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

Percentage Accurate: 99.4% → 99.3%

Time: 9.9s

Alternatives: 14

Speedup: N/A×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 99.4% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.3% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.3%

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

   1. associate-*l* 99.3%

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

   2. sub-neg 99.3%

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

   3. +-commutative 99.3%

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

   4. associate-+l+ 99.3%

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

   5. *-commutative 99.3%

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

   6. associate-/r* 99.3%

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

   7. metadata-eval 99.3%

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

   8. metadata-eval 99.3%

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

3. Simplified 99.3%

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

   1. associate-*r* 99.4%

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

   2. associate-+r+ 99.4%

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

   3. distribute-rgt-in 99.4%

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

   4. div-inv 99.3%

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

   5. div-inv 99.4%

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

   6. clear-num 99.3%

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

   7. div-inv 99.3%

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

   8. metadata-eval 99.3%

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

   9. +-commutative 99.3%

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

   10. distribute-rgt-in 99.3%

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

   11. metadata-eval 99.3%

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

   12. sub-neg 99.3%

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

   13. associate--l+ 99.3%

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

   14. distribute-lft-in 99.3%

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

   15. *-commutative 99.3%

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

   16. metadata-eval 99.3%

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

   17. sqrt-prod 99.3%

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

5. Applied egg-rr 99.5%

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

   1. distribute-lft-out 99.5%

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

   2. associate-+r+ 99.5%

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

7. Simplified 99.5%

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

8. Final simplification 99.5%

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

Alternative 2: 60.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \sqrt{x} \cdot \frac{0.3333333333333333}{x}\\ t_1 := \sqrt{x} \cdot -3\\ t_2 := \sqrt{x} \cdot \left(y \cdot 3\right)\\ \mathbf{if}\;x \leq 3.3 \cdot 10^{-45}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq 1.24 \cdot 10^{-31}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq 0.11:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq 1.75 \cdot 10^{+95}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 2.25 \cdot 10^{+135}:\\ \;\;\;\;3 \cdot \left(y \cdot \sqrt{x}\right)\\ \mathbf{elif}\;x \leq 2.9 \cdot 10^{+218}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (* (sqrt x) (/ 0.3333333333333333 x)))
        (t_1 (* (sqrt x) -3.0))
        (t_2 (* (sqrt x) (* y 3.0))))
   (if (<= x 3.3e-45)
     t_0
     (if (<= x 1.24e-31)
       t_2
       (if (<= x 0.11)
         t_0
         (if (<= x 1.75e+95)
           t_1
           (if (<= x 2.25e+135)
             (* 3.0 (* y (sqrt x)))
             (if (<= x 2.9e+218) t_1 t_2))))))))

C

double code(double x, double y) {
	double t_0 = sqrt(x) * (0.3333333333333333 / x);
	double t_1 = sqrt(x) * -3.0;
	double t_2 = sqrt(x) * (y * 3.0);
	double tmp;
	if (x <= 3.3e-45) {
		tmp = t_0;
	} else if (x <= 1.24e-31) {
		tmp = t_2;
	} else if (x <= 0.11) {
		tmp = t_0;
	} else if (x <= 1.75e+95) {
		tmp = t_1;
	} else if (x <= 2.25e+135) {
		tmp = 3.0 * (y * sqrt(x));
	} else if (x <= 2.9e+218) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_0 = sqrt(x) * (0.3333333333333333d0 / x)
    t_1 = sqrt(x) * (-3.0d0)
    t_2 = sqrt(x) * (y * 3.0d0)
    if (x <= 3.3d-45) then
        tmp = t_0
    else if (x <= 1.24d-31) then
        tmp = t_2
    else if (x <= 0.11d0) then
        tmp = t_0
    else if (x <= 1.75d+95) then
        tmp = t_1
    else if (x <= 2.25d+135) then
        tmp = 3.0d0 * (y * sqrt(x))
    else if (x <= 2.9d+218) then
        tmp = t_1
    else
        tmp = t_2
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double t_0 = Math.sqrt(x) * (0.3333333333333333 / x);
	double t_1 = Math.sqrt(x) * -3.0;
	double t_2 = Math.sqrt(x) * (y * 3.0);
	double tmp;
	if (x <= 3.3e-45) {
		tmp = t_0;
	} else if (x <= 1.24e-31) {
		tmp = t_2;
	} else if (x <= 0.11) {
		tmp = t_0;
	} else if (x <= 1.75e+95) {
		tmp = t_1;
	} else if (x <= 2.25e+135) {
		tmp = 3.0 * (y * Math.sqrt(x));
	} else if (x <= 2.9e+218) {
		tmp = t_1;
	} else {
		tmp = t_2;
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = math.sqrt(x) * (0.3333333333333333 / x)
	t_1 = math.sqrt(x) * -3.0
	t_2 = math.sqrt(x) * (y * 3.0)
	tmp = 0
	if x <= 3.3e-45:
		tmp = t_0
	elif x <= 1.24e-31:
		tmp = t_2
	elif x <= 0.11:
		tmp = t_0
	elif x <= 1.75e+95:
		tmp = t_1
	elif x <= 2.25e+135:
		tmp = 3.0 * (y * math.sqrt(x))
	elif x <= 2.9e+218:
		tmp = t_1
	else:
		tmp = t_2
	return tmp

Julia

function code(x, y)
	t_0 = Float64(sqrt(x) * Float64(0.3333333333333333 / x))
	t_1 = Float64(sqrt(x) * -3.0)
	t_2 = Float64(sqrt(x) * Float64(y * 3.0))
	tmp = 0.0
	if (x <= 3.3e-45)
		tmp = t_0;
	elseif (x <= 1.24e-31)
		tmp = t_2;
	elseif (x <= 0.11)
		tmp = t_0;
	elseif (x <= 1.75e+95)
		tmp = t_1;
	elseif (x <= 2.25e+135)
		tmp = Float64(3.0 * Float64(y * sqrt(x)));
	elseif (x <= 2.9e+218)
		tmp = t_1;
	else
		tmp = t_2;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = sqrt(x) * (0.3333333333333333 / x);
	t_1 = sqrt(x) * -3.0;
	t_2 = sqrt(x) * (y * 3.0);
	tmp = 0.0;
	if (x <= 3.3e-45)
		tmp = t_0;
	elseif (x <= 1.24e-31)
		tmp = t_2;
	elseif (x <= 0.11)
		tmp = t_0;
	elseif (x <= 1.75e+95)
		tmp = t_1;
	elseif (x <= 2.25e+135)
		tmp = 3.0 * (y * sqrt(x));
	elseif (x <= 2.9e+218)
		tmp = t_1;
	else
		tmp = t_2;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(N[Sqrt[x], $MachinePrecision] * N[(0.3333333333333333 / x), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(N[Sqrt[x], $MachinePrecision] * -3.0), $MachinePrecision]}, Block[{t$95$2 = N[(N[Sqrt[x], $MachinePrecision] * N[(y * 3.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, 3.3e-45], t$95$0, If[LessEqual[x, 1.24e-31], t$95$2, If[LessEqual[x, 0.11], t$95$0, If[LessEqual[x, 1.75e+95], t$95$1, If[LessEqual[x, 2.25e+135], N[(3.0 * N[(y * N[Sqrt[x], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2.9e+218], t$95$1, t$95$2]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if x < 3.3000000000000001e-45 or 1.24000000000000004e-31 < x < 0.110000000000000001

   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. distribute-lft-out-- 99.3%

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

      2. *-rgt-identity 99.3%

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

      3. associate-*l* 99.3%

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

      4. *-commutative 99.3%

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

      5. associate-*r* 99.2%

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

      6. distribute-rgt-out-- 99.3%

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

      7. +-commutative 99.3%

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

      8. distribute-lft-in 99.3%

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

      9. associate--l+ 99.3%

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

      10. *-commutative 99.3%

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

      11. associate-/r* 99.2%

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

      12. associate-*r/ 99.4%

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

      13. metadata-eval 99.4%

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

      14. metadata-eval 99.4%

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

      15. sub-neg 99.4%

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

      16. metadata-eval 99.4%

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

      17. metadata-eval 99.4%

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

      18. metadata-eval 99.4%

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

      19. fma-def 99.4%

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

   3. Simplified 99.4%

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

   4. Taylor expanded in x around 0 77.5%

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

   if 3.3000000000000001e-45 < x < 1.24000000000000004e-31 or 2.8999999999999999e218 < 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. distribute-lft-out-- 99.6%

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

      2. *-rgt-identity 99.6%

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

      3. associate-*l* 99.5%

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

      4. *-commutative 99.5%

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

      5. associate-*r* 99.5%

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

      6. distribute-rgt-out-- 99.5%

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

      7. +-commutative 99.5%

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

      8. distribute-lft-in 99.5%

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

      9. associate--l+ 99.5%

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

      10. *-commutative 99.5%

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

      11. associate-/r* 99.5%

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

      12. associate-*r/ 99.5%

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

      13. metadata-eval 99.5%

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

      14. metadata-eval 99.5%

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

      15. sub-neg 99.5%

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

      16. metadata-eval 99.5%

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

      17. metadata-eval 99.5%

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

      18. metadata-eval 99.5%

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

      19. fma-def 99.6%

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

   3. Simplified 99.6%

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

   4. Taylor expanded in y around inf 66.1%

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

   if 0.110000000000000001 < x < 1.75e95 or 2.25000000000000004e135 < x < 2.8999999999999999e218

   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. distribute-lft-out-- 99.3%

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

      2. *-rgt-identity 99.3%

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

      3. associate-*l* 99.3%

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

      4. *-commutative 99.3%

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

      5. associate-*r* 99.3%

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

      6. distribute-rgt-out-- 99.3%

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

      7. +-commutative 99.3%

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

      8. distribute-lft-in 99.3%

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

      9. associate--l+ 99.3%

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

      10. *-commutative 99.3%

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

      11. associate-/r* 99.3%

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

      12. associate-*r/ 99.3%

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

      13. metadata-eval 99.3%

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

      14. metadata-eval 99.3%

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

      15. sub-neg 99.3%

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

      16. metadata-eval 99.3%

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

      17. metadata-eval 99.3%

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

      18. metadata-eval 99.3%

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

      19. fma-def 99.3%

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

   3. Simplified 99.3%

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

   4. Taylor expanded in y around 0 70.7%

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

      1. sub-neg 70.7%

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

      2. associate-*r/ 70.6%

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

      3. metadata-eval 70.6%

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

      4. metadata-eval 70.6%

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

   6. Simplified 70.6%

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

   7. Taylor expanded in x around inf 65.4%

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

   if 1.75e95 < x < 2.25000000000000004e135

   1. Initial program 99.2%

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

      1. distribute-lft-out-- 99.2%

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

      2. *-rgt-identity 99.2%

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

      3. associate-*l* 99.3%

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

      4. *-commutative 99.3%

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

      5. associate-*r* 99.1%

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

      6. distribute-rgt-out-- 99.1%

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

      7. +-commutative 99.1%

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

      8. distribute-lft-in 99.1%

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

      9. associate--l+ 99.1%

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

      10. *-commutative 99.1%

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

      11. associate-/r* 99.1%

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

      12. associate-*r/ 99.1%

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

      13. metadata-eval 99.1%

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

      14. metadata-eval 99.1%

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

      15. sub-neg 99.1%

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

      16. metadata-eval 99.1%

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

      17. metadata-eval 99.1%

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

      18. metadata-eval 99.1%

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

      19. fma-def 99.3%

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

   3. Simplified 99.3%

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

   4. Taylor expanded in y around inf 77.8%

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

4. Final simplification 71.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 3.3 \cdot 10^{-45}:\\ \;\;\;\;\sqrt{x} \cdot \frac{0.3333333333333333}{x}\\ \mathbf{elif}\;x \leq 1.24 \cdot 10^{-31}:\\ \;\;\;\;\sqrt{x} \cdot \left(y \cdot 3\right)\\ \mathbf{elif}\;x \leq 0.11:\\ \;\;\;\;\sqrt{x} \cdot \frac{0.3333333333333333}{x}\\ \mathbf{elif}\;x \leq 1.75 \cdot 10^{+95}:\\ \;\;\;\;\sqrt{x} \cdot -3\\ \mathbf{elif}\;x \leq 2.25 \cdot 10^{+135}:\\ \;\;\;\;3 \cdot \left(y \cdot \sqrt{x}\right)\\ \mathbf{elif}\;x \leq 2.9 \cdot 10^{+218}:\\ \;\;\;\;\sqrt{x} \cdot -3\\ \mathbf{else}:\\ \;\;\;\;\sqrt{x} \cdot \left(y \cdot 3\right)\\ \end{array} \]

Alternative 3: 60.6% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \sqrt{x} \cdot -3\\ t_1 := \sqrt{x} \cdot \left(y \cdot 3\right)\\ \mathbf{if}\;x \leq 3.9 \cdot 10^{-45}:\\ \;\;\;\;\sqrt{x} \cdot \frac{0.3333333333333333}{x}\\ \mathbf{elif}\;x \leq 1.24 \cdot 10^{-31}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 0.11:\\ \;\;\;\;3 \cdot \left(\frac{0.1111111111111111}{x} \cdot \sqrt{x}\right)\\ \mathbf{elif}\;x \leq 8.8 \cdot 10^{+93}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq 2.4 \cdot 10^{+136}:\\ \;\;\;\;3 \cdot \left(y \cdot \sqrt{x}\right)\\ \mathbf{elif}\;x \leq 2.7 \cdot 10^{+217}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (* (sqrt x) -3.0)) (t_1 (* (sqrt x) (* y 3.0))))
   (if (<= x 3.9e-45)
     (* (sqrt x) (/ 0.3333333333333333 x))
     (if (<= x 1.24e-31)
       t_1
       (if (<= x 0.11)
         (* 3.0 (* (/ 0.1111111111111111 x) (sqrt x)))
         (if (<= x 8.8e+93)
           t_0
           (if (<= x 2.4e+136)
             (* 3.0 (* y (sqrt x)))
             (if (<= x 2.7e+217) t_0 t_1))))))))

C

double code(double x, double y) {
	double t_0 = sqrt(x) * -3.0;
	double t_1 = sqrt(x) * (y * 3.0);
	double tmp;
	if (x <= 3.9e-45) {
		tmp = sqrt(x) * (0.3333333333333333 / x);
	} else if (x <= 1.24e-31) {
		tmp = t_1;
	} else if (x <= 0.11) {
		tmp = 3.0 * ((0.1111111111111111 / x) * sqrt(x));
	} else if (x <= 8.8e+93) {
		tmp = t_0;
	} else if (x <= 2.4e+136) {
		tmp = 3.0 * (y * sqrt(x));
	} else if (x <= 2.7e+217) {
		tmp = t_0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = sqrt(x) * (-3.0d0)
    t_1 = sqrt(x) * (y * 3.0d0)
    if (x <= 3.9d-45) then
        tmp = sqrt(x) * (0.3333333333333333d0 / x)
    else if (x <= 1.24d-31) then
        tmp = t_1
    else if (x <= 0.11d0) then
        tmp = 3.0d0 * ((0.1111111111111111d0 / x) * sqrt(x))
    else if (x <= 8.8d+93) then
        tmp = t_0
    else if (x <= 2.4d+136) then
        tmp = 3.0d0 * (y * sqrt(x))
    else if (x <= 2.7d+217) then
        tmp = t_0
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double t_0 = Math.sqrt(x) * -3.0;
	double t_1 = Math.sqrt(x) * (y * 3.0);
	double tmp;
	if (x <= 3.9e-45) {
		tmp = Math.sqrt(x) * (0.3333333333333333 / x);
	} else if (x <= 1.24e-31) {
		tmp = t_1;
	} else if (x <= 0.11) {
		tmp = 3.0 * ((0.1111111111111111 / x) * Math.sqrt(x));
	} else if (x <= 8.8e+93) {
		tmp = t_0;
	} else if (x <= 2.4e+136) {
		tmp = 3.0 * (y * Math.sqrt(x));
	} else if (x <= 2.7e+217) {
		tmp = t_0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = math.sqrt(x) * -3.0
	t_1 = math.sqrt(x) * (y * 3.0)
	tmp = 0
	if x <= 3.9e-45:
		tmp = math.sqrt(x) * (0.3333333333333333 / x)
	elif x <= 1.24e-31:
		tmp = t_1
	elif x <= 0.11:
		tmp = 3.0 * ((0.1111111111111111 / x) * math.sqrt(x))
	elif x <= 8.8e+93:
		tmp = t_0
	elif x <= 2.4e+136:
		tmp = 3.0 * (y * math.sqrt(x))
	elif x <= 2.7e+217:
		tmp = t_0
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y)
	t_0 = Float64(sqrt(x) * -3.0)
	t_1 = Float64(sqrt(x) * Float64(y * 3.0))
	tmp = 0.0
	if (x <= 3.9e-45)
		tmp = Float64(sqrt(x) * Float64(0.3333333333333333 / x));
	elseif (x <= 1.24e-31)
		tmp = t_1;
	elseif (x <= 0.11)
		tmp = Float64(3.0 * Float64(Float64(0.1111111111111111 / x) * sqrt(x)));
	elseif (x <= 8.8e+93)
		tmp = t_0;
	elseif (x <= 2.4e+136)
		tmp = Float64(3.0 * Float64(y * sqrt(x)));
	elseif (x <= 2.7e+217)
		tmp = t_0;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = sqrt(x) * -3.0;
	t_1 = sqrt(x) * (y * 3.0);
	tmp = 0.0;
	if (x <= 3.9e-45)
		tmp = sqrt(x) * (0.3333333333333333 / x);
	elseif (x <= 1.24e-31)
		tmp = t_1;
	elseif (x <= 0.11)
		tmp = 3.0 * ((0.1111111111111111 / x) * sqrt(x));
	elseif (x <= 8.8e+93)
		tmp = t_0;
	elseif (x <= 2.4e+136)
		tmp = 3.0 * (y * sqrt(x));
	elseif (x <= 2.7e+217)
		tmp = t_0;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(N[Sqrt[x], $MachinePrecision] * -3.0), $MachinePrecision]}, Block[{t$95$1 = N[(N[Sqrt[x], $MachinePrecision] * N[(y * 3.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, 3.9e-45], N[(N[Sqrt[x], $MachinePrecision] * N[(0.3333333333333333 / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.24e-31], t$95$1, If[LessEqual[x, 0.11], N[(3.0 * N[(N[(0.1111111111111111 / x), $MachinePrecision] * N[Sqrt[x], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 8.8e+93], t$95$0, If[LessEqual[x, 2.4e+136], N[(3.0 * N[(y * N[Sqrt[x], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2.7e+217], t$95$0, t$95$1]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if x < 3.9e-45

   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. distribute-lft-out-- 99.3%

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

      2. *-rgt-identity 99.3%

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

      3. associate-*l* 99.3%

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

      4. *-commutative 99.3%

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

      5. associate-*r* 99.3%

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

      6. distribute-rgt-out-- 99.3%

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

      7. +-commutative 99.3%

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

      8. distribute-lft-in 99.3%

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

      9. associate--l+ 99.3%

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

      10. *-commutative 99.3%

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

      11. associate-/r* 99.2%

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

      12. associate-*r/ 99.4%

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

      13. metadata-eval 99.4%

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

      14. metadata-eval 99.4%

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

      15. sub-neg 99.4%

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

      16. metadata-eval 99.4%

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

      17. metadata-eval 99.4%

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

      18. metadata-eval 99.4%

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

      19. fma-def 99.4%

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

   3. Simplified 99.4%

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

   4. Taylor expanded in x around 0 79.6%

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

   if 3.9e-45 < x < 1.24000000000000004e-31 or 2.70000000000000003e217 < 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. distribute-lft-out-- 99.6%

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

      2. *-rgt-identity 99.6%

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

      3. associate-*l* 99.5%

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

      4. *-commutative 99.5%

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

      5. associate-*r* 99.5%

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

      6. distribute-rgt-out-- 99.5%

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

      7. +-commutative 99.5%

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

      8. distribute-lft-in 99.5%

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

      9. associate--l+ 99.5%

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

      10. *-commutative 99.5%

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

      11. associate-/r* 99.5%

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

      12. associate-*r/ 99.5%

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

      13. metadata-eval 99.5%

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

      14. metadata-eval 99.5%

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

      15. sub-neg 99.5%

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

      16. metadata-eval 99.5%

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

      17. metadata-eval 99.5%

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

      18. metadata-eval 99.5%

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

      19. fma-def 99.6%

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

   3. Simplified 99.6%

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

   4. Taylor expanded in y around inf 66.1%

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

   if 1.24000000000000004e-31 < x < 0.110000000000000001

   1. Initial program 99.4%

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

      1. associate-*l* 99.1%

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

      2. sub-neg 99.1%

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

      3. +-commutative 99.1%

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

      4. associate-+l+ 99.1%

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

      5. *-commutative 99.1%

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

      6. associate-/r* 99.2%

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

      7. metadata-eval 99.2%

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

      8. metadata-eval 99.2%

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

   3. Simplified 99.2%

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

   4. Taylor expanded in x around 0 64.8%

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

   if 0.110000000000000001 < x < 8.80000000000000084e93 or 2.4e136 < x < 2.70000000000000003e217

   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. distribute-lft-out-- 99.3%

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

      2. *-rgt-identity 99.3%

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

      3. associate-*l* 99.3%

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

      4. *-commutative 99.3%

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

      5. associate-*r* 99.3%

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

      6. distribute-rgt-out-- 99.3%

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

      7. +-commutative 99.3%

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

      8. distribute-lft-in 99.3%

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

      9. associate--l+ 99.3%

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

      10. *-commutative 99.3%

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

      11. associate-/r* 99.3%

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

      12. associate-*r/ 99.3%

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

      13. metadata-eval 99.3%

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

      14. metadata-eval 99.3%

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

      15. sub-neg 99.3%

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

      16. metadata-eval 99.3%

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

      17. metadata-eval 99.3%

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

      18. metadata-eval 99.3%

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

      19. fma-def 99.3%

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

   3. Simplified 99.3%

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

   4. Taylor expanded in y around 0 70.7%

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

      1. sub-neg 70.7%

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

      2. associate-*r/ 70.6%

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

      3. metadata-eval 70.6%

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

      4. metadata-eval 70.6%

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

   6. Simplified 70.6%

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

   7. Taylor expanded in x around inf 65.4%

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

   if 8.80000000000000084e93 < x < 2.4e136

   1. Initial program 99.2%

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

      1. distribute-lft-out-- 99.2%

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

      2. *-rgt-identity 99.2%

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

      3. associate-*l* 99.3%

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

      4. *-commutative 99.3%

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

      5. associate-*r* 99.1%

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

      6. distribute-rgt-out-- 99.1%

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

      7. +-commutative 99.1%

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

      8. distribute-lft-in 99.1%

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

      9. associate--l+ 99.1%

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

      10. *-commutative 99.1%

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

      11. associate-/r* 99.1%

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

      12. associate-*r/ 99.1%

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

      13. metadata-eval 99.1%

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

      14. metadata-eval 99.1%

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

      15. sub-neg 99.1%

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

      16. metadata-eval 99.1%

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

      17. metadata-eval 99.1%

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

      18. metadata-eval 99.1%

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

      19. fma-def 99.3%

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

   3. Simplified 99.3%

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

   4. Taylor expanded in y around inf 77.8%

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

4. Final simplification 71.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 3.9 \cdot 10^{-45}:\\ \;\;\;\;\sqrt{x} \cdot \frac{0.3333333333333333}{x}\\ \mathbf{elif}\;x \leq 1.24 \cdot 10^{-31}:\\ \;\;\;\;\sqrt{x} \cdot \left(y \cdot 3\right)\\ \mathbf{elif}\;x \leq 0.11:\\ \;\;\;\;3 \cdot \left(\frac{0.1111111111111111}{x} \cdot \sqrt{x}\right)\\ \mathbf{elif}\;x \leq 8.8 \cdot 10^{+93}:\\ \;\;\;\;\sqrt{x} \cdot -3\\ \mathbf{elif}\;x \leq 2.4 \cdot 10^{+136}:\\ \;\;\;\;3 \cdot \left(y \cdot \sqrt{x}\right)\\ \mathbf{elif}\;x \leq 2.7 \cdot 10^{+217}:\\ \;\;\;\;\sqrt{x} \cdot -3\\ \mathbf{else}:\\ \;\;\;\;\sqrt{x} \cdot \left(y \cdot 3\right)\\ \end{array} \]

Alternative 4: 85.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -8.8 \cdot 10^{-7}:\\ \;\;\;\;\left(y + -1\right) \cdot \left(\sqrt{x} \cdot 3\right)\\ \mathbf{elif}\;y \leq 2.8 \cdot 10^{+29}:\\ \;\;\;\;3 \cdot \left(\sqrt{x} \cdot \left(\frac{0.1111111111111111}{x} + -1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\sqrt{x} \cdot \left(y \cdot 3 - 3\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -8.8e-7)
   (* (+ y -1.0) (* (sqrt x) 3.0))
   (if (<= y 2.8e+29)
     (* 3.0 (* (sqrt x) (+ (/ 0.1111111111111111 x) -1.0)))
     (* (sqrt x) (- (* y 3.0) 3.0)))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -8.8e-7) {
		tmp = (y + -1.0) * (sqrt(x) * 3.0);
	} else if (y <= 2.8e+29) {
		tmp = 3.0 * (sqrt(x) * ((0.1111111111111111 / x) + -1.0));
	} else {
		tmp = sqrt(x) * ((y * 3.0) - 3.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (y <= (-8.8d-7)) then
        tmp = (y + (-1.0d0)) * (sqrt(x) * 3.0d0)
    else if (y <= 2.8d+29) then
        tmp = 3.0d0 * (sqrt(x) * ((0.1111111111111111d0 / x) + (-1.0d0)))
    else
        tmp = sqrt(x) * ((y * 3.0d0) - 3.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (y <= -8.8e-7) {
		tmp = (y + -1.0) * (Math.sqrt(x) * 3.0);
	} else if (y <= 2.8e+29) {
		tmp = 3.0 * (Math.sqrt(x) * ((0.1111111111111111 / x) + -1.0));
	} else {
		tmp = Math.sqrt(x) * ((y * 3.0) - 3.0);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -8.8e-7:
		tmp = (y + -1.0) * (math.sqrt(x) * 3.0)
	elif y <= 2.8e+29:
		tmp = 3.0 * (math.sqrt(x) * ((0.1111111111111111 / x) + -1.0))
	else:
		tmp = math.sqrt(x) * ((y * 3.0) - 3.0)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -8.8e-7)
		tmp = Float64(Float64(y + -1.0) * Float64(sqrt(x) * 3.0));
	elseif (y <= 2.8e+29)
		tmp = Float64(3.0 * Float64(sqrt(x) * Float64(Float64(0.1111111111111111 / x) + -1.0)));
	else
		tmp = Float64(sqrt(x) * Float64(Float64(y * 3.0) - 3.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -8.8e-7)
		tmp = (y + -1.0) * (sqrt(x) * 3.0);
	elseif (y <= 2.8e+29)
		tmp = 3.0 * (sqrt(x) * ((0.1111111111111111 / x) + -1.0));
	else
		tmp = sqrt(x) * ((y * 3.0) - 3.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -8.8e-7], N[(N[(y + -1.0), $MachinePrecision] * N[(N[Sqrt[x], $MachinePrecision] * 3.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.8e+29], N[(3.0 * N[(N[Sqrt[x], $MachinePrecision] * N[(N[(0.1111111111111111 / x), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[Sqrt[x], $MachinePrecision] * N[(N[(y * 3.0), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -8.8000000000000004e-7

   1. Initial program 99.5%

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

      1. associate-*l* 99.4%

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

      2. sub-neg 99.4%

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

      3. +-commutative 99.4%

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

      4. associate-+l+ 99.4%

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

      5. *-commutative 99.4%

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

      6. associate-/r* 99.4%

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

      7. metadata-eval 99.4%

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

      8. metadata-eval 99.4%

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

   3. Simplified 99.4%

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

      1. associate-*r* 99.4%

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

      2. associate-+r+ 99.4%

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

      3. distribute-rgt-in 99.4%

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

      4. div-inv 99.3%

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

      5. div-inv 99.4%

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

      6. clear-num 99.4%

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

      7. div-inv 99.5%

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

      8. metadata-eval 99.5%

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

      9. +-commutative 99.5%

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

      10. distribute-rgt-in 99.5%

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

      11. metadata-eval 99.5%

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

      12. sub-neg 99.5%

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

      13. associate--l+ 99.5%

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

      14. distribute-lft-in 99.4%

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

      15. *-commutative 99.4%

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

      16. metadata-eval 99.4%

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

      17. sqrt-prod 99.4%

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

   5. Applied egg-rr 99.4%

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

      1. distribute-lft-out 99.4%

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

      2. associate-+r+ 99.4%

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

   7. Simplified 99.4%

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

   8. Taylor expanded in y around inf 77.0%

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

   9. Taylor expanded in y around 0 77.0%

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

       1. *-commutative 77.0%

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

       2. metadata-eval 77.0%

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

       3. associate-*l* 77.0%

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

       4. associate-*r* 77.0%

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

       5. *-commutative 77.0%

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

       6. distribute-lft-in 77.0%

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

       7. +-commutative 77.0%

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

   11. Simplified 77.0%

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

   if -8.8000000000000004e-7 < y < 2.8e29

   1. Initial program 99.3%

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

      1. associate-*l* 99.4%

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

      2. sub-neg 99.4%

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

      3. +-commutative 99.4%

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

      4. associate-+l+ 99.4%

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

      5. *-commutative 99.4%

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

      6. associate-/r* 99.4%

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

      7. metadata-eval 99.4%

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

      8. metadata-eval 99.4%

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

   3. Simplified 99.4%

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

   4. Taylor expanded in y around 0 98.0%

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

      1. sub-neg 98.0%

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

      2. associate-*r/ 98.0%

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

      3. metadata-eval 98.0%

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

      4. metadata-eval 98.0%

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

   6. Simplified 98.0%

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

   if 2.8e29 < y

   1. Initial program 99.3%

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

      1. distribute-lft-out-- 99.3%

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

      2. *-rgt-identity 99.3%

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

      3. associate-*l* 99.2%

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

      4. *-commutative 99.2%

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

      5. associate-*r* 99.4%

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

      6. distribute-rgt-out-- 99.4%

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

      7. +-commutative 99.4%

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

      8. distribute-lft-in 99.4%

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

      9. associate--l+ 99.4%

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

      10. *-commutative 99.4%

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

      11. associate-/r* 99.4%

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

      12. associate-*r/ 99.4%

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

      13. metadata-eval 99.4%

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

      14. metadata-eval 99.4%

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

      15. sub-neg 99.4%

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

      16. metadata-eval 99.4%

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

      17. metadata-eval 99.4%

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

      18. metadata-eval 99.4%

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

      19. fma-def 99.6%

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

   3. Simplified 99.6%

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

   4. Taylor expanded in x around inf 82.4%

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

4. Final simplification 90.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -8.8 \cdot 10^{-7}:\\ \;\;\;\;\left(y + -1\right) \cdot \left(\sqrt{x} \cdot 3\right)\\ \mathbf{elif}\;y \leq 2.8 \cdot 10^{+29}:\\ \;\;\;\;3 \cdot \left(\sqrt{x} \cdot \left(\frac{0.1111111111111111}{x} + -1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\sqrt{x} \cdot \left(y \cdot 3 - 3\right)\\ \end{array} \]

Alternative 5: 85.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -4.8 \cdot 10^{-7}:\\ \;\;\;\;\left(y + -1\right) \cdot \left(\sqrt{x} \cdot 3\right)\\ \mathbf{elif}\;y \leq 2.5 \cdot 10^{+29}:\\ \;\;\;\;\sqrt{x \cdot 9} \cdot \left(\frac{0.1111111111111111}{x} + -1\right)\\ \mathbf{else}:\\ \;\;\;\;\sqrt{x} \cdot \left(y \cdot 3 - 3\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -4.8e-7)
   (* (+ y -1.0) (* (sqrt x) 3.0))
   (if (<= y 2.5e+29)
     (* (sqrt (* x 9.0)) (+ (/ 0.1111111111111111 x) -1.0))
     (* (sqrt x) (- (* y 3.0) 3.0)))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -4.8e-7) {
		tmp = (y + -1.0) * (sqrt(x) * 3.0);
	} else if (y <= 2.5e+29) {
		tmp = sqrt((x * 9.0)) * ((0.1111111111111111 / x) + -1.0);
	} else {
		tmp = sqrt(x) * ((y * 3.0) - 3.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (y <= (-4.8d-7)) then
        tmp = (y + (-1.0d0)) * (sqrt(x) * 3.0d0)
    else if (y <= 2.5d+29) then
        tmp = sqrt((x * 9.0d0)) * ((0.1111111111111111d0 / x) + (-1.0d0))
    else
        tmp = sqrt(x) * ((y * 3.0d0) - 3.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (y <= -4.8e-7) {
		tmp = (y + -1.0) * (Math.sqrt(x) * 3.0);
	} else if (y <= 2.5e+29) {
		tmp = Math.sqrt((x * 9.0)) * ((0.1111111111111111 / x) + -1.0);
	} else {
		tmp = Math.sqrt(x) * ((y * 3.0) - 3.0);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -4.8e-7:
		tmp = (y + -1.0) * (math.sqrt(x) * 3.0)
	elif y <= 2.5e+29:
		tmp = math.sqrt((x * 9.0)) * ((0.1111111111111111 / x) + -1.0)
	else:
		tmp = math.sqrt(x) * ((y * 3.0) - 3.0)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -4.8e-7)
		tmp = Float64(Float64(y + -1.0) * Float64(sqrt(x) * 3.0));
	elseif (y <= 2.5e+29)
		tmp = Float64(sqrt(Float64(x * 9.0)) * Float64(Float64(0.1111111111111111 / x) + -1.0));
	else
		tmp = Float64(sqrt(x) * Float64(Float64(y * 3.0) - 3.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -4.8e-7)
		tmp = (y + -1.0) * (sqrt(x) * 3.0);
	elseif (y <= 2.5e+29)
		tmp = sqrt((x * 9.0)) * ((0.1111111111111111 / x) + -1.0);
	else
		tmp = sqrt(x) * ((y * 3.0) - 3.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -4.8e-7], N[(N[(y + -1.0), $MachinePrecision] * N[(N[Sqrt[x], $MachinePrecision] * 3.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.5e+29], N[(N[Sqrt[N[(x * 9.0), $MachinePrecision]], $MachinePrecision] * N[(N[(0.1111111111111111 / x), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision], N[(N[Sqrt[x], $MachinePrecision] * N[(N[(y * 3.0), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -4.79999999999999957e-7

   1. Initial program 99.5%

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

      1. associate-*l* 99.4%

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

      2. sub-neg 99.4%

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

      3. +-commutative 99.4%

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

      4. associate-+l+ 99.4%

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

      5. *-commutative 99.4%

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

      6. associate-/r* 99.4%

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

      7. metadata-eval 99.4%

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

      8. metadata-eval 99.4%

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

   3. Simplified 99.4%

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

      1. associate-*r* 99.4%

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

      2. associate-+r+ 99.4%

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

      3. distribute-rgt-in 99.4%

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

      4. div-inv 99.3%

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

      5. div-inv 99.4%

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

      6. clear-num 99.4%

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

      7. div-inv 99.5%

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

      8. metadata-eval 99.5%

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

      9. +-commutative 99.5%

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

      10. distribute-rgt-in 99.5%

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

      11. metadata-eval 99.5%

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

      12. sub-neg 99.5%

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

      13. associate--l+ 99.5%

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

      14. distribute-lft-in 99.4%

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

      15. *-commutative 99.4%

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

      16. metadata-eval 99.4%

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

      17. sqrt-prod 99.4%

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

   5. Applied egg-rr 99.4%

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

      1. distribute-lft-out 99.4%

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

      2. associate-+r+ 99.4%

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

   7. Simplified 99.4%

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

   8. Taylor expanded in y around inf 77.0%

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

   9. Taylor expanded in y around 0 77.0%

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

       1. *-commutative 77.0%

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

       2. metadata-eval 77.0%

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

       3. associate-*l* 77.0%

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

       4. associate-*r* 77.0%

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

       5. *-commutative 77.0%

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

       6. distribute-lft-in 77.0%

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

       7. +-commutative 77.0%

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

   11. Simplified 77.0%

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

   if -4.79999999999999957e-7 < y < 2.5e29

   1. Initial program 99.3%

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

      1. associate-*l* 99.4%

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

      2. sub-neg 99.4%

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

      3. +-commutative 99.4%

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

      4. associate-+l+ 99.4%

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

      5. *-commutative 99.4%

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

      6. associate-/r* 99.4%

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

      7. metadata-eval 99.4%

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

      8. metadata-eval 99.4%

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

   3. Simplified 99.4%

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

      1. associate-*r* 99.4%

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

      2. associate-+r+ 99.4%

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

      3. distribute-rgt-in 99.4%

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

      4. div-inv 99.3%

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

      5. div-inv 99.4%

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

      6. clear-num 99.3%

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

      7. div-inv 99.3%

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

      8. metadata-eval 99.3%

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

      9. +-commutative 99.3%

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

      10. distribute-rgt-in 99.3%

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

      11. metadata-eval 99.3%

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

      12. sub-neg 99.3%

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

      13. associate--l+ 99.3%

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

      14. distribute-lft-in 99.3%

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

      15. *-commutative 99.3%

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

      16. metadata-eval 99.3%

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

      17. sqrt-prod 99.3%

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

   5. Applied egg-rr 99.6%

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

      1. distribute-lft-out 99.6%

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

      2. associate-+r+ 99.6%

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

   7. Simplified 99.6%

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

   8. Taylor expanded in y around 0 98.2%

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

   if 2.5e29 < y

   1. Initial program 99.3%

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

      1. distribute-lft-out-- 99.3%

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

      2. *-rgt-identity 99.3%

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

      3. associate-*l* 99.2%

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

      4. *-commutative 99.2%

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

      5. associate-*r* 99.4%

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

      6. distribute-rgt-out-- 99.4%

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

      7. +-commutative 99.4%

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

      8. distribute-lft-in 99.4%

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

      9. associate--l+ 99.4%

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

      10. *-commutative 99.4%

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

      11. associate-/r* 99.4%

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

      12. associate-*r/ 99.4%

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

      13. metadata-eval 99.4%

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

      14. metadata-eval 99.4%

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

      15. sub-neg 99.4%

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

      16. metadata-eval 99.4%

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

      17. metadata-eval 99.4%

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

      18. metadata-eval 99.4%

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

      19. fma-def 99.6%

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

   3. Simplified 99.6%

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

   4. Taylor expanded in x around inf 82.4%

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

4. Final simplification 90.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -4.8 \cdot 10^{-7}:\\ \;\;\;\;\left(y + -1\right) \cdot \left(\sqrt{x} \cdot 3\right)\\ \mathbf{elif}\;y \leq 2.5 \cdot 10^{+29}:\\ \;\;\;\;\sqrt{x \cdot 9} \cdot \left(\frac{0.1111111111111111}{x} + -1\right)\\ \mathbf{else}:\\ \;\;\;\;\sqrt{x} \cdot \left(y \cdot 3 - 3\right)\\ \end{array} \]

Alternative 6: 85.8% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -8.8 \cdot 10^{-7} \lor \neg \left(y \leq 6 \cdot 10^{+29}\right):\\ \;\;\;\;\sqrt{x} \cdot \left(y \cdot 3 - 3\right)\\ \mathbf{else}:\\ \;\;\;\;\sqrt{x} \cdot \left(-3 + \frac{0.3333333333333333}{x}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= y -8.8e-7) (not (<= y 6e+29)))
   (* (sqrt x) (- (* y 3.0) 3.0))
   (* (sqrt x) (+ -3.0 (/ 0.3333333333333333 x)))))

C

double code(double x, double y) {
	double tmp;
	if ((y <= -8.8e-7) || !(y <= 6e+29)) {
		tmp = sqrt(x) * ((y * 3.0) - 3.0);
	} else {
		tmp = sqrt(x) * (-3.0 + (0.3333333333333333 / x));
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if ((y <= (-8.8d-7)) .or. (.not. (y <= 6d+29))) then
        tmp = sqrt(x) * ((y * 3.0d0) - 3.0d0)
    else
        tmp = sqrt(x) * ((-3.0d0) + (0.3333333333333333d0 / x))
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((y <= -8.8e-7) || !(y <= 6e+29)) {
		tmp = Math.sqrt(x) * ((y * 3.0) - 3.0);
	} else {
		tmp = Math.sqrt(x) * (-3.0 + (0.3333333333333333 / x));
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (y <= -8.8e-7) or not (y <= 6e+29):
		tmp = math.sqrt(x) * ((y * 3.0) - 3.0)
	else:
		tmp = math.sqrt(x) * (-3.0 + (0.3333333333333333 / x))
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((y <= -8.8e-7) || !(y <= 6e+29))
		tmp = Float64(sqrt(x) * Float64(Float64(y * 3.0) - 3.0));
	else
		tmp = Float64(sqrt(x) * Float64(-3.0 + Float64(0.3333333333333333 / x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((y <= -8.8e-7) || ~((y <= 6e+29)))
		tmp = sqrt(x) * ((y * 3.0) - 3.0);
	else
		tmp = sqrt(x) * (-3.0 + (0.3333333333333333 / x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[y, -8.8e-7], N[Not[LessEqual[y, 6e+29]], $MachinePrecision]], N[(N[Sqrt[x], $MachinePrecision] * N[(N[(y * 3.0), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision], N[(N[Sqrt[x], $MachinePrecision] * N[(-3.0 + N[(0.3333333333333333 / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -8.8000000000000004e-7 or 5.9999999999999998e29 < y

   1. Initial program 99.4%

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

      1. distribute-lft-out-- 99.4%

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

      2. *-rgt-identity 99.4%

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

      3. associate-*l* 99.3%

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

      4. *-commutative 99.3%

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

      5. associate-*r* 99.4%

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

      6. distribute-rgt-out-- 99.4%

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

      7. +-commutative 99.4%

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

      8. distribute-lft-in 99.4%

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

      9. associate--l+ 99.4%

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

      10. *-commutative 99.4%

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

      11. associate-/r* 99.4%

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

      12. associate-*r/ 99.4%

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

      13. metadata-eval 99.4%

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

      14. metadata-eval 99.4%

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

      15. sub-neg 99.4%

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

      16. metadata-eval 99.4%

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

      17. metadata-eval 99.4%

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

      18. metadata-eval 99.4%

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

      19. fma-def 99.5%

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

   3. Simplified 99.5%

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

   4. Taylor expanded in x around inf 79.6%

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

   if -8.8000000000000004e-7 < y < 5.9999999999999998e29

   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. distribute-lft-out-- 99.3%

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

      2. *-rgt-identity 99.3%

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

      3. associate-*l* 99.3%

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

      4. *-commutative 99.3%

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

      5. associate-*r* 99.3%

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

      6. distribute-rgt-out-- 99.3%

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

      7. +-commutative 99.3%

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

      8. distribute-lft-in 99.3%

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

      9. associate--l+ 99.3%

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

      10. *-commutative 99.3%

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

      11. associate-/r* 99.3%

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

      12. associate-*r/ 99.3%

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

      13. metadata-eval 99.3%

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

      14. metadata-eval 99.3%

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

      15. sub-neg 99.3%

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

      16. metadata-eval 99.3%

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

      17. metadata-eval 99.3%

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

      18. metadata-eval 99.3%

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

      19. fma-def 99.3%

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

   3. Simplified 99.3%

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

   4. Taylor expanded in y around 0 98.0%

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

      1. sub-neg 98.0%

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

      2. associate-*r/ 98.0%

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

      3. metadata-eval 98.0%

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

      4. metadata-eval 98.0%

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

   6. Simplified 98.0%

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

4. Final simplification 90.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -8.8 \cdot 10^{-7} \lor \neg \left(y \leq 6 \cdot 10^{+29}\right):\\ \;\;\;\;\sqrt{x} \cdot \left(y \cdot 3 - 3\right)\\ \mathbf{else}:\\ \;\;\;\;\sqrt{x} \cdot \left(-3 + \frac{0.3333333333333333}{x}\right)\\ \end{array} \]

Alternative 7: 85.7% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.25 \cdot 10^{+16}:\\ \;\;\;\;3 \cdot \left(y \cdot \sqrt{x}\right)\\ \mathbf{elif}\;y \leq 1.4 \cdot 10^{+30}:\\ \;\;\;\;\sqrt{x} \cdot \left(-3 + \frac{0.3333333333333333}{x}\right)\\ \mathbf{else}:\\ \;\;\;\;\sqrt{x} \cdot \left(y \cdot 3\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -1.25e+16)
   (* 3.0 (* y (sqrt x)))
   (if (<= y 1.4e+30)
     (* (sqrt x) (+ -3.0 (/ 0.3333333333333333 x)))
     (* (sqrt x) (* y 3.0)))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -1.25e+16) {
		tmp = 3.0 * (y * sqrt(x));
	} else if (y <= 1.4e+30) {
		tmp = sqrt(x) * (-3.0 + (0.3333333333333333 / x));
	} else {
		tmp = sqrt(x) * (y * 3.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (y <= (-1.25d+16)) then
        tmp = 3.0d0 * (y * sqrt(x))
    else if (y <= 1.4d+30) then
        tmp = sqrt(x) * ((-3.0d0) + (0.3333333333333333d0 / x))
    else
        tmp = sqrt(x) * (y * 3.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (y <= -1.25e+16) {
		tmp = 3.0 * (y * Math.sqrt(x));
	} else if (y <= 1.4e+30) {
		tmp = Math.sqrt(x) * (-3.0 + (0.3333333333333333 / x));
	} else {
		tmp = Math.sqrt(x) * (y * 3.0);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -1.25e+16:
		tmp = 3.0 * (y * math.sqrt(x))
	elif y <= 1.4e+30:
		tmp = math.sqrt(x) * (-3.0 + (0.3333333333333333 / x))
	else:
		tmp = math.sqrt(x) * (y * 3.0)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -1.25e+16)
		tmp = Float64(3.0 * Float64(y * sqrt(x)));
	elseif (y <= 1.4e+30)
		tmp = Float64(sqrt(x) * Float64(-3.0 + Float64(0.3333333333333333 / x)));
	else
		tmp = Float64(sqrt(x) * Float64(y * 3.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -1.25e+16)
		tmp = 3.0 * (y * sqrt(x));
	elseif (y <= 1.4e+30)
		tmp = sqrt(x) * (-3.0 + (0.3333333333333333 / x));
	else
		tmp = sqrt(x) * (y * 3.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -1.25e+16], N[(3.0 * N[(y * N[Sqrt[x], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 1.4e+30], N[(N[Sqrt[x], $MachinePrecision] * N[(-3.0 + N[(0.3333333333333333 / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[Sqrt[x], $MachinePrecision] * N[(y * 3.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.25e16

   1. Initial program 99.5%

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

      1. distribute-lft-out-- 99.5%

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

      2. *-rgt-identity 99.5%

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

      3. associate-*l* 99.5%

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

      4. *-commutative 99.5%

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

      5. associate-*r* 99.4%

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

      6. distribute-rgt-out-- 99.4%

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

      7. +-commutative 99.4%

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

      8. distribute-lft-in 99.4%

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

      9. associate--l+ 99.4%

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

      10. *-commutative 99.4%

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

      11. associate-/r* 99.4%

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

      12. associate-*r/ 99.5%

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

      13. metadata-eval 99.5%

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

      14. metadata-eval 99.5%

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

      15. sub-neg 99.5%

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

      16. metadata-eval 99.5%

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

      17. metadata-eval 99.5%

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

      18. metadata-eval 99.5%

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

      19. fma-def 99.4%

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

   3. Simplified 99.4%

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

   4. Taylor expanded in y around inf 77.6%

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

   if -1.25e16 < y < 1.39999999999999992e30

   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. distribute-lft-out-- 99.3%

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

      2. *-rgt-identity 99.3%

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

      3. associate-*l* 99.3%

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

      4. *-commutative 99.3%

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

      5. associate-*r* 99.3%

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

      6. distribute-rgt-out-- 99.3%

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

      7. +-commutative 99.3%

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

      8. distribute-lft-in 99.3%

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

      9. associate--l+ 99.3%

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

      10. *-commutative 99.3%

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

      11. associate-/r* 99.3%

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

      12. associate-*r/ 99.3%

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

      13. metadata-eval 99.3%

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

      14. metadata-eval 99.3%

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

      15. sub-neg 99.3%

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

      16. metadata-eval 99.3%

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

      17. metadata-eval 99.3%

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

      18. metadata-eval 99.3%

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

      19. fma-def 99.3%

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

   3. Simplified 99.3%

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

   4. Taylor expanded in y around 0 97.3%

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

      1. sub-neg 97.3%

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

      2. associate-*r/ 97.3%

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

      3. metadata-eval 97.3%

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

      4. metadata-eval 97.3%

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

   6. Simplified 97.3%

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

   if 1.39999999999999992e30 < y

   1. Initial program 99.3%

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

      1. distribute-lft-out-- 99.3%

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

      2. *-rgt-identity 99.3%

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

      3. associate-*l* 99.2%

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

      4. *-commutative 99.2%

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

      5. associate-*r* 99.4%

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

      6. distribute-rgt-out-- 99.4%

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

      7. +-commutative 99.4%

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

      8. distribute-lft-in 99.4%

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

      9. associate--l+ 99.4%

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

      10. *-commutative 99.4%

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

      11. associate-/r* 99.4%

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

      12. associate-*r/ 99.4%

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

      13. metadata-eval 99.4%

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

      14. metadata-eval 99.4%

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

      15. sub-neg 99.4%

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

      16. metadata-eval 99.4%

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

      17. metadata-eval 99.4%

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

      18. metadata-eval 99.4%

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

      19. fma-def 99.6%

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

   3. Simplified 99.6%

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

   4. Taylor expanded in y around inf 82.4%

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

4. Final simplification 90.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.25 \cdot 10^{+16}:\\ \;\;\;\;3 \cdot \left(y \cdot \sqrt{x}\right)\\ \mathbf{elif}\;y \leq 1.4 \cdot 10^{+30}:\\ \;\;\;\;\sqrt{x} \cdot \left(-3 + \frac{0.3333333333333333}{x}\right)\\ \mathbf{else}:\\ \;\;\;\;\sqrt{x} \cdot \left(y \cdot 3\right)\\ \end{array} \]

Alternative 8: 85.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -8.8 \cdot 10^{-7}:\\ \;\;\;\;\left(y + -1\right) \cdot \left(\sqrt{x} \cdot 3\right)\\ \mathbf{elif}\;y \leq 2.4 \cdot 10^{+29}:\\ \;\;\;\;\sqrt{x} \cdot \left(-3 + \frac{0.3333333333333333}{x}\right)\\ \mathbf{else}:\\ \;\;\;\;\sqrt{x} \cdot \left(y \cdot 3 - 3\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -8.8e-7)
   (* (+ y -1.0) (* (sqrt x) 3.0))
   (if (<= y 2.4e+29)
     (* (sqrt x) (+ -3.0 (/ 0.3333333333333333 x)))
     (* (sqrt x) (- (* y 3.0) 3.0)))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -8.8e-7) {
		tmp = (y + -1.0) * (sqrt(x) * 3.0);
	} else if (y <= 2.4e+29) {
		tmp = sqrt(x) * (-3.0 + (0.3333333333333333 / x));
	} else {
		tmp = sqrt(x) * ((y * 3.0) - 3.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (y <= (-8.8d-7)) then
        tmp = (y + (-1.0d0)) * (sqrt(x) * 3.0d0)
    else if (y <= 2.4d+29) then
        tmp = sqrt(x) * ((-3.0d0) + (0.3333333333333333d0 / x))
    else
        tmp = sqrt(x) * ((y * 3.0d0) - 3.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (y <= -8.8e-7) {
		tmp = (y + -1.0) * (Math.sqrt(x) * 3.0);
	} else if (y <= 2.4e+29) {
		tmp = Math.sqrt(x) * (-3.0 + (0.3333333333333333 / x));
	} else {
		tmp = Math.sqrt(x) * ((y * 3.0) - 3.0);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -8.8e-7:
		tmp = (y + -1.0) * (math.sqrt(x) * 3.0)
	elif y <= 2.4e+29:
		tmp = math.sqrt(x) * (-3.0 + (0.3333333333333333 / x))
	else:
		tmp = math.sqrt(x) * ((y * 3.0) - 3.0)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -8.8e-7)
		tmp = Float64(Float64(y + -1.0) * Float64(sqrt(x) * 3.0));
	elseif (y <= 2.4e+29)
		tmp = Float64(sqrt(x) * Float64(-3.0 + Float64(0.3333333333333333 / x)));
	else
		tmp = Float64(sqrt(x) * Float64(Float64(y * 3.0) - 3.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -8.8e-7)
		tmp = (y + -1.0) * (sqrt(x) * 3.0);
	elseif (y <= 2.4e+29)
		tmp = sqrt(x) * (-3.0 + (0.3333333333333333 / x));
	else
		tmp = sqrt(x) * ((y * 3.0) - 3.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -8.8e-7], N[(N[(y + -1.0), $MachinePrecision] * N[(N[Sqrt[x], $MachinePrecision] * 3.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 2.4e+29], N[(N[Sqrt[x], $MachinePrecision] * N[(-3.0 + N[(0.3333333333333333 / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[Sqrt[x], $MachinePrecision] * N[(N[(y * 3.0), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -8.8000000000000004e-7

   1. Initial program 99.5%

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

      1. associate-*l* 99.4%

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

      2. sub-neg 99.4%

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

      3. +-commutative 99.4%

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

      4. associate-+l+ 99.4%

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

      5. *-commutative 99.4%

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

      6. associate-/r* 99.4%

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

      7. metadata-eval 99.4%

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

      8. metadata-eval 99.4%

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

   3. Simplified 99.4%

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

      1. associate-*r* 99.4%

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

      2. associate-+r+ 99.4%

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

      3. distribute-rgt-in 99.4%

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

      4. div-inv 99.3%

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

      5. div-inv 99.4%

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

      6. clear-num 99.4%

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

      7. div-inv 99.5%

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

      8. metadata-eval 99.5%

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

      9. +-commutative 99.5%

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

      10. distribute-rgt-in 99.5%

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

      11. metadata-eval 99.5%

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

      12. sub-neg 99.5%

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

      13. associate--l+ 99.5%

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

      14. distribute-lft-in 99.4%

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

      15. *-commutative 99.4%

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

      16. metadata-eval 99.4%

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

      17. sqrt-prod 99.4%

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

   5. Applied egg-rr 99.4%

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

      1. distribute-lft-out 99.4%

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

      2. associate-+r+ 99.4%

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

   7. Simplified 99.4%

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

   8. Taylor expanded in y around inf 77.0%

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

   9. Taylor expanded in y around 0 77.0%

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

       1. *-commutative 77.0%

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

       2. metadata-eval 77.0%

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

       3. associate-*l* 77.0%

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

       4. associate-*r* 77.0%

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

       5. *-commutative 77.0%

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

       6. distribute-lft-in 77.0%

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

       7. +-commutative 77.0%

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

   11. Simplified 77.0%

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

   if -8.8000000000000004e-7 < y < 2.4000000000000001e29

   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. distribute-lft-out-- 99.3%

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

      2. *-rgt-identity 99.3%

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

      3. associate-*l* 99.3%

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

      4. *-commutative 99.3%

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

      5. associate-*r* 99.3%

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

      6. distribute-rgt-out-- 99.3%

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

      7. +-commutative 99.3%

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

      8. distribute-lft-in 99.3%

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

      9. associate--l+ 99.3%

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

      10. *-commutative 99.3%

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

      11. associate-/r* 99.3%

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

      12. associate-*r/ 99.3%

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

      13. metadata-eval 99.3%

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

      14. metadata-eval 99.3%

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

      15. sub-neg 99.3%

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

      16. metadata-eval 99.3%

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

      17. metadata-eval 99.3%

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

      18. metadata-eval 99.3%

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

      19. fma-def 99.3%

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

   3. Simplified 99.3%

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

   4. Taylor expanded in y around 0 98.0%

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

      1. sub-neg 98.0%

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

      2. associate-*r/ 98.0%

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

      3. metadata-eval 98.0%

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

      4. metadata-eval 98.0%

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

   6. Simplified 98.0%

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

   if 2.4000000000000001e29 < y

   1. Initial program 99.3%

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

      1. distribute-lft-out-- 99.3%

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

      2. *-rgt-identity 99.3%

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

      3. associate-*l* 99.2%

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

      4. *-commutative 99.2%

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

      5. associate-*r* 99.4%

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

      6. distribute-rgt-out-- 99.4%

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

      7. +-commutative 99.4%

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

      8. distribute-lft-in 99.4%

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

      9. associate--l+ 99.4%

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

      10. *-commutative 99.4%

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

      11. associate-/r* 99.4%

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

      12. associate-*r/ 99.4%

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

      13. metadata-eval 99.4%

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

      14. metadata-eval 99.4%

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

      15. sub-neg 99.4%

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

      16. metadata-eval 99.4%

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

      17. metadata-eval 99.4%

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

      18. metadata-eval 99.4%

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

      19. fma-def 99.6%

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

   3. Simplified 99.6%

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

   4. Taylor expanded in x around inf 82.4%

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

4. Final simplification 90.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -8.8 \cdot 10^{-7}:\\ \;\;\;\;\left(y + -1\right) \cdot \left(\sqrt{x} \cdot 3\right)\\ \mathbf{elif}\;y \leq 2.4 \cdot 10^{+29}:\\ \;\;\;\;\sqrt{x} \cdot \left(-3 + \frac{0.3333333333333333}{x}\right)\\ \mathbf{else}:\\ \;\;\;\;\sqrt{x} \cdot \left(y \cdot 3 - 3\right)\\ \end{array} \]

Alternative 9: 99.4% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.3%

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

   1. associate-*l* 99.3%

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

   2. sub-neg 99.3%

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

   3. +-commutative 99.3%

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

   4. associate-+l+ 99.3%

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

   5. *-commutative 99.3%

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

   6. associate-/r* 99.3%

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

   7. metadata-eval 99.3%

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

   8. metadata-eval 99.3%

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

3. Simplified 99.3%

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

4. Final simplification 99.3%

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

Alternative 10: 99.4% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.3%

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

   1. *-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. sub-neg 99.3%

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

   4. distribute-lft-in 99.3%

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

   5. +-commutative 99.3%

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

   6. metadata-eval 99.3%

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

   7. metadata-eval 99.3%

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

   8. distribute-lft-in 99.3%

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

   9. fma-def 99.3%

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

   10. *-commutative 99.3%

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

   11. associate-/r* 99.3%

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

   12. associate-*r/ 99.4%

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

   13. metadata-eval 99.4%

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

   14. metadata-eval 99.4%

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

3. Simplified 99.4%

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

   1. fma-udef 99.4%

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

   2. +-commutative 99.4%

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

5. Applied egg-rr 99.4%

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

6. Final simplification 99.4%

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

Alternative 11: 60.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5.5 \cdot 10^{+15} \lor \neg \left(y \leq 8 \cdot 10^{-16}\right):\\ \;\;\;\;3 \cdot \left(y \cdot \sqrt{x}\right)\\ \mathbf{else}:\\ \;\;\;\;\sqrt{x} \cdot -3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= y -5.5e+15) (not (<= y 8e-16)))
   (* 3.0 (* y (sqrt x)))
   (* (sqrt x) -3.0)))

C

double code(double x, double y) {
	double tmp;
	if ((y <= -5.5e+15) || !(y <= 8e-16)) {
		tmp = 3.0 * (y * sqrt(x));
	} else {
		tmp = sqrt(x) * -3.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if ((y <= (-5.5d+15)) .or. (.not. (y <= 8d-16))) then
        tmp = 3.0d0 * (y * sqrt(x))
    else
        tmp = sqrt(x) * (-3.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if ((y <= -5.5e+15) || !(y <= 8e-16)) {
		tmp = 3.0 * (y * Math.sqrt(x));
	} else {
		tmp = Math.sqrt(x) * -3.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (y <= -5.5e+15) or not (y <= 8e-16):
		tmp = 3.0 * (y * math.sqrt(x))
	else:
		tmp = math.sqrt(x) * -3.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((y <= -5.5e+15) || !(y <= 8e-16))
		tmp = Float64(3.0 * Float64(y * sqrt(x)));
	else
		tmp = Float64(sqrt(x) * -3.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((y <= -5.5e+15) || ~((y <= 8e-16)))
		tmp = 3.0 * (y * sqrt(x));
	else
		tmp = sqrt(x) * -3.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[y, -5.5e+15], N[Not[LessEqual[y, 8e-16]], $MachinePrecision]], N[(3.0 * N[(y * N[Sqrt[x], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[Sqrt[x], $MachinePrecision] * -3.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -5.5e15 or 7.9999999999999998e-16 < y

   1. Initial program 99.4%

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

      1. distribute-lft-out-- 99.4%

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

      2. *-rgt-identity 99.4%

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

      3. associate-*l* 99.3%

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

      4. *-commutative 99.3%

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

      5. associate-*r* 99.4%

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

      6. distribute-rgt-out-- 99.4%

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

      7. +-commutative 99.4%

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

      8. distribute-lft-in 99.4%

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

      9. associate--l+ 99.4%

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

      10. *-commutative 99.4%

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

      11. associate-/r* 99.4%

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

      12. associate-*r/ 99.4%

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

      13. metadata-eval 99.4%

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

      14. metadata-eval 99.4%

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

      15. sub-neg 99.4%

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

      16. metadata-eval 99.4%

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

      17. metadata-eval 99.4%

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

      18. metadata-eval 99.4%

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

      19. fma-def 99.5%

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

   3. Simplified 99.5%

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

   4. Taylor expanded in y around inf 75.1%

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

   if -5.5e15 < y < 7.9999999999999998e-16

   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. distribute-lft-out-- 99.3%

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

      2. *-rgt-identity 99.3%

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

      3. associate-*l* 99.3%

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

      4. *-commutative 99.3%

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

      5. associate-*r* 99.3%

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

      6. distribute-rgt-out-- 99.3%

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

      7. +-commutative 99.3%

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

      8. distribute-lft-in 99.3%

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

      9. associate--l+ 99.3%

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

      10. *-commutative 99.3%

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

      11. associate-/r* 99.3%

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

      12. associate-*r/ 99.3%

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

      13. metadata-eval 99.3%

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

      14. metadata-eval 99.3%

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

      15. sub-neg 99.3%

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

      16. metadata-eval 99.3%

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

      17. metadata-eval 99.3%

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

      18. metadata-eval 99.3%

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

      19. fma-def 99.3%

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

   3. Simplified 99.3%

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

   4. Taylor expanded in y around 0 98.6%

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

      1. sub-neg 98.6%

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

      2. associate-*r/ 98.5%

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

      3. metadata-eval 98.5%

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

      4. metadata-eval 98.5%

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

   6. Simplified 98.5%

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

   7. Taylor expanded in x around inf 49.5%

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

4. Final simplification 61.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.5 \cdot 10^{+15} \lor \neg \left(y \leq 8 \cdot 10^{-16}\right):\\ \;\;\;\;3 \cdot \left(y \cdot \sqrt{x}\right)\\ \mathbf{else}:\\ \;\;\;\;\sqrt{x} \cdot -3\\ \end{array} \]

Alternative 12: 60.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5.5 \cdot 10^{+15}:\\ \;\;\;\;3 \cdot \left(y \cdot \sqrt{x}\right)\\ \mathbf{elif}\;y \leq 8 \cdot 10^{-16}:\\ \;\;\;\;\sqrt{x} \cdot -3\\ \mathbf{else}:\\ \;\;\;\;\sqrt{x} \cdot \left(y \cdot 3\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -5.5e+15)
   (* 3.0 (* y (sqrt x)))
   (if (<= y 8e-16) (* (sqrt x) -3.0) (* (sqrt x) (* y 3.0)))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -5.5e+15) {
		tmp = 3.0 * (y * sqrt(x));
	} else if (y <= 8e-16) {
		tmp = sqrt(x) * -3.0;
	} else {
		tmp = sqrt(x) * (y * 3.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (y <= (-5.5d+15)) then
        tmp = 3.0d0 * (y * sqrt(x))
    else if (y <= 8d-16) then
        tmp = sqrt(x) * (-3.0d0)
    else
        tmp = sqrt(x) * (y * 3.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (y <= -5.5e+15) {
		tmp = 3.0 * (y * Math.sqrt(x));
	} else if (y <= 8e-16) {
		tmp = Math.sqrt(x) * -3.0;
	} else {
		tmp = Math.sqrt(x) * (y * 3.0);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -5.5e+15:
		tmp = 3.0 * (y * math.sqrt(x))
	elif y <= 8e-16:
		tmp = math.sqrt(x) * -3.0
	else:
		tmp = math.sqrt(x) * (y * 3.0)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -5.5e+15)
		tmp = Float64(3.0 * Float64(y * sqrt(x)));
	elseif (y <= 8e-16)
		tmp = Float64(sqrt(x) * -3.0);
	else
		tmp = Float64(sqrt(x) * Float64(y * 3.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -5.5e+15)
		tmp = 3.0 * (y * sqrt(x));
	elseif (y <= 8e-16)
		tmp = sqrt(x) * -3.0;
	else
		tmp = sqrt(x) * (y * 3.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -5.5e+15], N[(3.0 * N[(y * N[Sqrt[x], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 8e-16], N[(N[Sqrt[x], $MachinePrecision] * -3.0), $MachinePrecision], N[(N[Sqrt[x], $MachinePrecision] * N[(y * 3.0), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -5.5e15

   1. Initial program 99.5%

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

      1. distribute-lft-out-- 99.5%

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

      2. *-rgt-identity 99.5%

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

      3. associate-*l* 99.5%

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

      4. *-commutative 99.5%

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

      5. associate-*r* 99.4%

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

      6. distribute-rgt-out-- 99.4%

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

      7. +-commutative 99.4%

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

      8. distribute-lft-in 99.4%

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

      9. associate--l+ 99.4%

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

      10. *-commutative 99.4%

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

      11. associate-/r* 99.4%

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

      12. associate-*r/ 99.5%

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

      13. metadata-eval 99.5%

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

      14. metadata-eval 99.5%

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

      15. sub-neg 99.5%

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

      16. metadata-eval 99.5%

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

      17. metadata-eval 99.5%

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

      18. metadata-eval 99.5%

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

      19. fma-def 99.4%

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

   3. Simplified 99.4%

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

   4. Taylor expanded in y around inf 77.6%

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

   if -5.5e15 < y < 7.9999999999999998e-16

   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. distribute-lft-out-- 99.3%

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

      2. *-rgt-identity 99.3%

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

      3. associate-*l* 99.3%

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

      4. *-commutative 99.3%

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

      5. associate-*r* 99.3%

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

      6. distribute-rgt-out-- 99.3%

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

      7. +-commutative 99.3%

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

      8. distribute-lft-in 99.3%

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

      9. associate--l+ 99.3%

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

      10. *-commutative 99.3%

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

      11. associate-/r* 99.3%

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

      12. associate-*r/ 99.3%

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

      13. metadata-eval 99.3%

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

      14. metadata-eval 99.3%

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

      15. sub-neg 99.3%

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

      16. metadata-eval 99.3%

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

      17. metadata-eval 99.3%

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

      18. metadata-eval 99.3%

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

      19. fma-def 99.3%

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

   3. Simplified 99.3%

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

   4. Taylor expanded in y around 0 98.6%

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

      1. sub-neg 98.6%

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

      2. associate-*r/ 98.5%

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

      3. metadata-eval 98.5%

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

      4. metadata-eval 98.5%

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

   6. Simplified 98.5%

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

   7. Taylor expanded in x around inf 49.5%

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

   if 7.9999999999999998e-16 < y

   1. Initial program 99.3%

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

      1. distribute-lft-out-- 99.3%

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

      2. *-rgt-identity 99.3%

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

      3. associate-*l* 99.2%

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

      4. *-commutative 99.2%

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

      5. associate-*r* 99.3%

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

      6. distribute-rgt-out-- 99.3%

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

      7. +-commutative 99.3%

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

      8. distribute-lft-in 99.4%

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

      9. associate--l+ 99.4%

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

      10. *-commutative 99.4%

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

      11. associate-/r* 99.3%

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

      12. associate-*r/ 99.4%

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

      13. metadata-eval 99.4%

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

      14. metadata-eval 99.4%

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

      15. sub-neg 99.4%

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

      16. metadata-eval 99.4%

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

      17. metadata-eval 99.4%

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

      18. metadata-eval 99.4%

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

      19. fma-def 99.6%

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

   3. Simplified 99.6%

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

   4. Taylor expanded in y around inf 72.9%

      \[\leadsto \sqrt{x} \cdot \color{blue}{\left(3 \cdot y\right)} \]
3. Recombined 3 regimes into one program.

4. Final simplification 61.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.5 \cdot 10^{+15}:\\ \;\;\;\;3 \cdot \left(y \cdot \sqrt{x}\right)\\ \mathbf{elif}\;y \leq 8 \cdot 10^{-16}:\\ \;\;\;\;\sqrt{x} \cdot -3\\ \mathbf{else}:\\ \;\;\;\;\sqrt{x} \cdot \left(y \cdot 3\right)\\ \end{array} \]

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 99.3%

   \[\left(3 \cdot \sqrt{x}\right) \cdot \left(\left(y + \frac{1}{x \cdot 9}\right) - 1\right) \]
2. Step-by-step derivation

   1. distribute-lft-out-- 99.3%

      \[\leadsto \color{blue}{\left(3 \cdot \sqrt{x}\right) \cdot \left(y + \frac{1}{x \cdot 9}\right) - \left(3 \cdot \sqrt{x}\right) \cdot 1} \]

   2. *-rgt-identity 99.3%

      \[\leadsto \left(3 \cdot \sqrt{x}\right) \cdot \left(y + \frac{1}{x \cdot 9}\right) - \color{blue}{3 \cdot \sqrt{x}} \]

   3. associate-*l* 99.3%

      \[\leadsto \color{blue}{3 \cdot \left(\sqrt{x} \cdot \left(y + \frac{1}{x \cdot 9}\right)\right)} - 3 \cdot \sqrt{x} \]

   4. *-commutative 99.3%

      \[\leadsto 3 \cdot \color{blue}{\left(\left(y + \frac{1}{x \cdot 9}\right) \cdot \sqrt{x}\right)} - 3 \cdot \sqrt{x} \]

   5. associate-*r* 99.3%

      \[\leadsto \color{blue}{\left(3 \cdot \left(y + \frac{1}{x \cdot 9}\right)\right) \cdot \sqrt{x}} - 3 \cdot \sqrt{x} \]

   6. distribute-rgt-out-- 99.3%

      \[\leadsto \color{blue}{\sqrt{x} \cdot \left(3 \cdot \left(y + \frac{1}{x \cdot 9}\right) - 3\right)} \]

   7. +-commutative 99.3%

      \[\leadsto \sqrt{x} \cdot \left(3 \cdot \color{blue}{\left(\frac{1}{x \cdot 9} + y\right)} - 3\right) \]

   8. distribute-lft-in 99.3%

      \[\leadsto \sqrt{x} \cdot \left(\color{blue}{\left(3 \cdot \frac{1}{x \cdot 9} + 3 \cdot y\right)} - 3\right) \]

   9. associate--l+ 99.3%

      \[\leadsto \sqrt{x} \cdot \color{blue}{\left(3 \cdot \frac{1}{x \cdot 9} + \left(3 \cdot y - 3\right)\right)} \]

   10. *-commutative 99.3%

       \[\leadsto \sqrt{x} \cdot \left(3 \cdot \frac{1}{\color{blue}{9 \cdot x}} + \left(3 \cdot y - 3\right)\right) \]

   11. associate-/r* 99.3%

       \[\leadsto \sqrt{x} \cdot \left(3 \cdot \color{blue}{\frac{\frac{1}{9}}{x}} + \left(3 \cdot y - 3\right)\right) \]

   12. associate-*r/ 99.4%

       \[\leadsto \sqrt{x} \cdot \left(\color{blue}{\frac{3 \cdot \frac{1}{9}}{x}} + \left(3 \cdot y - 3\right)\right) \]

   13. metadata-eval 99.4%

       \[\leadsto \sqrt{x} \cdot \left(\frac{3 \cdot \color{blue}{0.1111111111111111}}{x} + \left(3 \cdot y - 3\right)\right) \]

   14. metadata-eval 99.4%

       \[\leadsto \sqrt{x} \cdot \left(\frac{\color{blue}{0.3333333333333333}}{x} + \left(3 \cdot y - 3\right)\right) \]

   15. sub-neg 99.4%

       \[\leadsto \sqrt{x} \cdot \left(\frac{0.3333333333333333}{x} + \color{blue}{\left(3 \cdot y + \left(-3\right)\right)}\right) \]

   16. metadata-eval 99.4%

       \[\leadsto \sqrt{x} \cdot \left(\frac{0.3333333333333333}{x} + \left(3 \cdot y + \color{blue}{-3}\right)\right) \]

   17. metadata-eval 99.4%

       \[\leadsto \sqrt{x} \cdot \left(\frac{0.3333333333333333}{x} + \left(3 \cdot y + \color{blue}{3 \cdot -1}\right)\right) \]

   18. metadata-eval 99.4%

       \[\leadsto \sqrt{x} \cdot \left(\frac{0.3333333333333333}{x} + \left(3 \cdot y + 3 \cdot \color{blue}{\left(-1\right)}\right)\right) \]

   19. fma-def 99.4%

       \[\leadsto \sqrt{x} \cdot \left(\frac{0.3333333333333333}{x} + \color{blue}{\mathsf{fma}\left(3, y, 3 \cdot \left(-1\right)\right)}\right) \]

3. Simplified 99.4%

   \[\leadsto \color{blue}{\sqrt{x} \cdot \left(\frac{0.3333333333333333}{x} + \mathsf{fma}\left(3, y, -3\right)\right)} \]

4. Taylor expanded in y around 0 65.0%

   \[\leadsto \color{blue}{\sqrt{x} \cdot \left(0.3333333333333333 \cdot \frac{1}{x} - 3\right)} \]
5. Step-by-step derivation

   1. sub-neg 65.0%

      \[\leadsto \sqrt{x} \cdot \color{blue}{\left(0.3333333333333333 \cdot \frac{1}{x} + \left(-3\right)\right)} \]

   2. associate-*r/ 65.0%

      \[\leadsto \sqrt{x} \cdot \left(\color{blue}{\frac{0.3333333333333333 \cdot 1}{x}} + \left(-3\right)\right) \]

   3. metadata-eval 65.0%

      \[\leadsto \sqrt{x} \cdot \left(\frac{\color{blue}{0.3333333333333333}}{x} + \left(-3\right)\right) \]

   4. metadata-eval 65.0%

      \[\leadsto \sqrt{x} \cdot \left(\frac{0.3333333333333333}{x} + \color{blue}{-3}\right) \]

6. Simplified 65.0%

   \[\leadsto \color{blue}{\sqrt{x} \cdot \left(\frac{0.3333333333333333}{x} + -3\right)} \]

7. Taylor expanded in x around inf 28.3%

   \[\leadsto \sqrt{x} \cdot \color{blue}{-3} \]
8. 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 3.4%

      \[\leadsto \color{blue}{\sqrt{\left(\sqrt{x} \cdot -3\right) \cdot \left(\sqrt{x} \cdot -3\right)}} \]

   3. swap-sqr 3.4%

      \[\leadsto \sqrt{\color{blue}{\left(\sqrt{x} \cdot \sqrt{x}\right) \cdot \left(-3 \cdot -3\right)}} \]

   4. add-sqr-sqrt 3.4%

      \[\leadsto \sqrt{\color{blue}{x} \cdot \left(-3 \cdot -3\right)} \]

   5. metadata-eval 3.4%

      \[\leadsto \sqrt{x \cdot \color{blue}{9}} \]

9. Applied egg-rr 3.4%

   \[\leadsto \color{blue}{\sqrt{x \cdot 9}} \]

10. Final simplification 3.4%

    \[\leadsto \sqrt{x \cdot 9} \]

Alternative 14: 25.0% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \sqrt{x} \cdot -3 \end{array} \]

FPCore

(FPCore (x y) :precision binary64 (* (sqrt x) -3.0))

C

double code(double x, double y) {
	return sqrt(x) * -3.0;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = sqrt(x) * (-3.0d0)
end function

Java

public static double code(double x, double y) {
	return Math.sqrt(x) * -3.0;
}

Python

def code(x, y):
	return math.sqrt(x) * -3.0

Julia

function code(x, y)
	return Float64(sqrt(x) * -3.0)
end

MATLAB

function tmp = code(x, y)
	tmp = sqrt(x) * -3.0;
end

Wolfram

code[x_, y_] := N[(N[Sqrt[x], $MachinePrecision] * -3.0), $MachinePrecision]

Derivation

1. Initial program 99.3%

   \[\left(3 \cdot \sqrt{x}\right) \cdot \left(\left(y + \frac{1}{x \cdot 9}\right) - 1\right) \]
2. Step-by-step derivation

   1. distribute-lft-out-- 99.3%

      \[\leadsto \color{blue}{\left(3 \cdot \sqrt{x}\right) \cdot \left(y + \frac{1}{x \cdot 9}\right) - \left(3 \cdot \sqrt{x}\right) \cdot 1} \]

   2. *-rgt-identity 99.3%

      \[\leadsto \left(3 \cdot \sqrt{x}\right) \cdot \left(y + \frac{1}{x \cdot 9}\right) - \color{blue}{3 \cdot \sqrt{x}} \]

   3. associate-*l* 99.3%

      \[\leadsto \color{blue}{3 \cdot \left(\sqrt{x} \cdot \left(y + \frac{1}{x \cdot 9}\right)\right)} - 3 \cdot \sqrt{x} \]

   4. *-commutative 99.3%

      \[\leadsto 3 \cdot \color{blue}{\left(\left(y + \frac{1}{x \cdot 9}\right) \cdot \sqrt{x}\right)} - 3 \cdot \sqrt{x} \]

   5. associate-*r* 99.3%

      \[\leadsto \color{blue}{\left(3 \cdot \left(y + \frac{1}{x \cdot 9}\right)\right) \cdot \sqrt{x}} - 3 \cdot \sqrt{x} \]

   6. distribute-rgt-out-- 99.3%

      \[\leadsto \color{blue}{\sqrt{x} \cdot \left(3 \cdot \left(y + \frac{1}{x \cdot 9}\right) - 3\right)} \]

   7. +-commutative 99.3%

      \[\leadsto \sqrt{x} \cdot \left(3 \cdot \color{blue}{\left(\frac{1}{x \cdot 9} + y\right)} - 3\right) \]

   8. distribute-lft-in 99.3%

      \[\leadsto \sqrt{x} \cdot \left(\color{blue}{\left(3 \cdot \frac{1}{x \cdot 9} + 3 \cdot y\right)} - 3\right) \]

   9. associate--l+ 99.3%

      \[\leadsto \sqrt{x} \cdot \color{blue}{\left(3 \cdot \frac{1}{x \cdot 9} + \left(3 \cdot y - 3\right)\right)} \]

   10. *-commutative 99.3%

       \[\leadsto \sqrt{x} \cdot \left(3 \cdot \frac{1}{\color{blue}{9 \cdot x}} + \left(3 \cdot y - 3\right)\right) \]

   11. associate-/r* 99.3%

       \[\leadsto \sqrt{x} \cdot \left(3 \cdot \color{blue}{\frac{\frac{1}{9}}{x}} + \left(3 \cdot y - 3\right)\right) \]

   12. associate-*r/ 99.4%

       \[\leadsto \sqrt{x} \cdot \left(\color{blue}{\frac{3 \cdot \frac{1}{9}}{x}} + \left(3 \cdot y - 3\right)\right) \]

   13. metadata-eval 99.4%

       \[\leadsto \sqrt{x} \cdot \left(\frac{3 \cdot \color{blue}{0.1111111111111111}}{x} + \left(3 \cdot y - 3\right)\right) \]

   14. metadata-eval 99.4%

       \[\leadsto \sqrt{x} \cdot \left(\frac{\color{blue}{0.3333333333333333}}{x} + \left(3 \cdot y - 3\right)\right) \]

   15. sub-neg 99.4%

       \[\leadsto \sqrt{x} \cdot \left(\frac{0.3333333333333333}{x} + \color{blue}{\left(3 \cdot y + \left(-3\right)\right)}\right) \]

   16. metadata-eval 99.4%

       \[\leadsto \sqrt{x} \cdot \left(\frac{0.3333333333333333}{x} + \left(3 \cdot y + \color{blue}{-3}\right)\right) \]

   17. metadata-eval 99.4%

       \[\leadsto \sqrt{x} \cdot \left(\frac{0.3333333333333333}{x} + \left(3 \cdot y + \color{blue}{3 \cdot -1}\right)\right) \]

   18. metadata-eval 99.4%

       \[\leadsto \sqrt{x} \cdot \left(\frac{0.3333333333333333}{x} + \left(3 \cdot y + 3 \cdot \color{blue}{\left(-1\right)}\right)\right) \]

   19. fma-def 99.4%

       \[\leadsto \sqrt{x} \cdot \left(\frac{0.3333333333333333}{x} + \color{blue}{\mathsf{fma}\left(3, y, 3 \cdot \left(-1\right)\right)}\right) \]

3. Simplified 99.4%

   \[\leadsto \color{blue}{\sqrt{x} \cdot \left(\frac{0.3333333333333333}{x} + \mathsf{fma}\left(3, y, -3\right)\right)} \]

4. Taylor expanded in y around 0 65.0%

   \[\leadsto \color{blue}{\sqrt{x} \cdot \left(0.3333333333333333 \cdot \frac{1}{x} - 3\right)} \]
5. Step-by-step derivation

   1. sub-neg 65.0%

      \[\leadsto \sqrt{x} \cdot \color{blue}{\left(0.3333333333333333 \cdot \frac{1}{x} + \left(-3\right)\right)} \]

   2. associate-*r/ 65.0%

      \[\leadsto \sqrt{x} \cdot \left(\color{blue}{\frac{0.3333333333333333 \cdot 1}{x}} + \left(-3\right)\right) \]

   3. metadata-eval 65.0%

      \[\leadsto \sqrt{x} \cdot \left(\frac{\color{blue}{0.3333333333333333}}{x} + \left(-3\right)\right) \]

   4. metadata-eval 65.0%

      \[\leadsto \sqrt{x} \cdot \left(\frac{0.3333333333333333}{x} + \color{blue}{-3}\right) \]

6. Simplified 65.0%

   \[\leadsto \color{blue}{\sqrt{x} \cdot \left(\frac{0.3333333333333333}{x} + -3\right)} \]

7. Taylor expanded in x around inf 28.3%

   \[\leadsto \sqrt{x} \cdot \color{blue}{-3} \]

8. Final simplification 28.3%

   \[\leadsto \sqrt{x} \cdot -3 \]

Developer target: 99.4% accurate, 0.5× speedup

Math

\[\begin{array}{l} \\ 3 \cdot \left(y \cdot \sqrt{x} + \left(\frac{1}{x \cdot 9} - 1\right) \cdot \sqrt{x}\right) \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (* 3.0 (+ (* y (sqrt x)) (* (- (/ 1.0 (* x 9.0)) 1.0) (sqrt x)))))

C

double code(double x, double y) {
	return 3.0 * ((y * sqrt(x)) + (((1.0 / (x * 9.0)) - 1.0) * sqrt(x)));
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = 3.0d0 * ((y * sqrt(x)) + (((1.0d0 / (x * 9.0d0)) - 1.0d0) * sqrt(x)))
end function

Java

public static double code(double x, double y) {
	return 3.0 * ((y * Math.sqrt(x)) + (((1.0 / (x * 9.0)) - 1.0) * Math.sqrt(x)));
}

Python

def code(x, y):
	return 3.0 * ((y * math.sqrt(x)) + (((1.0 / (x * 9.0)) - 1.0) * math.sqrt(x)))

Julia

function code(x, y)
	return Float64(3.0 * Float64(Float64(y * sqrt(x)) + Float64(Float64(Float64(1.0 / Float64(x * 9.0)) - 1.0) * sqrt(x))))
end

MATLAB

function tmp = code(x, y)
	tmp = 3.0 * ((y * sqrt(x)) + (((1.0 / (x * 9.0)) - 1.0) * sqrt(x)));
end

Wolfram

code[x_, y_] := N[(3.0 * N[(N[(y * N[Sqrt[x], $MachinePrecision]), $MachinePrecision] + N[(N[(N[(1.0 / N[(x * 9.0), $MachinePrecision]), $MachinePrecision] - 1.0), $MachinePrecision] * N[Sqrt[x], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Reproduce

herbie shell --seed 2023308 
(FPCore (x y)
  :name "Numeric.SpecFunctions:incompleteGamma from math-functions-0.1.5.2, B"
  :precision binary64

  :herbie-target
  (* 3.0 (+ (* y (sqrt x)) (* (- (/ 1.0 (* x 9.0)) 1.0) (sqrt x))))

  (* (* 3.0 (sqrt x)) (- (+ y (/ 1.0 (* x 9.0))) 1.0)))