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

Percentage Accurate: 99.4% → 99.4%

Time: 10.8s

Alternatives: 14

Speedup: 1.0×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 99.4% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.4% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = sqrt((x * 9.0d0)) * ((0.1111111111111111d0 / x) + (y + (-1.0d0)))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

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. sub-neg 99.5%

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

   2. +-commutative 99.5%

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

   3. associate-+l+ 99.5%

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

   4. *-commutative 99.5%

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

   5. associate-/r* 99.5%

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

   6. metadata-eval 99.5%

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

   7. metadata-eval 99.5%

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

3. Simplified 99.5%

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

   1. *-commutative 99.5%

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

   2. metadata-eval 99.5%

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

   3. sqrt-prod 99.6%

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

6. Applied egg-rr 99.6%

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

7. Final simplification 99.6%

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

Alternative 2: 61.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 3 \cdot \left(y \cdot \sqrt{x}\right)\\ \mathbf{if}\;y \leq -21000:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq -1.6 \cdot 10^{-131}:\\ \;\;\;\;\sqrt{\frac{0.1111111111111111}{x}}\\ \mathbf{elif}\;y \leq 1.06 \cdot 10^{-98}:\\ \;\;\;\;\sqrt{x} \cdot -3\\ \mathbf{elif}\;y \leq 2.4 \cdot 10^{+69}:\\ \;\;\;\;0.3333333333333333 \cdot {x}^{-0.5}\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (* 3.0 (* y (sqrt x)))))
   (if (<= y -21000.0)
     t_0
     (if (<= y -1.6e-131)
       (sqrt (/ 0.1111111111111111 x))
       (if (<= y 1.06e-98)
         (* (sqrt x) -3.0)
         (if (<= y 2.4e+69) (* 0.3333333333333333 (pow x -0.5)) t_0))))))

C

double code(double x, double y) {
	double t_0 = 3.0 * (y * sqrt(x));
	double tmp;
	if (y <= -21000.0) {
		tmp = t_0;
	} else if (y <= -1.6e-131) {
		tmp = sqrt((0.1111111111111111 / x));
	} else if (y <= 1.06e-98) {
		tmp = sqrt(x) * -3.0;
	} else if (y <= 2.4e+69) {
		tmp = 0.3333333333333333 * pow(x, -0.5);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: t_0
    real(8) :: tmp
    t_0 = 3.0d0 * (y * sqrt(x))
    if (y <= (-21000.0d0)) then
        tmp = t_0
    else if (y <= (-1.6d-131)) then
        tmp = sqrt((0.1111111111111111d0 / x))
    else if (y <= 1.06d-98) then
        tmp = sqrt(x) * (-3.0d0)
    else if (y <= 2.4d+69) then
        tmp = 0.3333333333333333d0 * (x ** (-0.5d0))
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double t_0 = 3.0 * (y * Math.sqrt(x));
	double tmp;
	if (y <= -21000.0) {
		tmp = t_0;
	} else if (y <= -1.6e-131) {
		tmp = Math.sqrt((0.1111111111111111 / x));
	} else if (y <= 1.06e-98) {
		tmp = Math.sqrt(x) * -3.0;
	} else if (y <= 2.4e+69) {
		tmp = 0.3333333333333333 * Math.pow(x, -0.5);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = 3.0 * (y * math.sqrt(x))
	tmp = 0
	if y <= -21000.0:
		tmp = t_0
	elif y <= -1.6e-131:
		tmp = math.sqrt((0.1111111111111111 / x))
	elif y <= 1.06e-98:
		tmp = math.sqrt(x) * -3.0
	elif y <= 2.4e+69:
		tmp = 0.3333333333333333 * math.pow(x, -0.5)
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y)
	t_0 = Float64(3.0 * Float64(y * sqrt(x)))
	tmp = 0.0
	if (y <= -21000.0)
		tmp = t_0;
	elseif (y <= -1.6e-131)
		tmp = sqrt(Float64(0.1111111111111111 / x));
	elseif (y <= 1.06e-98)
		tmp = Float64(sqrt(x) * -3.0);
	elseif (y <= 2.4e+69)
		tmp = Float64(0.3333333333333333 * (x ^ -0.5));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = 3.0 * (y * sqrt(x));
	tmp = 0.0;
	if (y <= -21000.0)
		tmp = t_0;
	elseif (y <= -1.6e-131)
		tmp = sqrt((0.1111111111111111 / x));
	elseif (y <= 1.06e-98)
		tmp = sqrt(x) * -3.0;
	elseif (y <= 2.4e+69)
		tmp = 0.3333333333333333 * (x ^ -0.5);
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(3.0 * N[(y * N[Sqrt[x], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -21000.0], t$95$0, If[LessEqual[y, -1.6e-131], N[Sqrt[N[(0.1111111111111111 / x), $MachinePrecision]], $MachinePrecision], If[LessEqual[y, 1.06e-98], N[(N[Sqrt[x], $MachinePrecision] * -3.0), $MachinePrecision], If[LessEqual[y, 2.4e+69], N[(0.3333333333333333 * N[Power[x, -0.5], $MachinePrecision]), $MachinePrecision], t$95$0]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -21000 or 2.4000000000000002e69 < y

   1. Initial program 99.6%

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

      1. *-commutative 99.6%

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

      2. associate-*l* 99.5%

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

      3. associate--l+ 99.5%

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

      4. distribute-lft-in 99.4%

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

      5. fma-define 99.5%

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

      6. sub-neg 99.5%

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

      7. +-commutative 99.5%

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

      8. distribute-lft-in 99.5%

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

      9. metadata-eval 99.5%

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

      10. metadata-eval 99.5%

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

      11. *-commutative 99.5%

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

      12. associate-/r* 99.5%

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

      13. associate-*r/ 99.5%

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

      14. metadata-eval 99.5%

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

      15. metadata-eval 99.5%

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

   3. Simplified 99.5%

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

   5. Taylor expanded in y around inf 85.5%

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

   if -21000 < y < -1.6e-131

   1. Initial program 99.6%

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

      1. *-commutative 99.6%

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

      2. associate-*l* 99.4%

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

      3. associate--l+ 99.4%

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

      4. distribute-lft-in 99.4%

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

      5. fma-define 99.4%

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

      6. sub-neg 99.4%

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

      7. +-commutative 99.4%

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

      8. distribute-lft-in 99.4%

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

      9. metadata-eval 99.4%

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

      10. metadata-eval 99.4%

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

      11. *-commutative 99.4%

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

      12. associate-/r* 99.4%

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

      13. associate-*r/ 99.7%

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

      14. metadata-eval 99.7%

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

      15. metadata-eval 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in x around 0 77.7%

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

      1. metadata-eval 77.7%

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

      2. sqrt-prod 77.8%

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

      3. div-inv 77.8%

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

      4. pow1/2 77.8%

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

   7. Applied egg-rr 77.8%

      \[\leadsto \color{blue}{{\left(\frac{0.1111111111111111}{x}\right)}^{0.5}} \]
   8. Step-by-step derivation

      1. unpow1/2 77.8%

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

   9. Simplified 77.8%

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

   if -1.6e-131 < y < 1.0600000000000001e-98

   1. Initial program 99.4%

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

      1. *-commutative 99.4%

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

      2. associate-*l* 99.5%

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

      3. associate--l+ 99.5%

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

      4. distribute-lft-in 99.5%

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

      5. fma-define 99.5%

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

      6. sub-neg 99.5%

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

      7. +-commutative 99.5%

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

      8. distribute-lft-in 99.5%

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

      9. metadata-eval 99.5%

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

      10. metadata-eval 99.5%

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

      11. *-commutative 99.5%

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

      12. associate-/r* 99.5%

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

      13. associate-*r/ 99.4%

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

      14. metadata-eval 99.4%

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

      15. metadata-eval 99.4%

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

   3. Simplified 99.4%

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

   5. Taylor expanded in x around inf 58.1%

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

   6. Taylor expanded in y around 0 58.1%

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

      1. *-commutative 58.1%

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

   8. Simplified 58.1%

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

   if 1.0600000000000001e-98 < y < 2.4000000000000002e69

   1. Initial program 99.3%

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

      1. *-commutative 99.3%

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

      2. associate-*l* 99.3%

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

      3. associate--l+ 99.3%

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

      4. distribute-lft-in 99.3%

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

      5. fma-define 99.3%

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

      6. sub-neg 99.3%

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

      7. +-commutative 99.3%

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

      8. distribute-lft-in 99.3%

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

      9. metadata-eval 99.3%

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

      10. metadata-eval 99.3%

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

      11. *-commutative 99.3%

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

      12. associate-/r* 99.3%

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

      13. associate-*r/ 99.3%

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

      14. metadata-eval 99.3%

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

      15. metadata-eval 99.3%

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

   3. Simplified 99.3%

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

   5. Taylor expanded in x around 0 57.1%

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

      1. *-un-lft-identity 57.1%

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

      2. inv-pow 57.1%

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

      3. sqrt-pow1 57.1%

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

      4. metadata-eval 57.1%

         \[\leadsto 0.3333333333333333 \cdot \left(1 \cdot {x}^{\color{blue}{-0.5}}\right) \]

   7. Applied egg-rr 57.1%

      \[\leadsto 0.3333333333333333 \cdot \color{blue}{\left(1 \cdot {x}^{-0.5}\right)} \]
   8. Step-by-step derivation

      1. *-lft-identity 57.1%

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

   9. Simplified 57.1%

      \[\leadsto 0.3333333333333333 \cdot \color{blue}{{x}^{-0.5}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 71.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -21000:\\ \;\;\;\;3 \cdot \left(y \cdot \sqrt{x}\right)\\ \mathbf{elif}\;y \leq -1.6 \cdot 10^{-131}:\\ \;\;\;\;\sqrt{\frac{0.1111111111111111}{x}}\\ \mathbf{elif}\;y \leq 1.06 \cdot 10^{-98}:\\ \;\;\;\;\sqrt{x} \cdot -3\\ \mathbf{elif}\;y \leq 2.4 \cdot 10^{+69}:\\ \;\;\;\;0.3333333333333333 \cdot {x}^{-0.5}\\ \mathbf{else}:\\ \;\;\;\;3 \cdot \left(y \cdot \sqrt{x}\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 3: 61.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \sqrt{x} \cdot \left(y \cdot 3\right)\\ \mathbf{if}\;y \leq -21000:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq -9 \cdot 10^{-126}:\\ \;\;\;\;\sqrt{\frac{0.1111111111111111}{x}}\\ \mathbf{elif}\;y \leq 1.95 \cdot 10^{-106}:\\ \;\;\;\;\sqrt{x} \cdot -3\\ \mathbf{elif}\;y \leq 5.3 \cdot 10^{+70}:\\ \;\;\;\;0.3333333333333333 \cdot {x}^{-0.5}\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (* (sqrt x) (* y 3.0))))
   (if (<= y -21000.0)
     t_0
     (if (<= y -9e-126)
       (sqrt (/ 0.1111111111111111 x))
       (if (<= y 1.95e-106)
         (* (sqrt x) -3.0)
         (if (<= y 5.3e+70) (* 0.3333333333333333 (pow x -0.5)) t_0))))))

C

double code(double x, double y) {
	double t_0 = sqrt(x) * (y * 3.0);
	double tmp;
	if (y <= -21000.0) {
		tmp = t_0;
	} else if (y <= -9e-126) {
		tmp = sqrt((0.1111111111111111 / x));
	} else if (y <= 1.95e-106) {
		tmp = sqrt(x) * -3.0;
	} else if (y <= 5.3e+70) {
		tmp = 0.3333333333333333 * pow(x, -0.5);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: t_0
    real(8) :: tmp
    t_0 = sqrt(x) * (y * 3.0d0)
    if (y <= (-21000.0d0)) then
        tmp = t_0
    else if (y <= (-9d-126)) then
        tmp = sqrt((0.1111111111111111d0 / x))
    else if (y <= 1.95d-106) then
        tmp = sqrt(x) * (-3.0d0)
    else if (y <= 5.3d+70) then
        tmp = 0.3333333333333333d0 * (x ** (-0.5d0))
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double t_0 = Math.sqrt(x) * (y * 3.0);
	double tmp;
	if (y <= -21000.0) {
		tmp = t_0;
	} else if (y <= -9e-126) {
		tmp = Math.sqrt((0.1111111111111111 / x));
	} else if (y <= 1.95e-106) {
		tmp = Math.sqrt(x) * -3.0;
	} else if (y <= 5.3e+70) {
		tmp = 0.3333333333333333 * Math.pow(x, -0.5);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = math.sqrt(x) * (y * 3.0)
	tmp = 0
	if y <= -21000.0:
		tmp = t_0
	elif y <= -9e-126:
		tmp = math.sqrt((0.1111111111111111 / x))
	elif y <= 1.95e-106:
		tmp = math.sqrt(x) * -3.0
	elif y <= 5.3e+70:
		tmp = 0.3333333333333333 * math.pow(x, -0.5)
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y)
	t_0 = Float64(sqrt(x) * Float64(y * 3.0))
	tmp = 0.0
	if (y <= -21000.0)
		tmp = t_0;
	elseif (y <= -9e-126)
		tmp = sqrt(Float64(0.1111111111111111 / x));
	elseif (y <= 1.95e-106)
		tmp = Float64(sqrt(x) * -3.0);
	elseif (y <= 5.3e+70)
		tmp = Float64(0.3333333333333333 * (x ^ -0.5));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = sqrt(x) * (y * 3.0);
	tmp = 0.0;
	if (y <= -21000.0)
		tmp = t_0;
	elseif (y <= -9e-126)
		tmp = sqrt((0.1111111111111111 / x));
	elseif (y <= 1.95e-106)
		tmp = sqrt(x) * -3.0;
	elseif (y <= 5.3e+70)
		tmp = 0.3333333333333333 * (x ^ -0.5);
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(N[Sqrt[x], $MachinePrecision] * N[(y * 3.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -21000.0], t$95$0, If[LessEqual[y, -9e-126], N[Sqrt[N[(0.1111111111111111 / x), $MachinePrecision]], $MachinePrecision], If[LessEqual[y, 1.95e-106], N[(N[Sqrt[x], $MachinePrecision] * -3.0), $MachinePrecision], If[LessEqual[y, 5.3e+70], N[(0.3333333333333333 * N[Power[x, -0.5], $MachinePrecision]), $MachinePrecision], t$95$0]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -21000 or 5.3e70 < y

   1. Initial program 99.6%

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

      1. *-commutative 99.6%

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

      2. associate-*l* 99.5%

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

      3. associate--l+ 99.5%

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

      4. distribute-lft-in 99.4%

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

      5. fma-define 99.5%

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

      6. sub-neg 99.5%

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

      7. +-commutative 99.5%

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

      8. distribute-lft-in 99.5%

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

      9. metadata-eval 99.5%

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

      10. metadata-eval 99.5%

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

      11. *-commutative 99.5%

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

      12. associate-/r* 99.5%

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

      13. associate-*r/ 99.5%

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

      14. metadata-eval 99.5%

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

      15. metadata-eval 99.5%

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

   3. Simplified 99.5%

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

   5. Taylor expanded in y around inf 85.5%

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

      1. *-commutative 85.5%

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

      2. associate-*l* 85.5%

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

      3. *-commutative 85.5%

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

   7. Simplified 85.5%

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

   if -21000 < y < -9.0000000000000005e-126

   1. Initial program 99.6%

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

      1. *-commutative 99.6%

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

      2. associate-*l* 99.4%

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

      3. associate--l+ 99.4%

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

      4. distribute-lft-in 99.4%

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

      5. fma-define 99.4%

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

      6. sub-neg 99.4%

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

      7. +-commutative 99.4%

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

      8. distribute-lft-in 99.4%

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

      9. metadata-eval 99.4%

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

      10. metadata-eval 99.4%

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

      11. *-commutative 99.4%

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

      12. associate-/r* 99.4%

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

      13. associate-*r/ 99.7%

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

      14. metadata-eval 99.7%

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

      15. metadata-eval 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in x around 0 77.7%

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

      1. metadata-eval 77.7%

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

      2. sqrt-prod 77.8%

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

      3. div-inv 77.8%

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

      4. pow1/2 77.8%

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

   7. Applied egg-rr 77.8%

      \[\leadsto \color{blue}{{\left(\frac{0.1111111111111111}{x}\right)}^{0.5}} \]
   8. Step-by-step derivation

      1. unpow1/2 77.8%

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

   9. Simplified 77.8%

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

   if -9.0000000000000005e-126 < y < 1.95000000000000005e-106

   1. Initial program 99.4%

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

      1. *-commutative 99.4%

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

      2. associate-*l* 99.5%

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

      3. associate--l+ 99.5%

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

      4. distribute-lft-in 99.5%

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

      5. fma-define 99.5%

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

      6. sub-neg 99.5%

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

      7. +-commutative 99.5%

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

      8. distribute-lft-in 99.5%

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

      9. metadata-eval 99.5%

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

      10. metadata-eval 99.5%

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

      11. *-commutative 99.5%

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

      12. associate-/r* 99.5%

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

      13. associate-*r/ 99.4%

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

      14. metadata-eval 99.4%

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

      15. metadata-eval 99.4%

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

   3. Simplified 99.4%

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

   5. Taylor expanded in x around inf 58.1%

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

   6. Taylor expanded in y around 0 58.1%

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

      1. *-commutative 58.1%

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

   8. Simplified 58.1%

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

   if 1.95000000000000005e-106 < y < 5.3e70

   1. Initial program 99.3%

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

      1. *-commutative 99.3%

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

      2. associate-*l* 99.3%

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

      3. associate--l+ 99.3%

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

      4. distribute-lft-in 99.3%

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

      5. fma-define 99.3%

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

      6. sub-neg 99.3%

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

      7. +-commutative 99.3%

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

      8. distribute-lft-in 99.3%

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

      9. metadata-eval 99.3%

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

      10. metadata-eval 99.3%

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

      11. *-commutative 99.3%

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

      12. associate-/r* 99.3%

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

      13. associate-*r/ 99.3%

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

      14. metadata-eval 99.3%

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

      15. metadata-eval 99.3%

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

   3. Simplified 99.3%

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

   5. Taylor expanded in x around 0 57.1%

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

      1. *-un-lft-identity 57.1%

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

      2. inv-pow 57.1%

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

      3. sqrt-pow1 57.1%

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

      4. metadata-eval 57.1%

         \[\leadsto 0.3333333333333333 \cdot \left(1 \cdot {x}^{\color{blue}{-0.5}}\right) \]

   7. Applied egg-rr 57.1%

      \[\leadsto 0.3333333333333333 \cdot \color{blue}{\left(1 \cdot {x}^{-0.5}\right)} \]
   8. Step-by-step derivation

      1. *-lft-identity 57.1%

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

   9. Simplified 57.1%

      \[\leadsto 0.3333333333333333 \cdot \color{blue}{{x}^{-0.5}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 71.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -21000:\\ \;\;\;\;\sqrt{x} \cdot \left(y \cdot 3\right)\\ \mathbf{elif}\;y \leq -9 \cdot 10^{-126}:\\ \;\;\;\;\sqrt{\frac{0.1111111111111111}{x}}\\ \mathbf{elif}\;y \leq 1.95 \cdot 10^{-106}:\\ \;\;\;\;\sqrt{x} \cdot -3\\ \mathbf{elif}\;y \leq 5.3 \cdot 10^{+70}:\\ \;\;\;\;0.3333333333333333 \cdot {x}^{-0.5}\\ \mathbf{else}:\\ \;\;\;\;\sqrt{x} \cdot \left(y \cdot 3\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 4: 61.8% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \sqrt{x} \cdot \left(y \cdot 3\right)\\ \mathbf{if}\;y \leq -21000:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq -7.5 \cdot 10^{-131}:\\ \;\;\;\;\sqrt{x} \cdot \frac{0.3333333333333333}{x}\\ \mathbf{elif}\;y \leq 2.7 \cdot 10^{-108}:\\ \;\;\;\;\sqrt{x} \cdot -3\\ \mathbf{elif}\;y \leq 4.6 \cdot 10^{+69}:\\ \;\;\;\;0.3333333333333333 \cdot {x}^{-0.5}\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (* (sqrt x) (* y 3.0))))
   (if (<= y -21000.0)
     t_0
     (if (<= y -7.5e-131)
       (* (sqrt x) (/ 0.3333333333333333 x))
       (if (<= y 2.7e-108)
         (* (sqrt x) -3.0)
         (if (<= y 4.6e+69) (* 0.3333333333333333 (pow x -0.5)) t_0))))))

C

double code(double x, double y) {
	double t_0 = sqrt(x) * (y * 3.0);
	double tmp;
	if (y <= -21000.0) {
		tmp = t_0;
	} else if (y <= -7.5e-131) {
		tmp = sqrt(x) * (0.3333333333333333 / x);
	} else if (y <= 2.7e-108) {
		tmp = sqrt(x) * -3.0;
	} else if (y <= 4.6e+69) {
		tmp = 0.3333333333333333 * pow(x, -0.5);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: t_0
    real(8) :: tmp
    t_0 = sqrt(x) * (y * 3.0d0)
    if (y <= (-21000.0d0)) then
        tmp = t_0
    else if (y <= (-7.5d-131)) then
        tmp = sqrt(x) * (0.3333333333333333d0 / x)
    else if (y <= 2.7d-108) then
        tmp = sqrt(x) * (-3.0d0)
    else if (y <= 4.6d+69) then
        tmp = 0.3333333333333333d0 * (x ** (-0.5d0))
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double t_0 = Math.sqrt(x) * (y * 3.0);
	double tmp;
	if (y <= -21000.0) {
		tmp = t_0;
	} else if (y <= -7.5e-131) {
		tmp = Math.sqrt(x) * (0.3333333333333333 / x);
	} else if (y <= 2.7e-108) {
		tmp = Math.sqrt(x) * -3.0;
	} else if (y <= 4.6e+69) {
		tmp = 0.3333333333333333 * Math.pow(x, -0.5);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = math.sqrt(x) * (y * 3.0)
	tmp = 0
	if y <= -21000.0:
		tmp = t_0
	elif y <= -7.5e-131:
		tmp = math.sqrt(x) * (0.3333333333333333 / x)
	elif y <= 2.7e-108:
		tmp = math.sqrt(x) * -3.0
	elif y <= 4.6e+69:
		tmp = 0.3333333333333333 * math.pow(x, -0.5)
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y)
	t_0 = Float64(sqrt(x) * Float64(y * 3.0))
	tmp = 0.0
	if (y <= -21000.0)
		tmp = t_0;
	elseif (y <= -7.5e-131)
		tmp = Float64(sqrt(x) * Float64(0.3333333333333333 / x));
	elseif (y <= 2.7e-108)
		tmp = Float64(sqrt(x) * -3.0);
	elseif (y <= 4.6e+69)
		tmp = Float64(0.3333333333333333 * (x ^ -0.5));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = sqrt(x) * (y * 3.0);
	tmp = 0.0;
	if (y <= -21000.0)
		tmp = t_0;
	elseif (y <= -7.5e-131)
		tmp = sqrt(x) * (0.3333333333333333 / x);
	elseif (y <= 2.7e-108)
		tmp = sqrt(x) * -3.0;
	elseif (y <= 4.6e+69)
		tmp = 0.3333333333333333 * (x ^ -0.5);
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(N[Sqrt[x], $MachinePrecision] * N[(y * 3.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -21000.0], t$95$0, If[LessEqual[y, -7.5e-131], N[(N[Sqrt[x], $MachinePrecision] * N[(0.3333333333333333 / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.7e-108], N[(N[Sqrt[x], $MachinePrecision] * -3.0), $MachinePrecision], If[LessEqual[y, 4.6e+69], N[(0.3333333333333333 * N[Power[x, -0.5], $MachinePrecision]), $MachinePrecision], t$95$0]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -21000 or 4.60000000000000033e69 < y

   1. Initial program 99.6%

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

      1. *-commutative 99.6%

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

      2. associate-*l* 99.5%

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

      3. associate--l+ 99.5%

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

      4. distribute-lft-in 99.4%

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

      5. fma-define 99.5%

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

      6. sub-neg 99.5%

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

      7. +-commutative 99.5%

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

      8. distribute-lft-in 99.5%

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

      9. metadata-eval 99.5%

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

      10. metadata-eval 99.5%

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

      11. *-commutative 99.5%

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

      12. associate-/r* 99.5%

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

      13. associate-*r/ 99.5%

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

      14. metadata-eval 99.5%

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

      15. metadata-eval 99.5%

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

   3. Simplified 99.5%

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

   5. Taylor expanded in y around inf 85.5%

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

      1. *-commutative 85.5%

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

      2. associate-*l* 85.5%

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

      3. *-commutative 85.5%

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

   7. Simplified 85.5%

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

   if -21000 < y < -7.49999999999999964e-131

   1. Initial program 99.6%

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

      1. *-commutative 99.6%

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

      2. associate-*l* 99.4%

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

      3. associate--l+ 99.4%

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

      4. distribute-lft-in 99.4%

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

      5. fma-define 99.4%

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

      6. sub-neg 99.4%

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

      7. +-commutative 99.4%

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

      8. distribute-lft-in 99.4%

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

      9. metadata-eval 99.4%

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

      10. metadata-eval 99.4%

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

      11. *-commutative 99.4%

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

      12. associate-/r* 99.4%

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

      13. associate-*r/ 99.7%

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

      14. metadata-eval 99.7%

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

      15. metadata-eval 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in x around 0 77.8%

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

   if -7.49999999999999964e-131 < y < 2.70000000000000005e-108

   1. Initial program 99.4%

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

      1. *-commutative 99.4%

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

      2. associate-*l* 99.5%

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

      3. associate--l+ 99.5%

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

      4. distribute-lft-in 99.5%

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

      5. fma-define 99.5%

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

      6. sub-neg 99.5%

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

      7. +-commutative 99.5%

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

      8. distribute-lft-in 99.5%

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

      9. metadata-eval 99.5%

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

      10. metadata-eval 99.5%

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

      11. *-commutative 99.5%

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

      12. associate-/r* 99.5%

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

      13. associate-*r/ 99.4%

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

      14. metadata-eval 99.4%

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

      15. metadata-eval 99.4%

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

   3. Simplified 99.4%

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

   5. Taylor expanded in x around inf 58.1%

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

   6. Taylor expanded in y around 0 58.1%

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

      1. *-commutative 58.1%

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

   8. Simplified 58.1%

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

   if 2.70000000000000005e-108 < y < 4.60000000000000033e69

   1. Initial program 99.3%

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

      1. *-commutative 99.3%

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

      2. associate-*l* 99.3%

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

      3. associate--l+ 99.3%

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

      4. distribute-lft-in 99.3%

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

      5. fma-define 99.3%

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

      6. sub-neg 99.3%

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

      7. +-commutative 99.3%

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

      8. distribute-lft-in 99.3%

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

      9. metadata-eval 99.3%

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

      10. metadata-eval 99.3%

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

      11. *-commutative 99.3%

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

      12. associate-/r* 99.3%

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

      13. associate-*r/ 99.3%

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

      14. metadata-eval 99.3%

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

      15. metadata-eval 99.3%

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

   3. Simplified 99.3%

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

   5. Taylor expanded in x around 0 57.1%

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

      1. *-un-lft-identity 57.1%

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

      2. inv-pow 57.1%

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

      3. sqrt-pow1 57.1%

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

      4. metadata-eval 57.1%

         \[\leadsto 0.3333333333333333 \cdot \left(1 \cdot {x}^{\color{blue}{-0.5}}\right) \]

   7. Applied egg-rr 57.1%

      \[\leadsto 0.3333333333333333 \cdot \color{blue}{\left(1 \cdot {x}^{-0.5}\right)} \]
   8. Step-by-step derivation

      1. *-lft-identity 57.1%

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

   9. Simplified 57.1%

      \[\leadsto 0.3333333333333333 \cdot \color{blue}{{x}^{-0.5}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 71.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -21000:\\ \;\;\;\;\sqrt{x} \cdot \left(y \cdot 3\right)\\ \mathbf{elif}\;y \leq -7.5 \cdot 10^{-131}:\\ \;\;\;\;\sqrt{x} \cdot \frac{0.3333333333333333}{x}\\ \mathbf{elif}\;y \leq 2.7 \cdot 10^{-108}:\\ \;\;\;\;\sqrt{x} \cdot -3\\ \mathbf{elif}\;y \leq 4.6 \cdot 10^{+69}:\\ \;\;\;\;0.3333333333333333 \cdot {x}^{-0.5}\\ \mathbf{else}:\\ \;\;\;\;\sqrt{x} \cdot \left(y \cdot 3\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 5: 61.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := y \cdot \left(\sqrt{x} \cdot 3\right)\\ \mathbf{if}\;y \leq -21000:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq -1.9 \cdot 10^{-128}:\\ \;\;\;\;\sqrt{x} \cdot \frac{0.3333333333333333}{x}\\ \mathbf{elif}\;y \leq 5 \cdot 10^{-101}:\\ \;\;\;\;\sqrt{x} \cdot -3\\ \mathbf{elif}\;y \leq 1.9 \cdot 10^{+69}:\\ \;\;\;\;0.3333333333333333 \cdot {x}^{-0.5}\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (* y (* (sqrt x) 3.0))))
   (if (<= y -21000.0)
     t_0
     (if (<= y -1.9e-128)
       (* (sqrt x) (/ 0.3333333333333333 x))
       (if (<= y 5e-101)
         (* (sqrt x) -3.0)
         (if (<= y 1.9e+69) (* 0.3333333333333333 (pow x -0.5)) t_0))))))

C

double code(double x, double y) {
	double t_0 = y * (sqrt(x) * 3.0);
	double tmp;
	if (y <= -21000.0) {
		tmp = t_0;
	} else if (y <= -1.9e-128) {
		tmp = sqrt(x) * (0.3333333333333333 / x);
	} else if (y <= 5e-101) {
		tmp = sqrt(x) * -3.0;
	} else if (y <= 1.9e+69) {
		tmp = 0.3333333333333333 * pow(x, -0.5);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: t_0
    real(8) :: tmp
    t_0 = y * (sqrt(x) * 3.0d0)
    if (y <= (-21000.0d0)) then
        tmp = t_0
    else if (y <= (-1.9d-128)) then
        tmp = sqrt(x) * (0.3333333333333333d0 / x)
    else if (y <= 5d-101) then
        tmp = sqrt(x) * (-3.0d0)
    else if (y <= 1.9d+69) then
        tmp = 0.3333333333333333d0 * (x ** (-0.5d0))
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double t_0 = y * (Math.sqrt(x) * 3.0);
	double tmp;
	if (y <= -21000.0) {
		tmp = t_0;
	} else if (y <= -1.9e-128) {
		tmp = Math.sqrt(x) * (0.3333333333333333 / x);
	} else if (y <= 5e-101) {
		tmp = Math.sqrt(x) * -3.0;
	} else if (y <= 1.9e+69) {
		tmp = 0.3333333333333333 * Math.pow(x, -0.5);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = y * (math.sqrt(x) * 3.0)
	tmp = 0
	if y <= -21000.0:
		tmp = t_0
	elif y <= -1.9e-128:
		tmp = math.sqrt(x) * (0.3333333333333333 / x)
	elif y <= 5e-101:
		tmp = math.sqrt(x) * -3.0
	elif y <= 1.9e+69:
		tmp = 0.3333333333333333 * math.pow(x, -0.5)
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y)
	t_0 = Float64(y * Float64(sqrt(x) * 3.0))
	tmp = 0.0
	if (y <= -21000.0)
		tmp = t_0;
	elseif (y <= -1.9e-128)
		tmp = Float64(sqrt(x) * Float64(0.3333333333333333 / x));
	elseif (y <= 5e-101)
		tmp = Float64(sqrt(x) * -3.0);
	elseif (y <= 1.9e+69)
		tmp = Float64(0.3333333333333333 * (x ^ -0.5));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = y * (sqrt(x) * 3.0);
	tmp = 0.0;
	if (y <= -21000.0)
		tmp = t_0;
	elseif (y <= -1.9e-128)
		tmp = sqrt(x) * (0.3333333333333333 / x);
	elseif (y <= 5e-101)
		tmp = sqrt(x) * -3.0;
	elseif (y <= 1.9e+69)
		tmp = 0.3333333333333333 * (x ^ -0.5);
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(y * N[(N[Sqrt[x], $MachinePrecision] * 3.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -21000.0], t$95$0, If[LessEqual[y, -1.9e-128], N[(N[Sqrt[x], $MachinePrecision] * N[(0.3333333333333333 / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 5e-101], N[(N[Sqrt[x], $MachinePrecision] * -3.0), $MachinePrecision], If[LessEqual[y, 1.9e+69], N[(0.3333333333333333 * N[Power[x, -0.5], $MachinePrecision]), $MachinePrecision], t$95$0]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -21000 or 1.90000000000000014e69 < y

   1. Initial program 99.6%

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

      1. sub-neg 99.6%

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

      2. +-commutative 99.6%

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

      3. associate-+l+ 99.6%

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

      4. *-commutative 99.6%

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

      5. associate-/r* 99.6%

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

      6. metadata-eval 99.6%

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

      7. metadata-eval 99.6%

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

   3. Simplified 99.6%

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

      1. *-commutative 99.6%

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

      2. metadata-eval 99.6%

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

      3. sqrt-prod 99.7%

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

   6. Applied egg-rr 99.7%

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

   7. Taylor expanded in y around inf 85.5%

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

      1. associate-*r* 85.7%

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

      2. *-commutative 85.7%

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

   9. Simplified 85.7%

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

   if -21000 < y < -1.9000000000000001e-128

   1. Initial program 99.6%

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

      1. *-commutative 99.6%

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

      2. associate-*l* 99.4%

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

      3. associate--l+ 99.4%

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

      4. distribute-lft-in 99.4%

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

      5. fma-define 99.4%

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

      6. sub-neg 99.4%

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

      7. +-commutative 99.4%

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

      8. distribute-lft-in 99.4%

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

      9. metadata-eval 99.4%

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

      10. metadata-eval 99.4%

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

      11. *-commutative 99.4%

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

      12. associate-/r* 99.4%

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

      13. associate-*r/ 99.7%

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

      14. metadata-eval 99.7%

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

      15. metadata-eval 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in x around 0 77.8%

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

   if -1.9000000000000001e-128 < y < 5.0000000000000001e-101

   1. Initial program 99.4%

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

      1. *-commutative 99.4%

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

      2. associate-*l* 99.5%

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

      3. associate--l+ 99.5%

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

      4. distribute-lft-in 99.5%

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

      5. fma-define 99.5%

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

      6. sub-neg 99.5%

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

      7. +-commutative 99.5%

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

      8. distribute-lft-in 99.5%

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

      9. metadata-eval 99.5%

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

      10. metadata-eval 99.5%

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

      11. *-commutative 99.5%

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

      12. associate-/r* 99.5%

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

      13. associate-*r/ 99.4%

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

      14. metadata-eval 99.4%

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

      15. metadata-eval 99.4%

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

   3. Simplified 99.4%

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

   5. Taylor expanded in x around inf 58.1%

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

   6. Taylor expanded in y around 0 58.1%

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

      1. *-commutative 58.1%

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

   8. Simplified 58.1%

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

   if 5.0000000000000001e-101 < y < 1.90000000000000014e69

   1. Initial program 99.3%

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

      1. *-commutative 99.3%

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

      2. associate-*l* 99.3%

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

      3. associate--l+ 99.3%

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

      4. distribute-lft-in 99.3%

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

      5. fma-define 99.3%

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

      6. sub-neg 99.3%

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

      7. +-commutative 99.3%

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

      8. distribute-lft-in 99.3%

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

      9. metadata-eval 99.3%

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

      10. metadata-eval 99.3%

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

      11. *-commutative 99.3%

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

      12. associate-/r* 99.3%

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

      13. associate-*r/ 99.3%

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

      14. metadata-eval 99.3%

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

      15. metadata-eval 99.3%

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

   3. Simplified 99.3%

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

   5. Taylor expanded in x around 0 57.1%

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

      1. *-un-lft-identity 57.1%

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

      2. inv-pow 57.1%

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

      3. sqrt-pow1 57.1%

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

      4. metadata-eval 57.1%

         \[\leadsto 0.3333333333333333 \cdot \left(1 \cdot {x}^{\color{blue}{-0.5}}\right) \]

   7. Applied egg-rr 57.1%

      \[\leadsto 0.3333333333333333 \cdot \color{blue}{\left(1 \cdot {x}^{-0.5}\right)} \]
   8. Step-by-step derivation

      1. *-lft-identity 57.1%

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

   9. Simplified 57.1%

      \[\leadsto 0.3333333333333333 \cdot \color{blue}{{x}^{-0.5}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 72.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -21000:\\ \;\;\;\;y \cdot \left(\sqrt{x} \cdot 3\right)\\ \mathbf{elif}\;y \leq -1.9 \cdot 10^{-128}:\\ \;\;\;\;\sqrt{x} \cdot \frac{0.3333333333333333}{x}\\ \mathbf{elif}\;y \leq 5 \cdot 10^{-101}:\\ \;\;\;\;\sqrt{x} \cdot -3\\ \mathbf{elif}\;y \leq 1.9 \cdot 10^{+69}:\\ \;\;\;\;0.3333333333333333 \cdot {x}^{-0.5}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(\sqrt{x} \cdot 3\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 6: 61.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := y \cdot \left(\sqrt{x} \cdot 3\right)\\ \mathbf{if}\;y \leq -19000:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq -3.8 \cdot 10^{-132}:\\ \;\;\;\;\frac{1}{\sqrt{x \cdot 9}}\\ \mathbf{elif}\;y \leq 1.05 \cdot 10^{-101}:\\ \;\;\;\;\sqrt{x} \cdot -3\\ \mathbf{elif}\;y \leq 1.05 \cdot 10^{+70}:\\ \;\;\;\;0.3333333333333333 \cdot {x}^{-0.5}\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (* y (* (sqrt x) 3.0))))
   (if (<= y -19000.0)
     t_0
     (if (<= y -3.8e-132)
       (/ 1.0 (sqrt (* x 9.0)))
       (if (<= y 1.05e-101)
         (* (sqrt x) -3.0)
         (if (<= y 1.05e+70) (* 0.3333333333333333 (pow x -0.5)) t_0))))))

C

double code(double x, double y) {
	double t_0 = y * (sqrt(x) * 3.0);
	double tmp;
	if (y <= -19000.0) {
		tmp = t_0;
	} else if (y <= -3.8e-132) {
		tmp = 1.0 / sqrt((x * 9.0));
	} else if (y <= 1.05e-101) {
		tmp = sqrt(x) * -3.0;
	} else if (y <= 1.05e+70) {
		tmp = 0.3333333333333333 * pow(x, -0.5);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: t_0
    real(8) :: tmp
    t_0 = y * (sqrt(x) * 3.0d0)
    if (y <= (-19000.0d0)) then
        tmp = t_0
    else if (y <= (-3.8d-132)) then
        tmp = 1.0d0 / sqrt((x * 9.0d0))
    else if (y <= 1.05d-101) then
        tmp = sqrt(x) * (-3.0d0)
    else if (y <= 1.05d+70) then
        tmp = 0.3333333333333333d0 * (x ** (-0.5d0))
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double t_0 = y * (Math.sqrt(x) * 3.0);
	double tmp;
	if (y <= -19000.0) {
		tmp = t_0;
	} else if (y <= -3.8e-132) {
		tmp = 1.0 / Math.sqrt((x * 9.0));
	} else if (y <= 1.05e-101) {
		tmp = Math.sqrt(x) * -3.0;
	} else if (y <= 1.05e+70) {
		tmp = 0.3333333333333333 * Math.pow(x, -0.5);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = y * (math.sqrt(x) * 3.0)
	tmp = 0
	if y <= -19000.0:
		tmp = t_0
	elif y <= -3.8e-132:
		tmp = 1.0 / math.sqrt((x * 9.0))
	elif y <= 1.05e-101:
		tmp = math.sqrt(x) * -3.0
	elif y <= 1.05e+70:
		tmp = 0.3333333333333333 * math.pow(x, -0.5)
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y)
	t_0 = Float64(y * Float64(sqrt(x) * 3.0))
	tmp = 0.0
	if (y <= -19000.0)
		tmp = t_0;
	elseif (y <= -3.8e-132)
		tmp = Float64(1.0 / sqrt(Float64(x * 9.0)));
	elseif (y <= 1.05e-101)
		tmp = Float64(sqrt(x) * -3.0);
	elseif (y <= 1.05e+70)
		tmp = Float64(0.3333333333333333 * (x ^ -0.5));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = y * (sqrt(x) * 3.0);
	tmp = 0.0;
	if (y <= -19000.0)
		tmp = t_0;
	elseif (y <= -3.8e-132)
		tmp = 1.0 / sqrt((x * 9.0));
	elseif (y <= 1.05e-101)
		tmp = sqrt(x) * -3.0;
	elseif (y <= 1.05e+70)
		tmp = 0.3333333333333333 * (x ^ -0.5);
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(y * N[(N[Sqrt[x], $MachinePrecision] * 3.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -19000.0], t$95$0, If[LessEqual[y, -3.8e-132], N[(1.0 / N[Sqrt[N[(x * 9.0), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.05e-101], N[(N[Sqrt[x], $MachinePrecision] * -3.0), $MachinePrecision], If[LessEqual[y, 1.05e+70], N[(0.3333333333333333 * N[Power[x, -0.5], $MachinePrecision]), $MachinePrecision], t$95$0]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -19000 or 1.05000000000000004e70 < y

   1. Initial program 99.6%

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

      1. sub-neg 99.6%

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

      2. +-commutative 99.6%

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

      3. associate-+l+ 99.6%

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

      4. *-commutative 99.6%

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

      5. associate-/r* 99.6%

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

      6. metadata-eval 99.6%

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

      7. metadata-eval 99.6%

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

   3. Simplified 99.6%

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

      1. *-commutative 99.6%

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

      2. metadata-eval 99.6%

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

      3. sqrt-prod 99.7%

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

   6. Applied egg-rr 99.7%

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

   7. Taylor expanded in y around inf 85.5%

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

      1. associate-*r* 85.7%

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

      2. *-commutative 85.7%

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

   9. Simplified 85.7%

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

   if -19000 < y < -3.7999999999999997e-132

   1. Initial program 99.6%

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

      1. *-commutative 99.6%

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

      2. associate-*l* 99.4%

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

      3. associate--l+ 99.4%

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

      4. distribute-lft-in 99.4%

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

      5. fma-define 99.4%

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

      6. sub-neg 99.4%

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

      7. +-commutative 99.4%

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

      8. distribute-lft-in 99.4%

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

      9. metadata-eval 99.4%

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

      10. metadata-eval 99.4%

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

      11. *-commutative 99.4%

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

      12. associate-/r* 99.4%

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

      13. associate-*r/ 99.7%

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

      14. metadata-eval 99.7%

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

      15. metadata-eval 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in x around 0 77.7%

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

      1. metadata-eval 77.7%

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

      2. sqrt-prod 77.8%

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

      3. div-inv 77.8%

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

      4. pow1/2 77.8%

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

   7. Applied egg-rr 77.8%

      \[\leadsto \color{blue}{{\left(\frac{0.1111111111111111}{x}\right)}^{0.5}} \]
   8. Step-by-step derivation

      1. unpow1/2 77.8%

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

   9. Simplified 77.8%

      \[\leadsto \color{blue}{\sqrt{\frac{0.1111111111111111}{x}}} \]
   10. Step-by-step derivation

       1. clear-num 77.9%

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

       2. sqrt-div 78.0%

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

       3. metadata-eval 78.0%

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

       4. div-inv 78.0%

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

       5. metadata-eval 78.0%

          \[\leadsto \frac{1}{\sqrt{x \cdot \color{blue}{9}}} \]

   11. Applied egg-rr 78.0%

       \[\leadsto \color{blue}{\frac{1}{\sqrt{x \cdot 9}}} \]

   if -3.7999999999999997e-132 < y < 1.05000000000000008e-101

   1. Initial program 99.4%

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

      1. *-commutative 99.4%

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

      2. associate-*l* 99.5%

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

      3. associate--l+ 99.5%

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

      4. distribute-lft-in 99.5%

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

      5. fma-define 99.5%

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

      6. sub-neg 99.5%

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

      7. +-commutative 99.5%

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

      8. distribute-lft-in 99.5%

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

      9. metadata-eval 99.5%

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

      10. metadata-eval 99.5%

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

      11. *-commutative 99.5%

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

      12. associate-/r* 99.5%

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

      13. associate-*r/ 99.4%

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

      14. metadata-eval 99.4%

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

      15. metadata-eval 99.4%

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

   3. Simplified 99.4%

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

   5. Taylor expanded in x around inf 58.1%

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

   6. Taylor expanded in y around 0 58.1%

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

      1. *-commutative 58.1%

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

   8. Simplified 58.1%

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

   if 1.05000000000000008e-101 < y < 1.05000000000000004e70

   1. Initial program 99.3%

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

      1. *-commutative 99.3%

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

      2. associate-*l* 99.3%

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

      3. associate--l+ 99.3%

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

      4. distribute-lft-in 99.3%

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

      5. fma-define 99.3%

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

      6. sub-neg 99.3%

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

      7. +-commutative 99.3%

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

      8. distribute-lft-in 99.3%

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

      9. metadata-eval 99.3%

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

      10. metadata-eval 99.3%

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

      11. *-commutative 99.3%

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

      12. associate-/r* 99.3%

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

      13. associate-*r/ 99.3%

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

      14. metadata-eval 99.3%

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

      15. metadata-eval 99.3%

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

   3. Simplified 99.3%

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

   5. Taylor expanded in x around 0 57.1%

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

      1. *-un-lft-identity 57.1%

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

      2. inv-pow 57.1%

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

      3. sqrt-pow1 57.1%

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

      4. metadata-eval 57.1%

         \[\leadsto 0.3333333333333333 \cdot \left(1 \cdot {x}^{\color{blue}{-0.5}}\right) \]

   7. Applied egg-rr 57.1%

      \[\leadsto 0.3333333333333333 \cdot \color{blue}{\left(1 \cdot {x}^{-0.5}\right)} \]
   8. Step-by-step derivation

      1. *-lft-identity 57.1%

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

   9. Simplified 57.1%

      \[\leadsto 0.3333333333333333 \cdot \color{blue}{{x}^{-0.5}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 72.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -19000:\\ \;\;\;\;y \cdot \left(\sqrt{x} \cdot 3\right)\\ \mathbf{elif}\;y \leq -3.8 \cdot 10^{-132}:\\ \;\;\;\;\frac{1}{\sqrt{x \cdot 9}}\\ \mathbf{elif}\;y \leq 1.05 \cdot 10^{-101}:\\ \;\;\;\;\sqrt{x} \cdot -3\\ \mathbf{elif}\;y \leq 1.05 \cdot 10^{+70}:\\ \;\;\;\;0.3333333333333333 \cdot {x}^{-0.5}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(\sqrt{x} \cdot 3\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 7: 61.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := y \cdot \left(\sqrt{x} \cdot 3\right)\\ \mathbf{if}\;y \leq -390:\\ \;\;\;\;t\_0\\ \mathbf{elif}\;y \leq -8.2 \cdot 10^{-129}:\\ \;\;\;\;\frac{1}{\sqrt{\frac{x}{0.1111111111111111}}}\\ \mathbf{elif}\;y \leq 2.85 \cdot 10^{-101}:\\ \;\;\;\;\sqrt{x} \cdot -3\\ \mathbf{elif}\;y \leq 1.52 \cdot 10^{+69}:\\ \;\;\;\;0.3333333333333333 \cdot {x}^{-0.5}\\ \mathbf{else}:\\ \;\;\;\;t\_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (* y (* (sqrt x) 3.0))))
   (if (<= y -390.0)
     t_0
     (if (<= y -8.2e-129)
       (/ 1.0 (sqrt (/ x 0.1111111111111111)))
       (if (<= y 2.85e-101)
         (* (sqrt x) -3.0)
         (if (<= y 1.52e+69) (* 0.3333333333333333 (pow x -0.5)) t_0))))))

C

double code(double x, double y) {
	double t_0 = y * (sqrt(x) * 3.0);
	double tmp;
	if (y <= -390.0) {
		tmp = t_0;
	} else if (y <= -8.2e-129) {
		tmp = 1.0 / sqrt((x / 0.1111111111111111));
	} else if (y <= 2.85e-101) {
		tmp = sqrt(x) * -3.0;
	} else if (y <= 1.52e+69) {
		tmp = 0.3333333333333333 * pow(x, -0.5);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: t_0
    real(8) :: tmp
    t_0 = y * (sqrt(x) * 3.0d0)
    if (y <= (-390.0d0)) then
        tmp = t_0
    else if (y <= (-8.2d-129)) then
        tmp = 1.0d0 / sqrt((x / 0.1111111111111111d0))
    else if (y <= 2.85d-101) then
        tmp = sqrt(x) * (-3.0d0)
    else if (y <= 1.52d+69) then
        tmp = 0.3333333333333333d0 * (x ** (-0.5d0))
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double t_0 = y * (Math.sqrt(x) * 3.0);
	double tmp;
	if (y <= -390.0) {
		tmp = t_0;
	} else if (y <= -8.2e-129) {
		tmp = 1.0 / Math.sqrt((x / 0.1111111111111111));
	} else if (y <= 2.85e-101) {
		tmp = Math.sqrt(x) * -3.0;
	} else if (y <= 1.52e+69) {
		tmp = 0.3333333333333333 * Math.pow(x, -0.5);
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = y * (math.sqrt(x) * 3.0)
	tmp = 0
	if y <= -390.0:
		tmp = t_0
	elif y <= -8.2e-129:
		tmp = 1.0 / math.sqrt((x / 0.1111111111111111))
	elif y <= 2.85e-101:
		tmp = math.sqrt(x) * -3.0
	elif y <= 1.52e+69:
		tmp = 0.3333333333333333 * math.pow(x, -0.5)
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y)
	t_0 = Float64(y * Float64(sqrt(x) * 3.0))
	tmp = 0.0
	if (y <= -390.0)
		tmp = t_0;
	elseif (y <= -8.2e-129)
		tmp = Float64(1.0 / sqrt(Float64(x / 0.1111111111111111)));
	elseif (y <= 2.85e-101)
		tmp = Float64(sqrt(x) * -3.0);
	elseif (y <= 1.52e+69)
		tmp = Float64(0.3333333333333333 * (x ^ -0.5));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = y * (sqrt(x) * 3.0);
	tmp = 0.0;
	if (y <= -390.0)
		tmp = t_0;
	elseif (y <= -8.2e-129)
		tmp = 1.0 / sqrt((x / 0.1111111111111111));
	elseif (y <= 2.85e-101)
		tmp = sqrt(x) * -3.0;
	elseif (y <= 1.52e+69)
		tmp = 0.3333333333333333 * (x ^ -0.5);
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(y * N[(N[Sqrt[x], $MachinePrecision] * 3.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -390.0], t$95$0, If[LessEqual[y, -8.2e-129], N[(1.0 / N[Sqrt[N[(x / 0.1111111111111111), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.85e-101], N[(N[Sqrt[x], $MachinePrecision] * -3.0), $MachinePrecision], If[LessEqual[y, 1.52e+69], N[(0.3333333333333333 * N[Power[x, -0.5], $MachinePrecision]), $MachinePrecision], t$95$0]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -390 or 1.52e69 < y

   1. Initial program 99.6%

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

      1. sub-neg 99.6%

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

      2. +-commutative 99.6%

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

      3. associate-+l+ 99.6%

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

      4. *-commutative 99.6%

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

      5. associate-/r* 99.6%

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

      6. metadata-eval 99.6%

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

      7. metadata-eval 99.6%

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

   3. Simplified 99.6%

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

      1. *-commutative 99.6%

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

      2. metadata-eval 99.6%

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

      3. sqrt-prod 99.7%

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

   6. Applied egg-rr 99.7%

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

   7. Taylor expanded in y around inf 85.5%

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

      1. associate-*r* 85.7%

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

      2. *-commutative 85.7%

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

   9. Simplified 85.7%

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

   if -390 < y < -8.1999999999999999e-129

   1. Initial program 99.6%

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

      1. *-commutative 99.6%

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

      2. associate-*l* 99.4%

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

      3. associate--l+ 99.4%

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

      4. distribute-lft-in 99.4%

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

      5. fma-define 99.4%

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

      6. sub-neg 99.4%

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

      7. +-commutative 99.4%

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

      8. distribute-lft-in 99.4%

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

      9. metadata-eval 99.4%

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

      10. metadata-eval 99.4%

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

      11. *-commutative 99.4%

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

      12. associate-/r* 99.4%

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

      13. associate-*r/ 99.7%

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

      14. metadata-eval 99.7%

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

      15. metadata-eval 99.7%

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

   3. Simplified 99.7%

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

   5. Taylor expanded in x around 0 77.7%

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

      1. metadata-eval 77.7%

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

      2. sqrt-prod 77.8%

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

      3. div-inv 77.8%

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

      4. clear-num 77.9%

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

      5. sqrt-div 78.0%

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

      6. metadata-eval 78.0%

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

   7. Applied egg-rr 78.0%

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

   if -8.1999999999999999e-129 < y < 2.84999999999999992e-101

   1. Initial program 99.4%

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

      1. *-commutative 99.4%

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

      2. associate-*l* 99.5%

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

      3. associate--l+ 99.5%

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

      4. distribute-lft-in 99.5%

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

      5. fma-define 99.5%

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

      6. sub-neg 99.5%

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

      7. +-commutative 99.5%

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

      8. distribute-lft-in 99.5%

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

      9. metadata-eval 99.5%

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

      10. metadata-eval 99.5%

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

      11. *-commutative 99.5%

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

      12. associate-/r* 99.5%

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

      13. associate-*r/ 99.4%

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

      14. metadata-eval 99.4%

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

      15. metadata-eval 99.4%

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

   3. Simplified 99.4%

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

   5. Taylor expanded in x around inf 58.1%

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

   6. Taylor expanded in y around 0 58.1%

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

      1. *-commutative 58.1%

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

   8. Simplified 58.1%

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

   if 2.84999999999999992e-101 < y < 1.52e69

   1. Initial program 99.3%

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

      1. *-commutative 99.3%

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

      2. associate-*l* 99.3%

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

      3. associate--l+ 99.3%

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

      4. distribute-lft-in 99.3%

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

      5. fma-define 99.3%

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

      6. sub-neg 99.3%

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

      7. +-commutative 99.3%

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

      8. distribute-lft-in 99.3%

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

      9. metadata-eval 99.3%

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

      10. metadata-eval 99.3%

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

      11. *-commutative 99.3%

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

      12. associate-/r* 99.3%

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

      13. associate-*r/ 99.3%

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

      14. metadata-eval 99.3%

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

      15. metadata-eval 99.3%

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

   3. Simplified 99.3%

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

   5. Taylor expanded in x around 0 57.1%

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

      1. *-un-lft-identity 57.1%

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

      2. inv-pow 57.1%

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

      3. sqrt-pow1 57.1%

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

      4. metadata-eval 57.1%

         \[\leadsto 0.3333333333333333 \cdot \left(1 \cdot {x}^{\color{blue}{-0.5}}\right) \]

   7. Applied egg-rr 57.1%

      \[\leadsto 0.3333333333333333 \cdot \color{blue}{\left(1 \cdot {x}^{-0.5}\right)} \]
   8. Step-by-step derivation

      1. *-lft-identity 57.1%

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

   9. Simplified 57.1%

      \[\leadsto 0.3333333333333333 \cdot \color{blue}{{x}^{-0.5}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 72.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -390:\\ \;\;\;\;y \cdot \left(\sqrt{x} \cdot 3\right)\\ \mathbf{elif}\;y \leq -8.2 \cdot 10^{-129}:\\ \;\;\;\;\frac{1}{\sqrt{\frac{x}{0.1111111111111111}}}\\ \mathbf{elif}\;y \leq 2.85 \cdot 10^{-101}:\\ \;\;\;\;\sqrt{x} \cdot -3\\ \mathbf{elif}\;y \leq 1.52 \cdot 10^{+69}:\\ \;\;\;\;0.3333333333333333 \cdot {x}^{-0.5}\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(\sqrt{x} \cdot 3\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 8: 86.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -21000 \lor \neg \left(y \leq 450000000000\right):\\ \;\;\;\;y \cdot \left(\sqrt{x} \cdot 3\right)\\ \mathbf{else}:\\ \;\;\;\;\sqrt{x} \cdot \left(\frac{0.3333333333333333}{x} + -3\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= y -21000.0) (not (<= y 450000000000.0)))
   (* y (* (sqrt x) 3.0))
   (* (sqrt x) (+ (/ 0.3333333333333333 x) -3.0))))

C

double code(double x, double y) {
	double tmp;
	if ((y <= -21000.0) || !(y <= 450000000000.0)) {
		tmp = y * (sqrt(x) * 3.0);
	} else {
		tmp = sqrt(x) * ((0.3333333333333333 / x) + -3.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if ((y <= (-21000.0d0)) .or. (.not. (y <= 450000000000.0d0))) then
        tmp = y * (sqrt(x) * 3.0d0)
    else
        tmp = sqrt(x) * ((0.3333333333333333d0 / x) + (-3.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((y <= -21000.0) || !(y <= 450000000000.0)) {
		tmp = y * (Math.sqrt(x) * 3.0);
	} else {
		tmp = Math.sqrt(x) * ((0.3333333333333333 / x) + -3.0);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (y <= -21000.0) or not (y <= 450000000000.0):
		tmp = y * (math.sqrt(x) * 3.0)
	else:
		tmp = math.sqrt(x) * ((0.3333333333333333 / x) + -3.0)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((y <= -21000.0) || !(y <= 450000000000.0))
		tmp = Float64(y * Float64(sqrt(x) * 3.0));
	else
		tmp = Float64(sqrt(x) * Float64(Float64(0.3333333333333333 / x) + -3.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((y <= -21000.0) || ~((y <= 450000000000.0)))
		tmp = y * (sqrt(x) * 3.0);
	else
		tmp = sqrt(x) * ((0.3333333333333333 / x) + -3.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[y, -21000.0], N[Not[LessEqual[y, 450000000000.0]], $MachinePrecision]], N[(y * N[(N[Sqrt[x], $MachinePrecision] * 3.0), $MachinePrecision]), $MachinePrecision], N[(N[Sqrt[x], $MachinePrecision] * N[(N[(0.3333333333333333 / x), $MachinePrecision] + -3.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -21000 or 4.5e11 < y

   1. Initial program 99.6%

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

      1. sub-neg 99.6%

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

      2. +-commutative 99.6%

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

      3. associate-+l+ 99.6%

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

      4. *-commutative 99.6%

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

      5. associate-/r* 99.6%

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

      6. metadata-eval 99.6%

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

      7. metadata-eval 99.6%

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

   3. Simplified 99.6%

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

      1. *-commutative 99.6%

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

      2. metadata-eval 99.6%

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

      3. sqrt-prod 99.7%

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

   6. Applied egg-rr 99.7%

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

   7. Taylor expanded in y around inf 81.6%

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

      1. associate-*r* 81.8%

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

      2. *-commutative 81.8%

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

   9. Simplified 81.8%

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

   if -21000 < y < 4.5e11

   1. Initial program 99.4%

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

      1. *-commutative 99.4%

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

      2. associate-*l* 99.4%

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

      3. associate--l+ 99.4%

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

      4. distribute-lft-in 99.4%

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

      5. fma-define 99.4%

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

      6. sub-neg 99.4%

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

      7. +-commutative 99.4%

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

      8. distribute-lft-in 99.4%

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

      9. metadata-eval 99.4%

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

      10. metadata-eval 99.4%

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

      11. *-commutative 99.4%

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

      12. associate-/r* 99.4%

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

      13. associate-*r/ 99.4%

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

      14. metadata-eval 99.4%

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

      15. metadata-eval 99.4%

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

   3. Simplified 99.4%

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

   5. Taylor expanded in y around 0 97.5%

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

      1. sub-neg 97.5%

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

      2. associate-*r/ 98.3%

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

      3. metadata-eval 98.3%

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

      4. metadata-eval 98.3%

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

      5. +-commutative 98.3%

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

   7. Simplified 98.3%

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

4. Final simplification 90.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -21000 \lor \neg \left(y \leq 450000000000\right):\\ \;\;\;\;y \cdot \left(\sqrt{x} \cdot 3\right)\\ \mathbf{else}:\\ \;\;\;\;\sqrt{x} \cdot \left(\frac{0.3333333333333333}{x} + -3\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 9: 86.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5800 \lor \neg \left(y \leq 4.8 \cdot 10^{-8}\right):\\ \;\;\;\;\sqrt{x} \cdot \left(y \cdot 3 - 3\right)\\ \mathbf{else}:\\ \;\;\;\;\sqrt{x} \cdot \left(\frac{0.3333333333333333}{x} + -3\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= y -5800.0) (not (<= y 4.8e-8)))
   (* (sqrt x) (- (* y 3.0) 3.0))
   (* (sqrt x) (+ (/ 0.3333333333333333 x) -3.0))))

C

double code(double x, double y) {
	double tmp;
	if ((y <= -5800.0) || !(y <= 4.8e-8)) {
		tmp = sqrt(x) * ((y * 3.0) - 3.0);
	} else {
		tmp = sqrt(x) * ((0.3333333333333333 / x) + -3.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if ((y <= (-5800.0d0)) .or. (.not. (y <= 4.8d-8))) then
        tmp = sqrt(x) * ((y * 3.0d0) - 3.0d0)
    else
        tmp = sqrt(x) * ((0.3333333333333333d0 / x) + (-3.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((y <= -5800.0) || !(y <= 4.8e-8)) {
		tmp = Math.sqrt(x) * ((y * 3.0) - 3.0);
	} else {
		tmp = Math.sqrt(x) * ((0.3333333333333333 / x) + -3.0);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (y <= -5800.0) or not (y <= 4.8e-8):
		tmp = math.sqrt(x) * ((y * 3.0) - 3.0)
	else:
		tmp = math.sqrt(x) * ((0.3333333333333333 / x) + -3.0)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((y <= -5800.0) || !(y <= 4.8e-8))
		tmp = Float64(sqrt(x) * Float64(Float64(y * 3.0) - 3.0));
	else
		tmp = Float64(sqrt(x) * Float64(Float64(0.3333333333333333 / x) + -3.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((y <= -5800.0) || ~((y <= 4.8e-8)))
		tmp = sqrt(x) * ((y * 3.0) - 3.0);
	else
		tmp = sqrt(x) * ((0.3333333333333333 / x) + -3.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[y, -5800.0], N[Not[LessEqual[y, 4.8e-8]], $MachinePrecision]], N[(N[Sqrt[x], $MachinePrecision] * N[(N[(y * 3.0), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision], N[(N[Sqrt[x], $MachinePrecision] * N[(N[(0.3333333333333333 / x), $MachinePrecision] + -3.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -5800 or 4.79999999999999997e-8 < y

   1. Initial program 99.6%

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

      1. *-commutative 99.6%

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

      2. associate-*l* 99.4%

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

      3. associate--l+ 99.4%

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

      4. distribute-lft-in 99.4%

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

      5. fma-define 99.4%

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

      6. sub-neg 99.4%

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

      7. +-commutative 99.4%

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

      8. distribute-lft-in 99.4%

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

      9. metadata-eval 99.4%

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

      10. metadata-eval 99.4%

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

      11. *-commutative 99.4%

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

      12. associate-/r* 99.5%

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

      13. associate-*r/ 99.4%

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

      14. metadata-eval 99.4%

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

      15. metadata-eval 99.4%

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

   3. Simplified 99.4%

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

   5. Taylor expanded in x around inf 82.6%

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

   if -5800 < y < 4.79999999999999997e-8

   1. Initial program 99.4%

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

      1. *-commutative 99.4%

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

      2. associate-*l* 99.4%

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

      3. associate--l+ 99.4%

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

      4. distribute-lft-in 99.4%

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

      5. fma-define 99.4%

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

      6. sub-neg 99.4%

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

      7. +-commutative 99.4%

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

      8. distribute-lft-in 99.4%

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

      9. metadata-eval 99.4%

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

      10. metadata-eval 99.4%

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

      11. *-commutative 99.4%

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

      12. associate-/r* 99.4%

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

      13. associate-*r/ 99.4%

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

      14. metadata-eval 99.4%

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

      15. metadata-eval 99.4%

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

   3. Simplified 99.4%

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

   5. Taylor expanded in y around 0 98.3%

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

      1. sub-neg 98.3%

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

      2. associate-*r/ 99.1%

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

      3. metadata-eval 99.1%

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

      4. metadata-eval 99.1%

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

      5. +-commutative 99.1%

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

   7. Simplified 99.1%

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

4. Final simplification 90.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5800 \lor \neg \left(y \leq 4.8 \cdot 10^{-8}\right):\\ \;\;\;\;\sqrt{x} \cdot \left(y \cdot 3 - 3\right)\\ \mathbf{else}:\\ \;\;\;\;\sqrt{x} \cdot \left(\frac{0.3333333333333333}{x} + -3\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 10: 86.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -36 \lor \neg \left(y \leq 2.7 \cdot 10^{-8}\right):\\ \;\;\;\;\sqrt{x \cdot 9} \cdot \left(y + -1\right)\\ \mathbf{else}:\\ \;\;\;\;\sqrt{x} \cdot \left(\frac{0.3333333333333333}{x} + -3\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= y -36.0) (not (<= y 2.7e-8)))
   (* (sqrt (* x 9.0)) (+ y -1.0))
   (* (sqrt x) (+ (/ 0.3333333333333333 x) -3.0))))

C

double code(double x, double y) {
	double tmp;
	if ((y <= -36.0) || !(y <= 2.7e-8)) {
		tmp = sqrt((x * 9.0)) * (y + -1.0);
	} else {
		tmp = sqrt(x) * ((0.3333333333333333 / x) + -3.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if ((y <= (-36.0d0)) .or. (.not. (y <= 2.7d-8))) then
        tmp = sqrt((x * 9.0d0)) * (y + (-1.0d0))
    else
        tmp = sqrt(x) * ((0.3333333333333333d0 / x) + (-3.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((y <= -36.0) || !(y <= 2.7e-8)) {
		tmp = Math.sqrt((x * 9.0)) * (y + -1.0);
	} else {
		tmp = Math.sqrt(x) * ((0.3333333333333333 / x) + -3.0);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (y <= -36.0) or not (y <= 2.7e-8):
		tmp = math.sqrt((x * 9.0)) * (y + -1.0)
	else:
		tmp = math.sqrt(x) * ((0.3333333333333333 / x) + -3.0)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((y <= -36.0) || !(y <= 2.7e-8))
		tmp = Float64(sqrt(Float64(x * 9.0)) * Float64(y + -1.0));
	else
		tmp = Float64(sqrt(x) * Float64(Float64(0.3333333333333333 / x) + -3.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((y <= -36.0) || ~((y <= 2.7e-8)))
		tmp = sqrt((x * 9.0)) * (y + -1.0);
	else
		tmp = sqrt(x) * ((0.3333333333333333 / x) + -3.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[y, -36.0], N[Not[LessEqual[y, 2.7e-8]], $MachinePrecision]], N[(N[Sqrt[N[(x * 9.0), $MachinePrecision]], $MachinePrecision] * N[(y + -1.0), $MachinePrecision]), $MachinePrecision], N[(N[Sqrt[x], $MachinePrecision] * N[(N[(0.3333333333333333 / x), $MachinePrecision] + -3.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -36 or 2.70000000000000002e-8 < y

   1. Initial program 99.6%

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

   3. Taylor expanded in y around inf 82.8%

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

      1. *-commutative 99.6%

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

      2. metadata-eval 99.6%

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

      3. sqrt-prod 99.7%

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

   5. Applied egg-rr 82.9%

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

   if -36 < y < 2.70000000000000002e-8

   1. Initial program 99.4%

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

      1. *-commutative 99.4%

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

      2. associate-*l* 99.4%

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

      3. associate--l+ 99.4%

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

      4. distribute-lft-in 99.4%

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

      5. fma-define 99.4%

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

      6. sub-neg 99.4%

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

      7. +-commutative 99.4%

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

      8. distribute-lft-in 99.4%

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

      9. metadata-eval 99.4%

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

      10. metadata-eval 99.4%

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

      11. *-commutative 99.4%

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

      12. associate-/r* 99.4%

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

      13. associate-*r/ 99.4%

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

      14. metadata-eval 99.4%

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

      15. metadata-eval 99.4%

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

   3. Simplified 99.4%

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

   5. Taylor expanded in y around 0 98.3%

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

      1. sub-neg 98.3%

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

      2. associate-*r/ 99.1%

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

      3. metadata-eval 99.1%

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

      4. metadata-eval 99.1%

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

      5. +-commutative 99.1%

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

   7. Simplified 99.1%

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

4. Final simplification 91.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -36 \lor \neg \left(y \leq 2.7 \cdot 10^{-8}\right):\\ \;\;\;\;\sqrt{x \cdot 9} \cdot \left(y + -1\right)\\ \mathbf{else}:\\ \;\;\;\;\sqrt{x} \cdot \left(\frac{0.3333333333333333}{x} + -3\right)\\ \end{array} \]
5. Add Preprocessing

Alternative 11: 99.4% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.5%

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

   1. *-commutative 99.5%

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

   2. associate-*l* 99.4%

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

   3. associate--l+ 99.4%

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

   4. distribute-lft-in 99.4%

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

   5. fma-define 99.4%

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

   6. sub-neg 99.4%

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

   7. +-commutative 99.4%

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

   8. distribute-lft-in 99.4%

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

   9. metadata-eval 99.4%

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

   10. metadata-eval 99.4%

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

   11. *-commutative 99.4%

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

   12. associate-/r* 99.4%

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

   13. associate-*r/ 99.4%

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

   14. metadata-eval 99.4%

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

   15. metadata-eval 99.4%

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

3. Simplified 99.4%

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

   1. fma-undefine 99.4%

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

   2. +-commutative 99.4%

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

   3. +-commutative 99.4%

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

6. Applied egg-rr 99.4%

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

7. Final simplification 99.4%

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

Alternative 12: 61.3% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 2.9 \cdot 10^{-5}:\\ \;\;\;\;\sqrt{\frac{0.1111111111111111}{x}}\\ \mathbf{else}:\\ \;\;\;\;\sqrt{x} \cdot -3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x 2.9e-5) (sqrt (/ 0.1111111111111111 x)) (* (sqrt x) -3.0)))

C

double code(double x, double y) {
	double tmp;
	if (x <= 2.9e-5) {
		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 <= 2.9d-5) 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 <= 2.9e-5) {
		tmp = Math.sqrt((0.1111111111111111 / x));
	} else {
		tmp = Math.sqrt(x) * -3.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= 2.9e-5:
		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 <= 2.9e-5)
		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 <= 2.9e-5)
		tmp = sqrt((0.1111111111111111 / x));
	else
		tmp = sqrt(x) * -3.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, 2.9e-5], 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 < 2.9e-5

   1. Initial program 99.4%

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

      1. *-commutative 99.4%

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

      2. associate-*l* 99.4%

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

      3. associate--l+ 99.4%

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

      4. distribute-lft-in 99.4%

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

      5. fma-define 99.4%

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

      6. sub-neg 99.4%

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

      7. +-commutative 99.4%

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

      8. distribute-lft-in 99.4%

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

      9. metadata-eval 99.4%

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

      10. metadata-eval 99.4%

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

      11. *-commutative 99.4%

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

      12. associate-/r* 99.4%

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

      13. associate-*r/ 99.3%

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

      14. metadata-eval 99.3%

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

      15. metadata-eval 99.3%

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

   3. Simplified 99.3%

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

   5. Taylor expanded in x around 0 71.7%

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

      1. metadata-eval 71.7%

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

      2. sqrt-prod 71.9%

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

      3. div-inv 72.7%

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

      4. pow1/2 72.7%

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

   7. Applied egg-rr 72.7%

      \[\leadsto \color{blue}{{\left(\frac{0.1111111111111111}{x}\right)}^{0.5}} \]
   8. Step-by-step derivation

      1. unpow1/2 72.7%

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

   9. Simplified 72.7%

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

   if 2.9e-5 < x

   1. Initial program 99.6%

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

      1. *-commutative 99.6%

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

      2. associate-*l* 99.5%

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

      3. associate--l+ 99.5%

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

      4. distribute-lft-in 99.5%

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

      5. fma-define 99.5%

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

      6. sub-neg 99.5%

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

      7. +-commutative 99.5%

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

      8. distribute-lft-in 99.5%

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

      9. metadata-eval 99.5%

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

      10. metadata-eval 99.5%

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

      11. *-commutative 99.5%

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

      12. associate-/r* 99.5%

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

      13. associate-*r/ 99.5%

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

      14. metadata-eval 99.5%

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

      15. metadata-eval 99.5%

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

   3. Simplified 99.5%

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

   5. Taylor expanded in x around inf 97.9%

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

   6. Taylor expanded in y around 0 45.4%

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

      1. *-commutative 45.4%

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

   8. Simplified 45.4%

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

4. Final simplification 58.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 2.9 \cdot 10^{-5}:\\ \;\;\;\;\sqrt{\frac{0.1111111111111111}{x}}\\ \mathbf{else}:\\ \;\;\;\;\sqrt{x} \cdot -3\\ \end{array} \]
5. Add Preprocessing

Alternative 13: 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 99.5%

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

   1. *-commutative 99.5%

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

   2. associate-*l* 99.4%

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

   3. associate--l+ 99.4%

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

   4. distribute-lft-in 99.4%

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

   5. fma-define 99.4%

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

   6. sub-neg 99.4%

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

   7. +-commutative 99.4%

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

   8. distribute-lft-in 99.4%

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

   9. metadata-eval 99.4%

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

   10. metadata-eval 99.4%

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

   11. *-commutative 99.4%

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

   12. associate-/r* 99.4%

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

   13. associate-*r/ 99.4%

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

   14. metadata-eval 99.4%

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

   15. metadata-eval 99.4%

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

3. Simplified 99.4%

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

5. Taylor expanded in x around inf 64.6%

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

6. Taylor expanded in y around 0 25.1%

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

   1. *-commutative 25.1%

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

8. Simplified 25.1%

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

   1. add-sqr-sqrt 0.0%

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

   2. sqrt-unprod 3.3%

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

   3. swap-sqr 3.3%

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

   4. add-sqr-sqrt 3.3%

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

   5. metadata-eval 3.3%

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

10. Applied egg-rr 3.3%

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

11. Final simplification 3.3%

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

Alternative 14: 37.3% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \sqrt{\frac{0.1111111111111111}{x}} \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (sqrt (/ 0.1111111111111111 x)))

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_] := N[Sqrt[N[(0.1111111111111111 / x), $MachinePrecision]], $MachinePrecision]

Derivation

1. Initial program 99.5%

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

   1. *-commutative 99.5%

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

   2. associate-*l* 99.4%

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

   3. associate--l+ 99.4%

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

   4. distribute-lft-in 99.4%

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

   5. fma-define 99.4%

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

   6. sub-neg 99.4%

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

   7. +-commutative 99.4%

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

   8. distribute-lft-in 99.4%

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

   9. metadata-eval 99.4%

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

   10. metadata-eval 99.4%

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

   11. *-commutative 99.4%

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

   12. associate-/r* 99.4%

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

   13. associate-*r/ 99.4%

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

   14. metadata-eval 99.4%

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

   15. metadata-eval 99.4%

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

3. Simplified 99.4%

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

5. Taylor expanded in x around 0 34.7%

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

   1. metadata-eval 34.7%

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

   2. sqrt-prod 34.8%

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

   3. div-inv 35.1%

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

   4. pow1/2 35.1%

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

7. Applied egg-rr 35.1%

   \[\leadsto \color{blue}{{\left(\frac{0.1111111111111111}{x}\right)}^{0.5}} \]
8. Step-by-step derivation

   1. unpow1/2 35.1%

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

9. Simplified 35.1%

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

10. Final simplification 35.1%

    \[\leadsto \sqrt{\frac{0.1111111111111111}{x}} \]
11. Add Preprocessing

Developer target: 99.4% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

function code(x, y)
	return Float64(3.0 * Float64(Float64(y * sqrt(x)) + Float64(Float64(Float64(1.0 / Float64(x * 9.0)) - 1.0) * sqrt(x))))
end

MATLAB

function tmp = code(x, y)
	tmp = 3.0 * ((y * sqrt(x)) + (((1.0 / (x * 9.0)) - 1.0) * sqrt(x)));
end

Wolfram

code[x_, y_] := N[(3.0 * N[(N[(y * N[Sqrt[x], $MachinePrecision]), $MachinePrecision] + N[(N[(N[(1.0 / N[(x * 9.0), $MachinePrecision]), $MachinePrecision] - 1.0), $MachinePrecision] * N[Sqrt[x], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Reproduce

herbie shell --seed 2024079 
(FPCore (x y)
  :name "Numeric.SpecFunctions:incompleteGamma from math-functions-0.1.5.2, B"
  :precision binary64

  :alt
  (* 3.0 (+ (* y (sqrt x)) (* (- (/ 1.0 (* x 9.0)) 1.0) (sqrt x))))

  (* (* 3.0 (sqrt x)) (- (+ y (/ 1.0 (* x 9.0))) 1.0)))