-neg 99.6%

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

      16. metadata-eval 99.6%

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

      17. metadata-eval 99.6%

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

      18. metadata-eval 99.6%

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

      19. fma-def 99.5%

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

   3. Simplified 99.5%

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

   4. Taylor expanded in y around 0 70.4%

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

   5. Taylor expanded in x around inf 70.4%

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

4. Final simplification 71.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 4.5 \cdot 10^{-69}:\\ \;\;\;\;\sqrt{\frac{0.1111111111111111}{x}}\\ \mathbf{elif}\;x \leq 1.2 \cdot 10^{+39} \lor \neg \left(x \leq 1.55 \cdot 10^{+50}\right) \land x \leq 2 \cdot 10^{+170}:\\ \;\;\;\;3 \cdot \left(y \cdot \sqrt{x}\right)\\ \mathbf{else}:\\ \;\;\;\;\sqrt{x} \cdot -3\\ \end{array} \]

Alternative 3: 61.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 3.1 \cdot 10^{-65}:\\ \;\;\;\;\sqrt{\frac{0.1111111111111111}{x}}\\ \mathbf{elif}\;x \leq 3.2 \cdot 10^{+38}:\\ \;\;\;\;\sqrt{x} \cdot \left(y \cdot 3\right)\\ \mathbf{elif}\;x \leq 4 \cdot 10^{+51} \lor \neg \left(x \leq 1.15 \cdot 10^{+172}\right):\\ \;\;\;\;\sqrt{x} \cdot -3\\ \mathbf{else}:\\ \;\;\;\;3 \cdot \left(y \cdot \sqrt{x}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x 3.1e-65)
   (sqrt (/ 0.1111111111111111 x))
   (if (<= x 3.2e+38)
     (* (sqrt x) (* y 3.0))
     (if (or (<= x 4e+51) (not (<= x 1.15e+172)))
       (* (sqrt x) -3.0)
       (* 3.0 (* y (sqrt x)))))))

C

double code(double x, double y) {
	double tmp;
	if (x <= 3.1e-65) {
		tmp = sqrt((0.1111111111111111 / x));
	} else if (x <= 3.2e+38) {
		tmp = sqrt(x) * (y * 3.0);
	} else if ((x <= 4e+51) || !(x <= 1.15e+172)) {
		tmp = sqrt(x) * -3.0;
	} else {
		tmp = 3.0 * (y * sqrt(x));
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (x <= 3.1d-65) then
        tmp = sqrt((0.1111111111111111d0 / x))
    else if (x <= 3.2d+38) then
        tmp = sqrt(x) * (y * 3.0d0)
    else if ((x <= 4d+51) .or. (.not. (x <= 1.15d+172))) then
        tmp = sqrt(x) * (-3.0d0)
    else
        tmp = 3.0d0 * (y * sqrt(x))
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= 3.1e-65) {
		tmp = Math.sqrt((0.1111111111111111 / x));
	} else if (x <= 3.2e+38) {
		tmp = Math.sqrt(x) * (y * 3.0);
	} else if ((x <= 4e+51) || !(x <= 1.15e+172)) {
		tmp = Math.sqrt(x) * -3.0;
	} else {
		tmp = 3.0 * (y * Math.sqrt(x));
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= 3.1e-65:
		tmp = math.sqrt((0.1111111111111111 / x))
	elif x <= 3.2e+38:
		tmp = math.sqrt(x) * (y * 3.0)
	elif (x <= 4e+51) or not (x <= 1.15e+172):
		tmp = math.sqrt(x) * -3.0
	else:
		tmp = 3.0 * (y * math.sqrt(x))
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= 3.1e-65)
		tmp = sqrt(Float64(0.1111111111111111 / x));
	elseif (x <= 3.2e+38)
		tmp = Float64(sqrt(x) * Float64(y * 3.0));
	elseif ((x <= 4e+51) || !(x <= 1.15e+172))
		tmp = Float64(sqrt(x) * -3.0);
	else
		tmp = Float64(3.0 * Float64(y * sqrt(x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= 3.1e-65)
		tmp = sqrt((0.1111111111111111 / x));
	elseif (x <= 3.2e+38)
		tmp = sqrt(x) * (y * 3.0);
	elseif ((x <= 4e+51) || ~((x <= 1.15e+172)))
		tmp = sqrt(x) * -3.0;
	else
		tmp = 3.0 * (y * sqrt(x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, 3.1e-65], N[Sqrt[N[(0.1111111111111111 / x), $MachinePrecision]], $MachinePrecision], If[LessEqual[x, 3.2e+38], N[(N[Sqrt[x], $MachinePrecision] * N[(y * 3.0), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[x, 4e+51], N[Not[LessEqual[x, 1.15e+172]], $MachinePrecision]], N[(N[Sqrt[x], $MachinePrecision] * -3.0), $MachinePrecision], N[(3.0 * N[(y * N[Sqrt[x], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if x < 3.10000000000000016e-65

   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* 99.1%

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

      2. sub-neg 99.1%

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

      3. +-commutative 99.1%

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

      4. associate-+l+ 99.1%

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

      5. *-commutative 99.1%

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

      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. Step-by-step derivation

      1. associate-+r+ 99.3%

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

      2. distribute-rgt-in 99.3%

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

      3. div-inv 99.2%

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

      4. div-inv 99.3%

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

      5. clear-num 99.1%

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

      6. div-inv 99.1%

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

      7. metadata-eval 99.1%

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

      8. +-commutative 99.1%

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

      9. distribute-rgt-in 99.1%

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

      10. metadata-eval 99.1%

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

      11. sub-neg 99.1%

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

      12. associate-*r* 99.3%

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

      13. associate--l+ 99.3%

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

   5. Applied egg-rr 99.4%

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

      1. distribute-lft-out 99.4%

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

      2. associate-+r+ 99.4%

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

   7. Simplified 99.4%

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

   8. Taylor expanded in y around 0 78.5%

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

      1. associate-*r* 78.5%

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

      2. sub-neg 78.5%

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

      3. associate-*r/ 78.6%

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

      4. metadata-eval 78.6%

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

      5. metadata-eval 78.6%

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

      6. *-commutative 78.6%

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

      7. associate-*r* 78.5%

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

   10. Simplified 78.5%

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

   11. Taylor expanded in x around 0 78.6%

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

       1. add-sqr-sqrt 78.3%

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

       2. sqrt-unprod 78.6%

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

       3. *-commutative 78.6%

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

       4. *-commutative 78.6%

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

       5. swap-sqr 23.9%

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

       6. add-sqr-sqrt 23.9%

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

       7. frac-times 24.0%

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

       8. metadata-eval 24.0%

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

       9. pow2 24.0%

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

   13. Applied egg-rr 24.0%

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

       1. associate-*r/ 24.2%

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

       2. unpow2 24.2%

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

       3. times-frac 78.9%

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

       4. *-inverses 78.9%

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

   15. Simplified 78.9%

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

   if 3.10000000000000016e-65 < x < 3.19999999999999985e38

   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. distribute-lft-out-- 99.4%

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

      2. *-rgt-identity 99.4%

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

      3. associate-*l* 99.3%

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

      4. *-commutative 99.3%

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

      5. associate-*r* 99.4%

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

      6. distribute-rgt-out-- 99.4%

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

      7. +-commutative 99.4%

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

      8. distribute-lft-in 99.4%

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

      9. associate--l+ 99.4%

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

      10. *-commutative 99.4%

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

      11. associate-/r* 99.4%

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

      12. associate-*r/ 99.3%

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

      13. metadata-eval 99.3%

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

      14. metadata-eval 99.3%

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

      15. sub-neg 99.3%

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

      16. metadata-eval 99.3%

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

      17. metadata-eval 99.3%

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

      18. metadata-eval 99.3%

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

      19. fma-def 99.4%

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

   3. Simplified 99.4%

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

   4. Taylor expanded in y around inf 64.3%

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

   if 3.19999999999999985e38 < x < 4e51 or 1.15e172 < 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. distribute-lft-out-- 99.5%

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

      2. *-rgt-identity 99.5%

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

      3. associate-*l* 99.5%

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

      4. *-commutative 99.5%

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

      5. associate-*r* 99.6%

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

      6. distribute-rgt-out-- 99.6%

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

      7. +-commutative 99.6%

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

      8. distribute-lft-in 99.6%

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

      9. associate--l+ 99.6%

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

      10. *-commutative 99.6%

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

      11. associate-/r* 99.6%

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

      12. associate-*r/ 99.6%

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

      13. metadata-eval 99.6%

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

      14. metadata-eval 99.6%

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

      15. sub-neg 99.6%

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

      16. metadata-eval 99.6%

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

      17. metadata-eval 99.6%

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

      18. metadata-eval 99.6%

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

      19. fma-def 99.5%

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

   3. Simplified 99.5%

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

   4. Taylor expanded in y around 0 70.4%

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

   5. Taylor expanded in x around inf 70.4%

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

   if 4e51 < x < 1.15e172

   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. distribute-lft-out-- 99.5%

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

      2. *-rgt-identity 99.5%

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

      3. associate-*l* 99.5%

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

      4. *-commutative 99.5%

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

      5. associate-*r* 99.5%

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

      6. distribute-rgt-out-- 99.5%

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

      7. +-commutative 99.5%

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

      8. distribute-lft-in 99.5%

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

      9. associate--l+ 99.5%

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

      10. *-commutative 99.5%

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

      11. associate-/r* 99.5%

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

      12. associate-*r/ 99.5%

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

      13. metadata-eval 99.5%

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

      14. metadata-eval 99.5%

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

      15. sub-neg 99.5%

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

      16. metadata-eval 99.5%

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

      17. metadata-eval 99.5%

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

      18. metadata-eval 99.5%

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

      19. fma-def 99.5%

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

   3. Simplified 99.5%

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

   4. Taylor expanded in y around inf 63.2%

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

4. Final simplification 71.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 3.1 \cdot 10^{-65}:\\ \;\;\;\;\sqrt{\frac{0.1111111111111111}{x}}\\ \mathbf{elif}\;x \leq 3.2 \cdot 10^{+38}:\\ \;\;\;\;\sqrt{x} \cdot \left(y \cdot 3\right)\\ \mathbf{elif}\;x \leq 4 \cdot 10^{+51} \lor \neg \left(x \leq 1.15 \cdot 10^{+172}\right):\\ \;\;\;\;\sqrt{x} \cdot -3\\ \mathbf{else}:\\ \;\;\;\;3 \cdot \left(y \cdot \sqrt{x}\right)\\ \end{array} \]

Alternative 4: 61.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 2.5 \cdot 10^{-65}:\\ \;\;\;\;\sqrt{\frac{0.1111111111111111}{x}}\\ \mathbf{elif}\;x \leq 1.05 \cdot 10^{+40}:\\ \;\;\;\;\sqrt{x} \cdot \left(y \cdot 3\right)\\ \mathbf{elif}\;x \leq 8.2 \cdot 10^{+50}:\\ \;\;\;\;\sqrt{x} \cdot -3\\ \mathbf{elif}\;x \leq 6.5 \cdot 10^{+173}:\\ \;\;\;\;3 \cdot \left(y \cdot \sqrt{x}\right)\\ \mathbf{else}:\\ \;\;\;\;-\sqrt{x \cdot 9}\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x 2.5e-65)
   (sqrt (/ 0.1111111111111111 x))
   (if (<= x 1.05e+40)
     (* (sqrt x) (* y 3.0))
     (if (<= x 8.2e+50)
       (* (sqrt x) -3.0)
       (if (<= x 6.5e+173) (* 3.0 (* y (sqrt x))) (- (sqrt (* x 9.0))))))))

C

double code(double x, double y) {
	double tmp;
	if (x <= 2.5e-65) {
		tmp = sqrt((0.1111111111111111 / x));
	} else if (x <= 1.05e+40) {
		tmp = sqrt(x) * (y * 3.0);
	} else if (x <= 8.2e+50) {
		tmp = sqrt(x) * -3.0;
	} else if (x <= 6.5e+173) {
		tmp = 3.0 * (y * sqrt(x));
	} else {
		tmp = -sqrt((x * 9.0));
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (x <= 2.5d-65) then
        tmp = sqrt((0.1111111111111111d0 / x))
    else if (x <= 1.05d+40) then
        tmp = sqrt(x) * (y * 3.0d0)
    else if (x <= 8.2d+50) then
        tmp = sqrt(x) * (-3.0d0)
    else if (x <= 6.5d+173) then
        tmp = 3.0d0 * (y * sqrt(x))
    else
        tmp = -sqrt((x * 9.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= 2.5e-65) {
		tmp = Math.sqrt((0.1111111111111111 / x));
	} else if (x <= 1.05e+40) {
		tmp = Math.sqrt(x) * (y * 3.0);
	} else if (x <= 8.2e+50) {
		tmp = Math.sqrt(x) * -3.0;
	} else if (x <= 6.5e+173) {
		tmp = 3.0 * (y * Math.sqrt(x));
	} else {
		tmp = -Math.sqrt((x * 9.0));
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= 2.5e-65:
		tmp = math.sqrt((0.1111111111111111 / x))
	elif x <= 1.05e+40:
		tmp = math.sqrt(x) * (y * 3.0)
	elif x <= 8.2e+50:
		tmp = math.sqrt(x) * -3.0
	elif x <= 6.5e+173:
		tmp = 3.0 * (y * math.sqrt(x))
	else:
		tmp = -math.sqrt((x * 9.0))
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= 2.5e-65)
		tmp = sqrt(Float64(0.1111111111111111 / x));
	elseif (x <= 1.05e+40)
		tmp = Float64(sqrt(x) * Float64(y * 3.0));
	elseif (x <= 8.2e+50)
		tmp = Float64(sqrt(x) * -3.0);
	elseif (x <= 6.5e+173)
		tmp = Float64(3.0 * Float64(y * sqrt(x)));
	else
		tmp = Float64(-sqrt(Float64(x * 9.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= 2.5e-65)
		tmp = sqrt((0.1111111111111111 / x));
	elseif (x <= 1.05e+40)
		tmp = sqrt(x) * (y * 3.0);
	elseif (x <= 8.2e+50)
		tmp = sqrt(x) * -3.0;
	elseif (x <= 6.5e+173)
		tmp = 3.0 * (y * sqrt(x));
	else
		tmp = -sqrt((x * 9.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, 2.5e-65], N[Sqrt[N[(0.1111111111111111 / x), $MachinePrecision]], $MachinePrecision], If[LessEqual[x, 1.05e+40], N[(N[Sqrt[x], $MachinePrecision] * N[(y * 3.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 8.2e+50], N[(N[Sqrt[x], $MachinePrecision] * -3.0), $MachinePrecision], If[LessEqual[x, 6.5e+173], N[(3.0 * N[(y * N[Sqrt[x], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], (-N[Sqrt[N[(x * 9.0), $MachinePrecision]], $MachinePrecision])]]]]

Derivation

1. Split input into 5 regimes

2. if x < 2.49999999999999991e-65

   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* 99.1%

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

      2. sub-neg 99.1%

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

      3. +-commutative 99.1%

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

      4. associate-+l+ 99.1%

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

      5. *-commutative 99.1%

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

      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. Step-by-step derivation

      1. associate-+r+ 99.3%

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

      2. distribute-rgt-in 99.3%

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

      3. div-inv 99.2%

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

      4. div-inv 99.3%

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

      5. clear-num 99.1%

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

      6. div-inv 99.1%

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

      7. metadata-eval 99.1%

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

      8. +-commutative 99.1%

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

      9. distribute-rgt-in 99.1%

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

      10. metadata-eval 99.1%

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

      11. sub-neg 99.1%

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

      12. associate-*r* 99.3%

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

      13. associate--l+ 99.3%

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

   5. Applied egg-rr 99.4%

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

      1. distribute-lft-out 99.4%

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

      2. associate-+r+ 99.4%

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

   7. Simplified 99.4%

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

   8. Taylor expanded in y around 0 78.5%

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

      1. associate-*r* 78.5%

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

      2. sub-neg 78.5%

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

      3. associate-*r/ 78.6%

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

      4. metadata-eval 78.6%

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

      5. metadata-eval 78.6%

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

      6. *-commutative 78.6%

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

      7. associate-*r* 78.5%

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

   10. Simplified 78.5%

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

   11. Taylor expanded in x around 0 78.6%

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

       1. add-sqr-sqrt 78.3%

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

       2. sqrt-unprod 78.6%

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

       3. *-commutative 78.6%

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

       4. *-commutative 78.6%

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

       5. swap-sqr 23.9%

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

       6. add-sqr-sqrt 23.9%

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

       7. frac-times 24.0%

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

       8. metadata-eval 24.0%

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

       9. pow2 24.0%

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

   13. Applied egg-rr 24.0%

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

       1. associate-*r/ 24.2%

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

       2. unpow2 24.2%

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

       3. times-frac 78.9%

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

       4. *-inverses 78.9%

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

   15. Simplified 78.9%

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

   if 2.49999999999999991e-65 < x < 1.05000000000000005e40

   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. distribute-lft-out-- 99.4%

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

      2. *-rgt-identity 99.4%

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

      3. associate-*l* 99.3%

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

      4. *-commutative 99.3%

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

      5. associate-*r* 99.4%

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

      6. distribute-rgt-out-- 99.4%

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

      7. +-commutative 99.4%

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

      8. distribute-lft-in 99.4%

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

      9. associate--l+ 99.4%

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

      10. *-commutative 99.4%

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

      11. associate-/r* 99.4%

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

      12. associate-*r/ 99.3%

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

      13. metadata-eval 99.3%

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

      14. metadata-eval 99.3%

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

      15. sub-neg 99.3%

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

      16. metadata-eval 99.3%

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

      17. metadata-eval 99.3%

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

      18. metadata-eval 99.3%

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

      19. fma-def 99.4%

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

   3. Simplified 99.4%

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

   4. Taylor expanded in y around inf 64.3%

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

   if 1.05000000000000005e40 < x < 8.2000000000000002e50

   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. distribute-lft-out-- 99.4%

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

      2. *-rgt-identity 99.4%

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

      3. associate-*l* 99.4%

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

      4. *-commutative 99.4%

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

      5. associate-*r* 99.4%

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

      6. distribute-rgt-out-- 99.4%

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

      7. +-commutative 99.4%

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

      8. distribute-lft-in 99.4%

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

      9. associate--l+ 99.4%

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

      10. *-commutative 99.4%

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

      11. associate-/r* 99.4%

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

      12. associate-*r/ 99.4%

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

      13. metadata-eval 99.4%

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

      14. metadata-eval 99.4%

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

      15. sub-neg 99.4%

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

      16. metadata-eval 99.4%

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

      17. metadata-eval 99.4%

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

      18. metadata-eval 99.4%

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

      19. fma-def 99.4%

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

   3. Simplified 99.4%

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

   4. Taylor expanded in y around 0 99.4%

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

   5. Taylor expanded in x around inf 99.4%

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

   if 8.2000000000000002e50 < x < 6.4999999999999997e173

   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. distribute-lft-out-- 99.5%

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

      2. *-rgt-identity 99.5%

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

      3. associate-*l* 99.5%

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

      4. *-commutative 99.5%

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

      5. associate-*r* 99.5%

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

      6. distribute-rgt-out-- 99.5%

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

      7. +-commutative 99.5%

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

      8. distribute-lft-in 99.5%

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

      9. associate--l+ 99.5%

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

      10. *-commutative 99.5%

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

      11. associate-/r* 99.5%

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

      12. associate-*r/ 99.5%

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

      13. metadata-eval 99.5%

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

      14. metadata-eval 99.5%

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

      15. sub-neg 99.5%

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

      16. metadata-eval 99.5%

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

      17. metadata-eval 99.5%

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

      18. metadata-eval 99.5%

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

      19. fma-def 99.5%

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

   3. Simplified 99.5%

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

   4. Taylor expanded in y around inf 63.2%

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

   if 6.4999999999999997e173 < 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* 99.5%

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

      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. Step-by-step derivation

      1. associate-+r+ 99.5%

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

      2. distribute-rgt-in 99.5%

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

      3. div-inv 99.5%

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

      4. div-inv 99.5%

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

      5. clear-num 99.5%

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

      6. div-inv 99.5%

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

      7. metadata-eval 99.5%

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

      8. +-commutative 99.5%

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

      9. distribute-rgt-in 99.5%

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

      10. metadata-eval 99.5%

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

      11. sub-neg 99.5%

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

      12. associate-*r* 99.5%

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

      13. associate--l+ 99.5%

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

   5. Applied egg-rr 99.7%

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

      1. distribute-lft-out 99.7%

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

      2. associate-+r+ 99.7%

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

   7. Simplified 99.7%

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

   8. Taylor expanded in y around 0 68.3%

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

   9. Taylor expanded in x around inf 68.3%

      \[\leadsto \sqrt{x \cdot 9} \cdot \color{blue}{-1} \]
3. Recombined 5 regimes into one program.

4. Final simplification 71.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 2.5 \cdot 10^{-65}:\\ \;\;\;\;\sqrt{\frac{0.1111111111111111}{x}}\\ \mathbf{elif}\;x \leq 1.05 \cdot 10^{+40}:\\ \;\;\;\;\sqrt{x} \cdot \left(y \cdot 3\right)\\ \mathbf{elif}\;x \leq 8.2 \cdot 10^{+50}:\\ \;\;\;\;\sqrt{x} \cdot -3\\ \mathbf{elif}\;x \leq 6.5 \cdot 10^{+173}:\\ \;\;\;\;3 \cdot \left(y \cdot \sqrt{x}\right)\\ \mathbf{else}:\\ \;\;\;\;-\sqrt{x \cdot 9}\\ \end{array} \]

Alternative 5: 99.4% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.4%

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

   1. associate-*l* 99.3%

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

   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. Final simplification 99.4%

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

Alternative 6: 85.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 4.5 \cdot 10^{-66}:\\ \;\;\;\;\sqrt{\frac{0.1111111111111111}{x}}\\ \mathbf{else}:\\ \;\;\;\;3 \cdot \left(\sqrt{x} \cdot \left(y + -1\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x 4.5e-66)
   (sqrt (/ 0.1111111111111111 x))
   (* 3.0 (* (sqrt x) (+ y -1.0)))))

C

double code(double x, double y) {
	double tmp;
	if (x <= 4.5e-66) {
		tmp = sqrt((0.1111111111111111 / x));
	} else {
		tmp = 3.0 * (sqrt(x) * (y + -1.0));
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (x <= 4.5d-66) then
        tmp = sqrt((0.1111111111111111d0 / x))
    else
        tmp = 3.0d0 * (sqrt(x) * (y + (-1.0d0)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= 4.5e-66) {
		tmp = Math.sqrt((0.1111111111111111 / x));
	} else {
		tmp = 3.0 * (Math.sqrt(x) * (y + -1.0));
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= 4.5e-66:
		tmp = math.sqrt((0.1111111111111111 / x))
	else:
		tmp = 3.0 * (math.sqrt(x) * (y + -1.0))
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= 4.5e-66)
		tmp = sqrt(Float64(0.1111111111111111 / x));
	else
		tmp = Float64(3.0 * Float64(sqrt(x) * Float64(y + -1.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= 4.5e-66)
		tmp = sqrt((0.1111111111111111 / x));
	else
		tmp = 3.0 * (sqrt(x) * (y + -1.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, 4.5e-66], N[Sqrt[N[(0.1111111111111111 / x), $MachinePrecision]], $MachinePrecision], N[(3.0 * N[(N[Sqrt[x], $MachinePrecision] * N[(y + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < 4.4999999999999998e-66

   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* 99.1%

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

      2. sub-neg 99.1%

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

      3. +-commutative 99.1%

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

      4. associate-+l+ 99.1%

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

      5. *-commutative 99.1%

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

      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. Step-by-step derivation

      1. associate-+r+ 99.3%

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

      2. distribute-rgt-in 99.3%

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

      3. div-inv 99.2%

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

      4. div-inv 99.3%

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

      5. clear-num 99.1%

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

      6. div-inv 99.1%

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

      7. metadata-eval 99.1%

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

      8. +-commutative 99.1%

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

      9. distribute-rgt-in 99.1%

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

      10. metadata-eval 99.1%

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

      11. sub-neg 99.1%

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

      12. associate-*r* 99.3%

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

      13. associate--l+ 99.3%

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

   5. Applied egg-rr 99.4%

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

      1. distribute-lft-out 99.4%

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

      2. associate-+r+ 99.4%

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

   7. Simplified 99.4%

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

   8. Taylor expanded in y around 0 78.5%

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

      1. associate-*r* 78.5%

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

      2. sub-neg 78.5%

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

      3. associate-*r/ 78.6%

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

      4. metadata-eval 78.6%

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

      5. metadata-eval 78.6%

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

      6. *-commutative 78.6%

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

      7. associate-*r* 78.5%

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

   10. Simplified 78.5%

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

   11. Taylor expanded in x around 0 78.6%

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

       1. add-sqr-sqrt 78.3%

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

       2. sqrt-unprod 78.6%

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

       3. *-commutative 78.6%

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

       4. *-commutative 78.6%

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

       5. swap-sqr 23.9%

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

       6. add-sqr-sqrt 23.9%

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

       7. frac-times 24.0%

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

       8. metadata-eval 24.0%

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

       9. pow2 24.0%

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

   13. Applied egg-rr 24.0%

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

       1. associate-*r/ 24.2%

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

       2. unpow2 24.2%

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

       3. times-frac 78.9%

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

       4. *-inverses 78.9%

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

   15. Simplified 78.9%

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

   if 4.4999999999999998e-66 < 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* 99.5%

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

      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. Taylor expanded in x around inf 94.2%

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

4. Final simplification 88.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 4.5 \cdot 10^{-66}:\\ \;\;\;\;\sqrt{\frac{0.1111111111111111}{x}}\\ \mathbf{else}:\\ \;\;\;\;3 \cdot \left(\sqrt{x} \cdot \left(y + -1\right)\right)\\ \end{array} \]

Alternative 7: 85.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 4.2 \cdot 10^{-65}:\\ \;\;\;\;\sqrt{\frac{0.1111111111111111}{x}}\\ \mathbf{else}:\\ \;\;\;\;\sqrt{x} \cdot \left(y \cdot 3 - 3\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x 4.2e-65)
   (sqrt (/ 0.1111111111111111 x))
   (* (sqrt x) (- (* y 3.0) 3.0))))

C

double code(double x, double y) {
	double tmp;
	if (x <= 4.2e-65) {
		tmp = sqrt((0.1111111111111111 / x));
	} else {
		tmp = sqrt(x) * ((y * 3.0) - 3.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (x <= 4.2d-65) then
        tmp = sqrt((0.1111111111111111d0 / x))
    else
        tmp = sqrt(x) * ((y * 3.0d0) - 3.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= 4.2e-65) {
		tmp = Math.sqrt((0.1111111111111111 / x));
	} else {
		tmp = Math.sqrt(x) * ((y * 3.0) - 3.0);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= 4.2e-65:
		tmp = math.sqrt((0.1111111111111111 / x))
	else:
		tmp = math.sqrt(x) * ((y * 3.0) - 3.0)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= 4.2e-65)
		tmp = sqrt(Float64(0.1111111111111111 / x));
	else
		tmp = Float64(sqrt(x) * Float64(Float64(y * 3.0) - 3.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= 4.2e-65)
		tmp = sqrt((0.1111111111111111 / x));
	else
		tmp = sqrt(x) * ((y * 3.0) - 3.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, 4.2e-65], N[Sqrt[N[(0.1111111111111111 / x), $MachinePrecision]], $MachinePrecision], N[(N[Sqrt[x], $MachinePrecision] * N[(N[(y * 3.0), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < 4.20000000000000006e-65

   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* 99.1%

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

      2. sub-neg 99.1%

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

      3. +-commutative 99.1%

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

      4. associate-+l+ 99.1%

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

      5. *-commutative 99.1%

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

      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. Step-by-step derivation

      1. associate-+r+ 99.3%

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

      2. distribute-rgt-in 99.3%

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

      3. div-inv 99.2%

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

      4. div-inv 99.3%

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

      5. clear-num 99.1%

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

      6. div-inv 99.1%

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

      7. metadata-eval 99.1%

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

      8. +-commutative 99.1%

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

      9. distribute-rgt-in 99.1%

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

      10. metadata-eval 99.1%

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

      11. sub-neg 99.1%

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

      12. associate-*r* 99.3%

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

      13. associate--l+ 99.3%

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

   5. Applied egg-rr 99.4%

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

      1. distribute-lft-out 99.4%

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

      2. associate-+r+ 99.4%

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

   7. Simplified 99.4%

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

   8. Taylor expanded in y around 0 78.5%

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

      1. associate-*r* 78.5%

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

      2. sub-neg 78.5%

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

      3. associate-*r/ 78.6%

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

      4. metadata-eval 78.6%

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

      5. metadata-eval 78.6%

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

      6. *-commutative 78.6%

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

      7. associate-*r* 78.5%

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

   10. Simplified 78.5%

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

   11. Taylor expanded in x around 0 78.6%

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

       1. add-sqr-sqrt 78.3%

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

       2. sqrt-unprod 78.6%

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

       3. *-commutative 78.6%

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

       4. *-commutative 78.6%

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

       5. swap-sqr 23.9%

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

       6. add-sqr-sqrt 23.9%

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

       7. frac-times 24.0%

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

       8. metadata-eval 24.0%

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

       9. pow2 24.0%

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

   13. Applied egg-rr 24.0%

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

       1. associate-*r/ 24.2%

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

       2. unpow2 24.2%

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

       3. times-frac 78.9%

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

       4. *-inverses 78.9%

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

   15. Simplified 78.9%

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

   if 4.20000000000000006e-65 < 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. distribute-lft-out-- 99.5%

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

      2. *-rgt-identity 99.5%

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

      3. associate-*l* 99.5%

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

      4. *-commutative 99.5%

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

      5. associate-*r* 99.5%

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

      6. distribute-rgt-out-- 99.5%

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

      7. +-commutative 99.5%

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

      8. distribute-lft-in 99.5%

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

      9. associate--l+ 99.5%

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

      10. *-commutative 99.5%

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

      11. associate-/r* 99.5%

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

      12. associate-*r/ 99.5%

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

      13. metadata-eval 99.5%

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

      14. metadata-eval 99.5%

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

      15. sub-neg 99.5%

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

      16. metadata-eval 99.5%

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

      17. metadata-eval 99.5%

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

      18. metadata-eval 99.5%

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

      19. fma-def 99.5%

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

   3. Simplified 99.5%

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

   4. Taylor expanded in x around inf 94.2%

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

4. Final simplification 88.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 4.2 \cdot 10^{-65}:\\ \;\;\;\;\sqrt{\frac{0.1111111111111111}{x}}\\ \mathbf{else}:\\ \;\;\;\;\sqrt{x} \cdot \left(y \cdot 3 - 3\right)\\ \end{array} \]

Alternative 8: 85.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 4.4 \cdot 10^{-66}:\\ \;\;\;\;\sqrt{\frac{0.1111111111111111}{x}}\\ \mathbf{else}:\\ \;\;\;\;\sqrt{x \cdot 9} \cdot \left(y + -1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x 4.4e-66)
   (sqrt (/ 0.1111111111111111 x))
   (* (sqrt (* x 9.0)) (+ y -1.0))))

C

double code(double x, double y) {
	double tmp;
	if (x <= 4.4e-66) {
		tmp = sqrt((0.1111111111111111 / x));
	} 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 <= 4.4d-66) then
        tmp = sqrt((0.1111111111111111d0 / x))
    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 <= 4.4e-66) {
		tmp = Math.sqrt((0.1111111111111111 / x));
	} else {
		tmp = Math.sqrt((x * 9.0)) * (y + -1.0);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= 4.4e-66:
		tmp = math.sqrt((0.1111111111111111 / x))
	else:
		tmp = math.sqrt((x * 9.0)) * (y + -1.0)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= 4.4e-66)
		tmp = sqrt(Float64(0.1111111111111111 / x));
	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 <= 4.4e-66)
		tmp = sqrt((0.1111111111111111 / x));
	else
		tmp = sqrt((x * 9.0)) * (y + -1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, 4.4e-66], N[Sqrt[N[(0.1111111111111111 / x), $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 < 4.4000000000000002e-66

   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* 99.1%

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

      2. sub-neg 99.1%

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

      3. +-commutative 99.1%

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

      4. associate-+l+ 99.1%

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

      5. *-commutative 99.1%

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

      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. Step-by-step derivation

      1. associate-+r+ 99.3%

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

      2. distribute-rgt-in 99.3%

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

      3. div-inv 99.2%

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

      4. div-inv 99.3%

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

      5. clear-num 99.1%

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

      6. div-inv 99.1%

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

      7. metadata-eval 99.1%

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

      8. +-commutative 99.1%

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

      9. distribute-rgt-in 99.1%

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

      10. metadata-eval 99.1%

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

      11. sub-neg 99.1%

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

      12. associate-*r* 99.3%

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

      13. associate--l+ 99.3%

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

   5. Applied egg-rr 99.4%

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

      1. distribute-lft-out 99.4%

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

      2. associate-+r+ 99.4%

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

   7. Simplified 99.4%

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

   8. Taylor expanded in y around 0 78.5%

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

      1. associate-*r* 78.5%

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

      2. sub-neg 78.5%

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

      3. associate-*r/ 78.6%

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

      4. metadata-eval 78.6%

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

      5. metadata-eval 78.6%

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

      6. *-commutative 78.6%

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

      7. associate-*r* 78.5%

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

   10. Simplified 78.5%

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

   11. Taylor expanded in x around 0 78.6%

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

       1. add-sqr-sqrt 78.3%

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

       2. sqrt-unprod 78.6%

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

       3. *-commutative 78.6%

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

       4. *-commutative 78.6%

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

       5. swap-sqr 23.9%

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

       6. add-sqr-sqrt 23.9%

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

       7. frac-times 24.0%

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

       8. metadata-eval 24.0%

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

       9. pow2 24.0%

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

   13. Applied egg-rr 24.0%

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

       1. associate-*r/ 24.2%

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

       2. unpow2 24.2%

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

       3. times-frac 78.9%

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

       4. *-inverses 78.9%

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

   15. Simplified 78.9%

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

   if 4.4000000000000002e-66 < 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* 99.5%

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

      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. Step-by-step derivation

      1. associate-+r+ 99.5%

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

      2. distribute-rgt-in 99.5%

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

      3. div-inv 99.4%

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

      4. div-inv 99.5%

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

      5. clear-num 99.5%

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

      6. div-inv 99.5%

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

      7. metadata-eval 99.5%

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

      8. +-commutative 99.5%

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

      9. distribute-rgt-in 99.5%

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

      10. metadata-eval 99.5%

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

      11. sub-neg 99.5%

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

      12. associate-*r* 99.5%

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

      13. associate--l+ 99.5%

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

   5. Applied egg-rr 99.6%

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

      1. distribute-lft-out 99.6%

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

      2. associate-+r+ 99.6%

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

   7. Simplified 99.6%

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

   8. Taylor expanded in y around inf 94.3%

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

4. Final simplification 88.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 4.4 \cdot 10^{-66}:\\ \;\;\;\;\sqrt{\frac{0.1111111111111111}{x}}\\ \mathbf{else}:\\ \;\;\;\;\sqrt{x \cdot 9} \cdot \left(y + -1\right)\\ \end{array} \]

Alternative 9: 60.9% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 0.11:\\ \;\;\;\;\frac{0.3333333333333333}{\sqrt{x}}\\ \mathbf{else}:\\ \;\;\;\;\sqrt{x} \cdot -3\\ \end{array} \end{array} \]

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Split input into 2 regimes

2. if x < 0.110000000000000001

   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* 99.2%

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

      2. sub-neg 99.2%

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

      3. +-commutative 99.2%

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

      4. associate-+l+ 99.2%

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

      5. *-commutative 99.2%

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

      6. associate-/r* 99.2%

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

      7. metadata-eval 99.2%

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

      8. metadata-eval 99.2%

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

   3. Simplified 99.2%

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

      1. associate-+r+ 99.2%

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

      2. distribute-rgt-in 99.3%

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

      3. div-inv 99.2%

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

      4. div-inv 99.3%

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

      5. clear-num 99.2%

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

      6. div-inv 99.2%

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

      7. metadata-eval 99.2%

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

      8. +-commutative 99.2%

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

      9. distribute-rgt-in 99.2%

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

      10. metadata-eval 99.2%

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

      11. sub-neg 99.2%

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

      12. associate-*r* 99.4%

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

      13. associate--l+ 99.4%

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

   5. Applied egg-rr 99.4%

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

      1. distribute-lft-out 99.4%

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

      2. associate-+r+ 99.4%

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

   7. Simplified 99.4%

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

   8. Taylor expanded in y around 0 70.8%

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

      1. associate-*r* 70.9%

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

      2. sub-neg 70.9%

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

      3. associate-*r/ 71.0%

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

      4. metadata-eval 71.0%

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

      5. metadata-eval 71.0%

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

      6. *-commutative 71.0%

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

      7. associate-*r* 70.9%

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

   10. Simplified 70.9%

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

   11. Taylor expanded in x around 0 70.3%

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

       1. expm1-log1p-u 65.5%

          \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{0.3333333333333333}{x} \cdot \sqrt{x}\right)\right)} \]

       2. expm1-udef 65.5%

          \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(\frac{0.3333333333333333}{x} \cdot \sqrt{x}\right)} - 1} \]

       3. *-commutative 65.5%

          \[\leadsto e^{\mathsf{log1p}\left(\color{blue}{\sqrt{x} \cdot \frac{0.3333333333333333}{x}}\right)} - 1 \]

   13. Applied egg-rr 65.5%

       \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(\sqrt{x} \cdot \frac{0.3333333333333333}{x}\right)} - 1} \]
   14. Step-by-step derivation

       1. expm1-def 65.5%

          \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\sqrt{x} \cdot \frac{0.3333333333333333}{x}\right)\right)} \]

       2. expm1-log1p 70.3%

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

       3. associate-*r/ 70.2%

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

       4. rem-square-sqrt 70.2%

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

       5. associate-/l/ 70.4%

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

       6. associate-/l* 70.4%

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

       7. associate-/r/ 70.4%

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

       8. *-inverses 70.4%

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

       9. metadata-eval 70.4%

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

   15. Simplified 70.4%

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

   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. Step-by-step derivation

      1. distribute-lft-out-- 99.5%

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

      2. *-rgt-identity 99.5%

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

      3. associate-*l* 99.5%

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

      4. *-commutative 99.5%

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

      5. associate-*r* 99.5%

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

      6. distribute-rgt-out-- 99.5%

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

      7. +-commutative 99.5%

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

      8. distribute-lft-in 99.5%

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

      9. associate--l+ 99.5%

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

      10. *-commutative 99.5%

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

      11. associate-/r* 99.5%

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

      12. associate-*r/ 99.5%

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

      13. metadata-eval 99.5%

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

      14. metadata-eval 99.5%

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

      15. sub-neg 99.5%

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

      16. metadata-eval 99.5%

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

      17. metadata-eval 99.5%

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

      18. metadata-eval 99.5%

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

      19. fma-def 99.5%

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

   3. Simplified 99.5%

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

   4. Taylor expanded in y around 0 55.0%

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

   5. Taylor expanded in x around inf 53.6%

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

4. Final simplification 61.5%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 0.11:\\ \;\;\;\;\frac{0.3333333333333333}{\sqrt{x}}\\ \mathbf{else}:\\ \;\;\;\;\sqrt{x} \cdot -3\\ \end{array} \]

Alternative 10: 61.1% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 0.11:\\ \;\;\;\;\sqrt{\frac{0.1111111111111111}{x}}\\ \mathbf{else}:\\ \;\;\;\;\sqrt{x} \cdot -3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x 0.11) (sqrt (/ 0.1111111111111111 x)) (* (sqrt x) -3.0)))

C

double code(double x, double y) {
	double tmp;
	if (x <= 0.11) {
		tmp = sqrt((0.1111111111111111 / x));
	} else {
		tmp = sqrt(x) * -3.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (x <= 0.11d0) then
        tmp = sqrt((0.1111111111111111d0 / x))
    else
        tmp = sqrt(x) * (-3.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= 0.11) {
		tmp = Math.sqrt((0.1111111111111111 / x));
	} else {
		tmp = Math.sqrt(x) * -3.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= 0.11:
		tmp = math.sqrt((0.1111111111111111 / x))
	else:
		tmp = math.sqrt(x) * -3.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= 0.11)
		tmp = sqrt(Float64(0.1111111111111111 / x));
	else
		tmp = Float64(sqrt(x) * -3.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= 0.11)
		tmp = sqrt((0.1111111111111111 / x));
	else
		tmp = sqrt(x) * -3.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, 0.11], N[Sqrt[N[(0.1111111111111111 / x), $MachinePrecision]], $MachinePrecision], N[(N[Sqrt[x], $MachinePrecision] * -3.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < 0.110000000000000001

   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* 99.2%

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

      2. sub-neg 99.2%

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

      3. +-commutative 99.2%

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

      4. associate-+l+ 99.2%

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

      5. *-commutative 99.2%

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

      6. associate-/r* 99.2%

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

      7. metadata-eval 99.2%

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

      8. metadata-eval 99.2%

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

   3. Simplified 99.2%

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

      1. associate-+r+ 99.2%

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

      2. distribute-rgt-in 99.3%

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

      3. div-inv 99.2%

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

      4. div-inv 99.3%

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

      5. clear-num 99.2%

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

      6. div-inv 99.2%

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

      7. metadata-eval 99.2%

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

      8. +-commutative 99.2%

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

      9. distribute-rgt-in 99.2%

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

      10. metadata-eval 99.2%

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

      11. sub-neg 99.2%

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

      12. associate-*r* 99.4%

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

      13. associate--l+ 99.4%

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

   5. Applied egg-rr 99.4%

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

      1. distribute-lft-out 99.4%

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

      2. associate-+r+ 99.4%

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

   7. Simplified 99.4%

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

   8. Taylor expanded in y around 0 70.8%

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

      1. associate-*r* 70.9%

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

      2. sub-neg 70.9%

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

      3. associate-*r/ 71.0%

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

      4. metadata-eval 71.0%

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

      5. metadata-eval 71.0%

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

      6. *-commutative 71.0%

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

      7. associate-*r* 70.9%

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

   10. Simplified 70.9%

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

   11. Taylor expanded in x around 0 70.3%

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

       1. add-sqr-sqrt 70.0%

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

       2. sqrt-unprod 70.3%

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

       3. *-commutative 70.3%

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

       4. *-commutative 70.3%

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

       5. swap-sqr 24.6%

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

       6. add-sqr-sqrt 24.6%

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

       7. frac-times 24.7%

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

       8. metadata-eval 24.7%

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

       9. pow2 24.7%

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

   13. Applied egg-rr 24.7%

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

       1. associate-*r/ 24.9%

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

       2. unpow2 24.9%

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

       3. times-frac 70.6%

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

       4. *-inverses 70.6%

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

   15. Simplified 70.6%

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

   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. Step-by-step derivation

      1. distribute-lft-out-- 99.5%

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

      2. *-rgt-identity 99.5%

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

      3. associate-*l* 99.5%

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

      4. *-commutative 99.5%

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

      5. associate-*r* 99.5%

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

      6. distribute-rgt-out-- 99.5%

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

      7. +-commutative 99.5%

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

      8. distribute-lft-in 99.5%

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

      9. associate--l+ 99.5%

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

      10. *-commutative 99.5%

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

      11. associate-/r* 99.5%

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

      12. associate-*r/ 99.5%

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

      13. metadata-eval 99.5%

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

      14. metadata-eval 99.5%

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

      15. sub-neg 99.5%

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

      16. metadata-eval 99.5%

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

      17. metadata-eval 99.5%

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

      18. metadata-eval 99.5%

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

      19. fma-def 99.5%

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

   3. Simplified 99.5%

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

   4. Taylor expanded in y around 0 55.0%

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

   5. Taylor expanded in x around inf 53.6%

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

4. Final simplification 61.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 0.11:\\ \;\;\;\;\sqrt{\frac{0.1111111111111111}{x}}\\ \mathbf{else}:\\ \;\;\;\;\sqrt{x} \cdot -3\\ \end{array} \]

Alternative 11: 3.3% accurate, 1.1× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_] := N[Sqrt[N[(x * 9.0), $MachinePrecision]], $MachinePrecision]

Derivation

1. Initial program 99.4%

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

   1. distribute-lft-out-- 99.4%

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

   2. *-rgt-identity 99.4%

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

   3. associate-*l* 99.3%

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

   4. *-commutative 99.3%

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

   5. associate-*r* 99.4%

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

   6. distribute-rgt-out-- 99.4%

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

   7. +-commutative 99.4%

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

   8. distribute-lft-in 99.4%

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

   9. associate--l+ 99.4%

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

   10. *-commutative 99.4%

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

   11. associate-/r* 99.4%

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

   12. associate-*r/ 99.4%

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

   13. metadata-eval 99.4%

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

   14. metadata-eval 99.4%

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

   15. sub-neg 99.4%

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

   16. metadata-eval 99.4%

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

   17. metadata-eval 99.4%

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

   18. metadata-eval 99.4%

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

   19. fma-def 99.4%

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

3. Simplified 99.4%

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

4. Taylor expanded in y around 0 62.5%

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

5. Taylor expanded in x around inf 29.1%

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

   1. expm1-log1p-u 0.9%

      \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\sqrt{x} \cdot -3\right)\right)} \]

   2. expm1-udef 1.2%

      \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(\sqrt{x} \cdot -3\right)} - 1} \]

   3. add-sqr-sqrt 0.0%

      \[\leadsto e^{\mathsf{log1p}\left(\color{blue}{\sqrt{\sqrt{x} \cdot -3} \cdot \sqrt{\sqrt{x} \cdot -3}}\right)} - 1 \]

   4. sqrt-unprod 2.3%

      \[\leadsto e^{\mathsf{log1p}\left(\color{blue}{\sqrt{\left(\sqrt{x} \cdot -3\right) \cdot \left(\sqrt{x} \cdot -3\right)}}\right)} - 1 \]

   5. swap-sqr 2.3%

      \[\leadsto e^{\mathsf{log1p}\left(\sqrt{\color{blue}{\left(\sqrt{x} \cdot \sqrt{x}\right) \cdot \left(-3 \cdot -3\right)}}\right)} - 1 \]

   6. add-sqr-sqrt 2.3%

      \[\leadsto e^{\mathsf{log1p}\left(\sqrt{\color{blue}{x} \cdot \left(-3 \cdot -3\right)}\right)} - 1 \]

   7. metadata-eval 2.3%

      \[\leadsto e^{\mathsf{log1p}\left(\sqrt{x \cdot \color{blue}{9}}\right)} - 1 \]

7. Applied egg-rr 2.3%

   \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(\sqrt{x \cdot 9}\right)} - 1} \]
8. Step-by-step derivation

   1. expm1-def 3.0%

      \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\sqrt{x \cdot 9}\right)\right)} \]

   2. expm1-log1p 3.0%

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

9. Simplified 3.0%

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

10. Final simplification 3.0%

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

Alternative 12: 25.5% accurate, 1.1× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.4%

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

   1. distribute-lft-out-- 99.4%

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

   2. *-rgt-identity 99.4%

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

   3. associate-*l* 99.3%

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

   4. *-commutative 99.3%

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

   5. associate-*r* 99.4%

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

   6. distribute-rgt-out-- 99.4%

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

   7. +-commutative 99.4%

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

   8. distribute-lft-in 99.4%

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

   9. associate--l+ 99.4%

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

   10. *-commutative 99.4%

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

   11. associate-/r* 99.4%

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

   12. associate-*r/ 99.4%

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

   13. metadata-eval 99.4%

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

   14. metadata-eval 99.4%

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

   15. sub-neg 99.4%

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

   16. metadata-eval 99.4%

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

   17. metadata-eval 99.4%

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

   18. metadata-eval 99.4%

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

   19. fma-def 99.4%

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

3. Simplified 99.4%

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

4. Taylor expanded in y around 0 62.5%

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

5. Taylor expanded in x around inf 29.1%

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

6. Final simplification 29.1%

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

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 2023318 
(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)))