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

Percentage Accurate: 99.4% → 99.4%

Time: 10.4s

Alternatives: 12

Speedup: N/A×

Specification

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Initial Program: 99.4% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Alternative 1: 99.4% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.4%

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

   1. +-commutative 99.4%

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

   2. associate--l+ 99.4%

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

   3. distribute-rgt-in 99.4%

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

   4. remove-double-neg 99.4%

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

   5. distribute-lft-neg-in 99.4%

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

   6. distribute-rgt-neg-in 99.4%

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

   7. mul-1-neg 99.4%

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

   8. metadata-eval 99.4%

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

   9. *-commutative 99.4%

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

   10. associate-/r* 99.4%

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

   11. distribute-neg-frac 99.4%

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

   12. *-commutative 99.4%

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

   13. associate-/r/ 99.4%

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

   14. associate-/l/ 99.4%

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

   15. associate-/r/ 99.4%

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

3. Simplified 99.4%

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

   1. expm1-log1p-u 96.4%

      \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(3 \cdot \sqrt{x}\right)\right)} \cdot \left(\frac{0.1111111111111111}{x} + \left(y - 1\right)\right) \]

   2. expm1-udef 50.7%

      \[\leadsto \color{blue}{\left(e^{\mathsf{log1p}\left(3 \cdot \sqrt{x}\right)} - 1\right)} \cdot \left(\frac{0.1111111111111111}{x} + \left(y - 1\right)\right) \]

   3. *-commutative 50.7%

      \[\leadsto \left(e^{\mathsf{log1p}\left(\color{blue}{\sqrt{x} \cdot 3}\right)} - 1\right) \cdot \left(\frac{0.1111111111111111}{x} + \left(y - 1\right)\right) \]

   4. metadata-eval 50.7%

      \[\leadsto \left(e^{\mathsf{log1p}\left(\sqrt{x} \cdot \color{blue}{\sqrt{9}}\right)} - 1\right) \cdot \left(\frac{0.1111111111111111}{x} + \left(y - 1\right)\right) \]

   5. sqrt-prod 50.7%

      \[\leadsto \left(e^{\mathsf{log1p}\left(\color{blue}{\sqrt{x \cdot 9}}\right)} - 1\right) \cdot \left(\frac{0.1111111111111111}{x} + \left(y - 1\right)\right) \]

5. Applied egg-rr 50.7%

   \[\leadsto \color{blue}{\left(e^{\mathsf{log1p}\left(\sqrt{x \cdot 9}\right)} - 1\right)} \cdot \left(\frac{0.1111111111111111}{x} + \left(y - 1\right)\right) \]
6. Step-by-step derivation

   1. expm1-def 96.5%

      \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\sqrt{x \cdot 9}\right)\right)} \cdot \left(\frac{0.1111111111111111}{x} + \left(y - 1\right)\right) \]

   2. expm1-log1p 99.5%

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

7. Simplified 99.5%

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

   1. expm1-log1p-u 96.4%

      \[\leadsto \sqrt{x \cdot 9} \cdot \left(\color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{0.1111111111111111}{x}\right)\right)} + \left(y - 1\right)\right) \]

   2. expm1-udef 96.4%

      \[\leadsto \sqrt{x \cdot 9} \cdot \left(\color{blue}{\left(e^{\mathsf{log1p}\left(\frac{0.1111111111111111}{x}\right)} - 1\right)} + \left(y - 1\right)\right) \]

   3. log1p-udef 96.4%

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

   4. +-commutative 96.4%

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

   5. add-exp-log 99.5%

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

9. Applied egg-rr 99.5%

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

10. Final simplification 99.5%

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

Alternative 2: 60.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \sqrt{x} \cdot \frac{0.3333333333333333}{x}\\ t_1 := 3 \cdot \left(y \cdot \sqrt{x}\right)\\ \mathbf{if}\;x \leq 1.7 \cdot 10^{-90}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq 1.85 \cdot 10^{-69}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 2.05 \cdot 10^{-21}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq 2.8 \cdot 10^{+47} \lor \neg \left(x \leq 2.1 \cdot 10^{+105}\right) \land \left(x \leq 3.3 \cdot 10^{+159} \lor \neg \left(x \leq 8.5 \cdot 10^{+184}\right) \land x \leq 4.3 \cdot 10^{+220}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;\sqrt{x} \cdot -3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (* (sqrt x) (/ 0.3333333333333333 x)))
        (t_1 (* 3.0 (* y (sqrt x)))))
   (if (<= x 1.7e-90)
     t_0
     (if (<= x 1.85e-69)
       t_1
       (if (<= x 2.05e-21)
         t_0
         (if (or (<= x 2.8e+47)
                 (and (not (<= x 2.1e+105))
                      (or (<= x 3.3e+159)
                          (and (not (<= x 8.5e+184)) (<= x 4.3e+220)))))
           t_1
           (* (sqrt x) -3.0)))))))

C

double code(double x, double y) {
	double t_0 = sqrt(x) * (0.3333333333333333 / x);
	double t_1 = 3.0 * (y * sqrt(x));
	double tmp;
	if (x <= 1.7e-90) {
		tmp = t_0;
	} else if (x <= 1.85e-69) {
		tmp = t_1;
	} else if (x <= 2.05e-21) {
		tmp = t_0;
	} else if ((x <= 2.8e+47) || (!(x <= 2.1e+105) && ((x <= 3.3e+159) || (!(x <= 8.5e+184) && (x <= 4.3e+220))))) {
		tmp = t_1;
	} 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) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = sqrt(x) * (0.3333333333333333d0 / x)
    t_1 = 3.0d0 * (y * sqrt(x))
    if (x <= 1.7d-90) then
        tmp = t_0
    else if (x <= 1.85d-69) then
        tmp = t_1
    else if (x <= 2.05d-21) then
        tmp = t_0
    else if ((x <= 2.8d+47) .or. (.not. (x <= 2.1d+105)) .and. (x <= 3.3d+159) .or. (.not. (x <= 8.5d+184)) .and. (x <= 4.3d+220)) then
        tmp = t_1
    else
        tmp = sqrt(x) * (-3.0d0)
    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 = 3.0 * (y * Math.sqrt(x));
	double tmp;
	if (x <= 1.7e-90) {
		tmp = t_0;
	} else if (x <= 1.85e-69) {
		tmp = t_1;
	} else if (x <= 2.05e-21) {
		tmp = t_0;
	} else if ((x <= 2.8e+47) || (!(x <= 2.1e+105) && ((x <= 3.3e+159) || (!(x <= 8.5e+184) && (x <= 4.3e+220))))) {
		tmp = t_1;
	} else {
		tmp = Math.sqrt(x) * -3.0;
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = math.sqrt(x) * (0.3333333333333333 / x)
	t_1 = 3.0 * (y * math.sqrt(x))
	tmp = 0
	if x <= 1.7e-90:
		tmp = t_0
	elif x <= 1.85e-69:
		tmp = t_1
	elif x <= 2.05e-21:
		tmp = t_0
	elif (x <= 2.8e+47) or (not (x <= 2.1e+105) and ((x <= 3.3e+159) or (not (x <= 8.5e+184) and (x <= 4.3e+220)))):
		tmp = t_1
	else:
		tmp = math.sqrt(x) * -3.0
	return tmp

Julia

function code(x, y)
	t_0 = Float64(sqrt(x) * Float64(0.3333333333333333 / x))
	t_1 = Float64(3.0 * Float64(y * sqrt(x)))
	tmp = 0.0
	if (x <= 1.7e-90)
		tmp = t_0;
	elseif (x <= 1.85e-69)
		tmp = t_1;
	elseif (x <= 2.05e-21)
		tmp = t_0;
	elseif ((x <= 2.8e+47) || (!(x <= 2.1e+105) && ((x <= 3.3e+159) || (!(x <= 8.5e+184) && (x <= 4.3e+220)))))
		tmp = t_1;
	else
		tmp = Float64(sqrt(x) * -3.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = sqrt(x) * (0.3333333333333333 / x);
	t_1 = 3.0 * (y * sqrt(x));
	tmp = 0.0;
	if (x <= 1.7e-90)
		tmp = t_0;
	elseif (x <= 1.85e-69)
		tmp = t_1;
	elseif (x <= 2.05e-21)
		tmp = t_0;
	elseif ((x <= 2.8e+47) || (~((x <= 2.1e+105)) && ((x <= 3.3e+159) || (~((x <= 8.5e+184)) && (x <= 4.3e+220)))))
		tmp = t_1;
	else
		tmp = sqrt(x) * -3.0;
	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[(3.0 * N[(y * N[Sqrt[x], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, 1.7e-90], t$95$0, If[LessEqual[x, 1.85e-69], t$95$1, If[LessEqual[x, 2.05e-21], t$95$0, If[Or[LessEqual[x, 2.8e+47], And[N[Not[LessEqual[x, 2.1e+105]], $MachinePrecision], Or[LessEqual[x, 3.3e+159], And[N[Not[LessEqual[x, 8.5e+184]], $MachinePrecision], LessEqual[x, 4.3e+220]]]]], t$95$1, N[(N[Sqrt[x], $MachinePrecision] * -3.0), $MachinePrecision]]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < 1.69999999999999997e-90 or 1.8500000000000001e-69 < x < 2.04999999999999997e-21

   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%

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

      2. associate--l+ 99.3%

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

      3. distribute-lft-in 99.3%

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

      4. +-commutative 99.3%

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

      5. *-commutative 99.3%

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

      6. associate-*r* 99.3%

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

      7. cancel-sign-sub 99.3%

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

      8. *-commutative 99.3%

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

      9. associate-*r* 99.4%

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

      10. *-commutative 99.4%

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

      11. distribute-rgt-out-- 99.4%

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

      12. distribute-lft-neg-in 99.4%

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

      13. cancel-sign-sub 99.4%

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

      14. +-commutative 99.4%

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

      15. *-commutative 99.4%

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

      16. distribute-rgt-in 99.4%

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

   3. Simplified 99.4%

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

   4. Taylor expanded in x around 0 79.5%

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

   if 1.69999999999999997e-90 < x < 1.8500000000000001e-69 or 2.04999999999999997e-21 < x < 2.79999999999999988e47 or 2.1000000000000001e105 < x < 3.2999999999999999e159 or 8.50000000000000043e184 < x < 4.3e220

   1. Initial program 99.4%

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

      1. +-commutative 99.4%

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

      2. associate--l+ 99.4%

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

      3. distribute-lft-in 99.4%

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

      4. +-commutative 99.4%

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

      5. *-commutative 99.4%

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

      6. associate-*r* 99.4%

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

      7. cancel-sign-sub 99.4%

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

      8. *-commutative 99.4%

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

      9. associate-*r* 99.4%

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

      10. *-commutative 99.4%

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

      11. distribute-rgt-out-- 99.4%

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

      12. distribute-lft-neg-in 99.4%

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

      13. cancel-sign-sub 99.4%

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

      14. +-commutative 99.4%

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

      15. *-commutative 99.4%

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

      16. distribute-rgt-in 99.4%

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

   3. Simplified 99.5%

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

   4. Taylor expanded in y around inf 69.5%

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

   if 2.79999999999999988e47 < x < 2.1000000000000001e105 or 3.2999999999999999e159 < x < 8.50000000000000043e184 or 4.3e220 < x

   1. Initial program 99.5%

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

      1. associate--l+ 99.5%

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

      2. associate-/r* 99.5%

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

   3. Simplified 99.5%

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

   4. Taylor expanded in x around inf 99.5%

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

   5. Taylor expanded in y around 0 64.4%

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

      1. *-commutative 64.4%

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

   7. Simplified 64.4%

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

4. Final simplification 72.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 1.7 \cdot 10^{-90}:\\ \;\;\;\;\sqrt{x} \cdot \frac{0.3333333333333333}{x}\\ \mathbf{elif}\;x \leq 1.85 \cdot 10^{-69}:\\ \;\;\;\;3 \cdot \left(y \cdot \sqrt{x}\right)\\ \mathbf{elif}\;x \leq 2.05 \cdot 10^{-21}:\\ \;\;\;\;\sqrt{x} \cdot \frac{0.3333333333333333}{x}\\ \mathbf{elif}\;x \leq 2.8 \cdot 10^{+47} \lor \neg \left(x \leq 2.1 \cdot 10^{+105}\right) \land \left(x \leq 3.3 \cdot 10^{+159} \lor \neg \left(x \leq 8.5 \cdot 10^{+184}\right) \land x \leq 4.3 \cdot 10^{+220}\right):\\ \;\;\;\;3 \cdot \left(y \cdot \sqrt{x}\right)\\ \mathbf{else}:\\ \;\;\;\;\sqrt{x} \cdot -3\\ \end{array} \]

Alternative 3: 60.7% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \sqrt{x} \cdot \frac{0.3333333333333333}{x}\\ t_1 := \sqrt{x} \cdot \left(y \cdot 3\right)\\ t_2 := \sqrt{x} \cdot -3\\ t_3 := 3 \cdot \left(y \cdot \sqrt{x}\right)\\ \mathbf{if}\;x \leq 1.7 \cdot 10^{-90}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq 2.1 \cdot 10^{-69}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \leq 6.2 \cdot 10^{-22}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq 3.6 \cdot 10^{+47}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 2.6 \cdot 10^{+106}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq 3.2 \cdot 10^{+159}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 1.25 \cdot 10^{+185} \lor \neg \left(x \leq 4.2 \cdot 10^{+220}\right):\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (* (sqrt x) (/ 0.3333333333333333 x)))
        (t_1 (* (sqrt x) (* y 3.0)))
        (t_2 (* (sqrt x) -3.0))
        (t_3 (* 3.0 (* y (sqrt x)))))
   (if (<= x 1.7e-90)
     t_0
     (if (<= x 2.1e-69)
       t_3
       (if (<= x 6.2e-22)
         t_0
         (if (<= x 3.6e+47)
           t_1
           (if (<= x 2.6e+106)
             t_2
             (if (<= x 3.2e+159)
               t_1
               (if (or (<= x 1.25e+185) (not (<= x 4.2e+220))) t_2 t_3)))))))))

C

double code(double x, double y) {
	double t_0 = sqrt(x) * (0.3333333333333333 / x);
	double t_1 = sqrt(x) * (y * 3.0);
	double t_2 = sqrt(x) * -3.0;
	double t_3 = 3.0 * (y * sqrt(x));
	double tmp;
	if (x <= 1.7e-90) {
		tmp = t_0;
	} else if (x <= 2.1e-69) {
		tmp = t_3;
	} else if (x <= 6.2e-22) {
		tmp = t_0;
	} else if (x <= 3.6e+47) {
		tmp = t_1;
	} else if (x <= 2.6e+106) {
		tmp = t_2;
	} else if (x <= 3.2e+159) {
		tmp = t_1;
	} else if ((x <= 1.25e+185) || !(x <= 4.2e+220)) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	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) :: t_3
    real(8) :: tmp
    t_0 = sqrt(x) * (0.3333333333333333d0 / x)
    t_1 = sqrt(x) * (y * 3.0d0)
    t_2 = sqrt(x) * (-3.0d0)
    t_3 = 3.0d0 * (y * sqrt(x))
    if (x <= 1.7d-90) then
        tmp = t_0
    else if (x <= 2.1d-69) then
        tmp = t_3
    else if (x <= 6.2d-22) then
        tmp = t_0
    else if (x <= 3.6d+47) then
        tmp = t_1
    else if (x <= 2.6d+106) then
        tmp = t_2
    else if (x <= 3.2d+159) then
        tmp = t_1
    else if ((x <= 1.25d+185) .or. (.not. (x <= 4.2d+220))) then
        tmp = t_2
    else
        tmp = t_3
    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) * (y * 3.0);
	double t_2 = Math.sqrt(x) * -3.0;
	double t_3 = 3.0 * (y * Math.sqrt(x));
	double tmp;
	if (x <= 1.7e-90) {
		tmp = t_0;
	} else if (x <= 2.1e-69) {
		tmp = t_3;
	} else if (x <= 6.2e-22) {
		tmp = t_0;
	} else if (x <= 3.6e+47) {
		tmp = t_1;
	} else if (x <= 2.6e+106) {
		tmp = t_2;
	} else if (x <= 3.2e+159) {
		tmp = t_1;
	} else if ((x <= 1.25e+185) || !(x <= 4.2e+220)) {
		tmp = t_2;
	} else {
		tmp = t_3;
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = math.sqrt(x) * (0.3333333333333333 / x)
	t_1 = math.sqrt(x) * (y * 3.0)
	t_2 = math.sqrt(x) * -3.0
	t_3 = 3.0 * (y * math.sqrt(x))
	tmp = 0
	if x <= 1.7e-90:
		tmp = t_0
	elif x <= 2.1e-69:
		tmp = t_3
	elif x <= 6.2e-22:
		tmp = t_0
	elif x <= 3.6e+47:
		tmp = t_1
	elif x <= 2.6e+106:
		tmp = t_2
	elif x <= 3.2e+159:
		tmp = t_1
	elif (x <= 1.25e+185) or not (x <= 4.2e+220):
		tmp = t_2
	else:
		tmp = t_3
	return tmp

Julia

function code(x, y)
	t_0 = Float64(sqrt(x) * Float64(0.3333333333333333 / x))
	t_1 = Float64(sqrt(x) * Float64(y * 3.0))
	t_2 = Float64(sqrt(x) * -3.0)
	t_3 = Float64(3.0 * Float64(y * sqrt(x)))
	tmp = 0.0
	if (x <= 1.7e-90)
		tmp = t_0;
	elseif (x <= 2.1e-69)
		tmp = t_3;
	elseif (x <= 6.2e-22)
		tmp = t_0;
	elseif (x <= 3.6e+47)
		tmp = t_1;
	elseif (x <= 2.6e+106)
		tmp = t_2;
	elseif (x <= 3.2e+159)
		tmp = t_1;
	elseif ((x <= 1.25e+185) || !(x <= 4.2e+220))
		tmp = t_2;
	else
		tmp = t_3;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = sqrt(x) * (0.3333333333333333 / x);
	t_1 = sqrt(x) * (y * 3.0);
	t_2 = sqrt(x) * -3.0;
	t_3 = 3.0 * (y * sqrt(x));
	tmp = 0.0;
	if (x <= 1.7e-90)
		tmp = t_0;
	elseif (x <= 2.1e-69)
		tmp = t_3;
	elseif (x <= 6.2e-22)
		tmp = t_0;
	elseif (x <= 3.6e+47)
		tmp = t_1;
	elseif (x <= 2.6e+106)
		tmp = t_2;
	elseif (x <= 3.2e+159)
		tmp = t_1;
	elseif ((x <= 1.25e+185) || ~((x <= 4.2e+220)))
		tmp = t_2;
	else
		tmp = t_3;
	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] * N[(y * 3.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[Sqrt[x], $MachinePrecision] * -3.0), $MachinePrecision]}, Block[{t$95$3 = N[(3.0 * N[(y * N[Sqrt[x], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, 1.7e-90], t$95$0, If[LessEqual[x, 2.1e-69], t$95$3, If[LessEqual[x, 6.2e-22], t$95$0, If[LessEqual[x, 3.6e+47], t$95$1, If[LessEqual[x, 2.6e+106], t$95$2, If[LessEqual[x, 3.2e+159], t$95$1, If[Or[LessEqual[x, 1.25e+185], N[Not[LessEqual[x, 4.2e+220]], $MachinePrecision]], t$95$2, t$95$3]]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if x < 1.69999999999999997e-90 or 2.1e-69 < x < 6.20000000000000025e-22

   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%

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

      2. associate--l+ 99.3%

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

      3. distribute-lft-in 99.3%

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

      4. +-commutative 99.3%

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

      5. *-commutative 99.3%

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

      6. associate-*r* 99.3%

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

      7. cancel-sign-sub 99.3%

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

      8. *-commutative 99.3%

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

      9. associate-*r* 99.4%

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

      10. *-commutative 99.4%

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

      11. distribute-rgt-out-- 99.4%

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

      12. distribute-lft-neg-in 99.4%

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

      13. cancel-sign-sub 99.4%

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

      14. +-commutative 99.4%

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

      15. *-commutative 99.4%

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

      16. distribute-rgt-in 99.4%

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

   3. Simplified 99.4%

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

   4. Taylor expanded in x around 0 79.5%

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

   if 1.69999999999999997e-90 < x < 2.1e-69 or 1.24999999999999997e185 < x < 4.20000000000000014e220

   1. Initial program 99.5%

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

      1. +-commutative 99.5%

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

      2. associate--l+ 99.5%

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

      3. distribute-lft-in 99.5%

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

      4. +-commutative 99.5%

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

      5. *-commutative 99.5%

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

      6. associate-*r* 99.4%

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

      7. cancel-sign-sub 99.4%

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

      8. *-commutative 99.4%

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

      9. associate-*r* 99.2%

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

      10. *-commutative 99.2%

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

      11. distribute-rgt-out-- 99.2%

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

      12. distribute-lft-neg-in 99.2%

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

      13. cancel-sign-sub 99.2%

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

      14. +-commutative 99.2%

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

      15. *-commutative 99.2%

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

      16. distribute-rgt-in 99.2%

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

   3. Simplified 99.4%

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

   4. Taylor expanded in y around inf 76.7%

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

   if 6.20000000000000025e-22 < x < 3.60000000000000008e47 or 2.6000000000000002e106 < x < 3.19999999999999985e159

   1. Initial program 99.4%

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

      1. +-commutative 99.4%

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

      2. associate--l+ 99.4%

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

      3. distribute-lft-in 99.4%

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

      4. +-commutative 99.4%

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

      5. *-commutative 99.4%

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

      6. associate-*r* 99.4%

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

      7. cancel-sign-sub 99.4%

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

      8. *-commutative 99.4%

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

      9. associate-*r* 99.4%

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

      10. *-commutative 99.4%

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

      11. distribute-rgt-out-- 99.4%

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

      12. distribute-lft-neg-in 99.4%

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

      13. cancel-sign-sub 99.4%

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

      14. +-commutative 99.4%

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

      15. *-commutative 99.4%

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

      16. distribute-rgt-in 99.4%

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

   3. Simplified 99.5%

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

   4. Taylor expanded in y around inf 66.0%

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

      1. associate-*r* 66.1%

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

   6. Simplified 66.1%

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

   if 3.60000000000000008e47 < x < 2.6000000000000002e106 or 3.19999999999999985e159 < x < 1.24999999999999997e185 or 4.20000000000000014e220 < x

   1. Initial program 99.5%

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

      1. associate--l+ 99.5%

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

      2. associate-/r* 99.5%

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

   3. Simplified 99.5%

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

   4. Taylor expanded in x around inf 99.5%

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

   5. Taylor expanded in y around 0 64.4%

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

      1. *-commutative 64.4%

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

   7. Simplified 64.4%

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

4. Final simplification 72.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 1.7 \cdot 10^{-90}:\\ \;\;\;\;\sqrt{x} \cdot \frac{0.3333333333333333}{x}\\ \mathbf{elif}\;x \leq 2.1 \cdot 10^{-69}:\\ \;\;\;\;3 \cdot \left(y \cdot \sqrt{x}\right)\\ \mathbf{elif}\;x \leq 6.2 \cdot 10^{-22}:\\ \;\;\;\;\sqrt{x} \cdot \frac{0.3333333333333333}{x}\\ \mathbf{elif}\;x \leq 3.6 \cdot 10^{+47}:\\ \;\;\;\;\sqrt{x} \cdot \left(y \cdot 3\right)\\ \mathbf{elif}\;x \leq 2.6 \cdot 10^{+106}:\\ \;\;\;\;\sqrt{x} \cdot -3\\ \mathbf{elif}\;x \leq 3.2 \cdot 10^{+159}:\\ \;\;\;\;\sqrt{x} \cdot \left(y \cdot 3\right)\\ \mathbf{elif}\;x \leq 1.25 \cdot 10^{+185} \lor \neg \left(x \leq 4.2 \cdot 10^{+220}\right):\\ \;\;\;\;\sqrt{x} \cdot -3\\ \mathbf{else}:\\ \;\;\;\;3 \cdot \left(y \cdot \sqrt{x}\right)\\ \end{array} \]

Alternative 4: 60.6% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \sqrt{x} \cdot \frac{0.3333333333333333}{x}\\ t_1 := \sqrt{x} \cdot -3\\ t_2 := 3 \cdot \left(y \cdot \sqrt{x}\right)\\ \mathbf{if}\;x \leq 1.7 \cdot 10^{-90}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq 1.35 \cdot 10^{-68}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq 2.5 \cdot 10^{-23}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq 9.5 \cdot 10^{+47}:\\ \;\;\;\;y \cdot \left(3 \cdot \sqrt{x}\right)\\ \mathbf{elif}\;x \leq 9.8 \cdot 10^{+104}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 4.4 \cdot 10^{+159}:\\ \;\;\;\;\sqrt{x} \cdot \left(y \cdot 3\right)\\ \mathbf{elif}\;x \leq 8.8 \cdot 10^{+184} \lor \neg \left(x \leq 3.3 \cdot 10^{+220}\right):\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_2\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (* (sqrt x) (/ 0.3333333333333333 x)))
        (t_1 (* (sqrt x) -3.0))
        (t_2 (* 3.0 (* y (sqrt x)))))
   (if (<= x 1.7e-90)
     t_0
     (if (<= x 1.35e-68)
       t_2
       (if (<= x 2.5e-23)
         t_0
         (if (<= x 9.5e+47)
           (* y (* 3.0 (sqrt x)))
           (if (<= x 9.8e+104)
             t_1
             (if (<= x 4.4e+159)
               (* (sqrt x) (* y 3.0))
               (if (or (<= x 8.8e+184) (not (<= x 3.3e+220))) 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 = 3.0 * (y * sqrt(x));
	double tmp;
	if (x <= 1.7e-90) {
		tmp = t_0;
	} else if (x <= 1.35e-68) {
		tmp = t_2;
	} else if (x <= 2.5e-23) {
		tmp = t_0;
	} else if (x <= 9.5e+47) {
		tmp = y * (3.0 * sqrt(x));
	} else if (x <= 9.8e+104) {
		tmp = t_1;
	} else if (x <= 4.4e+159) {
		tmp = sqrt(x) * (y * 3.0);
	} else if ((x <= 8.8e+184) || !(x <= 3.3e+220)) {
		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 = 3.0d0 * (y * sqrt(x))
    if (x <= 1.7d-90) then
        tmp = t_0
    else if (x <= 1.35d-68) then
        tmp = t_2
    else if (x <= 2.5d-23) then
        tmp = t_0
    else if (x <= 9.5d+47) then
        tmp = y * (3.0d0 * sqrt(x))
    else if (x <= 9.8d+104) then
        tmp = t_1
    else if (x <= 4.4d+159) then
        tmp = sqrt(x) * (y * 3.0d0)
    else if ((x <= 8.8d+184) .or. (.not. (x <= 3.3d+220))) 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 = 3.0 * (y * Math.sqrt(x));
	double tmp;
	if (x <= 1.7e-90) {
		tmp = t_0;
	} else if (x <= 1.35e-68) {
		tmp = t_2;
	} else if (x <= 2.5e-23) {
		tmp = t_0;
	} else if (x <= 9.5e+47) {
		tmp = y * (3.0 * Math.sqrt(x));
	} else if (x <= 9.8e+104) {
		tmp = t_1;
	} else if (x <= 4.4e+159) {
		tmp = Math.sqrt(x) * (y * 3.0);
	} else if ((x <= 8.8e+184) || !(x <= 3.3e+220)) {
		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 = 3.0 * (y * math.sqrt(x))
	tmp = 0
	if x <= 1.7e-90:
		tmp = t_0
	elif x <= 1.35e-68:
		tmp = t_2
	elif x <= 2.5e-23:
		tmp = t_0
	elif x <= 9.5e+47:
		tmp = y * (3.0 * math.sqrt(x))
	elif x <= 9.8e+104:
		tmp = t_1
	elif x <= 4.4e+159:
		tmp = math.sqrt(x) * (y * 3.0)
	elif (x <= 8.8e+184) or not (x <= 3.3e+220):
		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(3.0 * Float64(y * sqrt(x)))
	tmp = 0.0
	if (x <= 1.7e-90)
		tmp = t_0;
	elseif (x <= 1.35e-68)
		tmp = t_2;
	elseif (x <= 2.5e-23)
		tmp = t_0;
	elseif (x <= 9.5e+47)
		tmp = Float64(y * Float64(3.0 * sqrt(x)));
	elseif (x <= 9.8e+104)
		tmp = t_1;
	elseif (x <= 4.4e+159)
		tmp = Float64(sqrt(x) * Float64(y * 3.0));
	elseif ((x <= 8.8e+184) || !(x <= 3.3e+220))
		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 = 3.0 * (y * sqrt(x));
	tmp = 0.0;
	if (x <= 1.7e-90)
		tmp = t_0;
	elseif (x <= 1.35e-68)
		tmp = t_2;
	elseif (x <= 2.5e-23)
		tmp = t_0;
	elseif (x <= 9.5e+47)
		tmp = y * (3.0 * sqrt(x));
	elseif (x <= 9.8e+104)
		tmp = t_1;
	elseif (x <= 4.4e+159)
		tmp = sqrt(x) * (y * 3.0);
	elseif ((x <= 8.8e+184) || ~((x <= 3.3e+220)))
		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[(3.0 * N[(y * N[Sqrt[x], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, 1.7e-90], t$95$0, If[LessEqual[x, 1.35e-68], t$95$2, If[LessEqual[x, 2.5e-23], t$95$0, If[LessEqual[x, 9.5e+47], N[(y * N[(3.0 * N[Sqrt[x], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 9.8e+104], t$95$1, If[LessEqual[x, 4.4e+159], N[(N[Sqrt[x], $MachinePrecision] * N[(y * 3.0), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[x, 8.8e+184], N[Not[LessEqual[x, 3.3e+220]], $MachinePrecision]], t$95$1, t$95$2]]]]]]]]]]

Derivation

1. Split input into 5 regimes

2. if x < 1.69999999999999997e-90 or 1.3500000000000001e-68 < x < 2.5000000000000001e-23

   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%

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

      2. associate--l+ 99.3%

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

      3. distribute-lft-in 99.3%

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

      4. +-commutative 99.3%

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

      5. *-commutative 99.3%

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

      6. associate-*r* 99.3%

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

      7. cancel-sign-sub 99.3%

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

      8. *-commutative 99.3%

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

      9. associate-*r* 99.4%

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

      10. *-commutative 99.4%

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

      11. distribute-rgt-out-- 99.4%

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

      12. distribute-lft-neg-in 99.4%

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

      13. cancel-sign-sub 99.4%

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

      14. +-commutative 99.4%

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

      15. *-commutative 99.4%

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

      16. distribute-rgt-in 99.4%

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

   3. Simplified 99.4%

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

   4. Taylor expanded in x around 0 79.5%

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

   if 1.69999999999999997e-90 < x < 1.3500000000000001e-68 or 8.8e184 < x < 3.30000000000000021e220

   1. Initial program 99.5%

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

      1. +-commutative 99.5%

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

      2. associate--l+ 99.5%

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

      3. distribute-lft-in 99.5%

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

      4. +-commutative 99.5%

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

      5. *-commutative 99.5%

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

      6. associate-*r* 99.4%

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

      7. cancel-sign-sub 99.4%

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

      8. *-commutative 99.4%

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

      9. associate-*r* 99.2%

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

      10. *-commutative 99.2%

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

      11. distribute-rgt-out-- 99.2%

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

      12. distribute-lft-neg-in 99.2%

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

      13. cancel-sign-sub 99.2%

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

      14. +-commutative 99.2%

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

      15. *-commutative 99.2%

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

      16. distribute-rgt-in 99.2%

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

   3. Simplified 99.4%

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

   4. Taylor expanded in y around inf 76.7%

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

   if 2.5000000000000001e-23 < x < 9.50000000000000001e47

   1. Initial program 99.4%

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

      1. +-commutative 99.4%

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

      2. associate--l+ 99.4%

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

      3. distribute-lft-in 99.4%

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

      4. +-commutative 99.4%

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

      5. *-commutative 99.4%

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

      6. associate-*r* 99.4%

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

      7. cancel-sign-sub 99.4%

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

      8. *-commutative 99.4%

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

      9. associate-*r* 99.4%

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

      10. *-commutative 99.4%

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

      11. distribute-rgt-out-- 99.4%

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

      12. distribute-lft-neg-in 99.4%

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

      13. cancel-sign-sub 99.4%

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

      14. +-commutative 99.4%

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

      15. *-commutative 99.4%

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

      16. distribute-rgt-in 99.4%

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

   3. Simplified 99.4%

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

   4. Taylor expanded in y around inf 69.8%

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

      1. add-cube-cbrt 69.3%

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

      2. pow3 69.3%

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

      3. associate-*r* 69.1%

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

   6. Applied egg-rr 69.1%

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

      1. rem-cube-cbrt 70.0%

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

      2. *-commutative 70.0%

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

      3. associate-*r* 70.0%

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

   8. Applied egg-rr 70.0%

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

   if 9.50000000000000001e47 < x < 9.7999999999999997e104 or 4.3999999999999998e159 < x < 8.8e184 or 3.30000000000000021e220 < x

   1. Initial program 99.5%

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

      1. associate--l+ 99.5%

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

      2. associate-/r* 99.5%

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

   3. Simplified 99.5%

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

   4. Taylor expanded in x around inf 99.5%

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

   5. Taylor expanded in y around 0 64.4%

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

      1. *-commutative 64.4%

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

   7. Simplified 64.4%

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

   if 9.7999999999999997e104 < x < 4.3999999999999998e159

   1. Initial program 99.4%

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

      1. +-commutative 99.4%

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

      2. associate--l+ 99.4%

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

      3. distribute-lft-in 99.4%

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

      4. +-commutative 99.4%

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

      5. *-commutative 99.4%

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

      6. associate-*r* 99.4%

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

      7. cancel-sign-sub 99.4%

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

      8. *-commutative 99.4%

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

      9. associate-*r* 99.5%

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

      10. *-commutative 99.5%

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

      11. distribute-rgt-out-- 99.5%

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

      12. distribute-lft-neg-in 99.5%

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

      13. cancel-sign-sub 99.5%

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

      14. +-commutative 99.5%

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

      15. *-commutative 99.5%

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

      16. distribute-rgt-in 99.5%

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

   3. Simplified 99.5%

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

   4. Taylor expanded in y around inf 61.8%

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

      1. associate-*r* 62.0%

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

   6. Simplified 62.0%

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

4. Final simplification 72.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 1.7 \cdot 10^{-90}:\\ \;\;\;\;\sqrt{x} \cdot \frac{0.3333333333333333}{x}\\ \mathbf{elif}\;x \leq 1.35 \cdot 10^{-68}:\\ \;\;\;\;3 \cdot \left(y \cdot \sqrt{x}\right)\\ \mathbf{elif}\;x \leq 2.5 \cdot 10^{-23}:\\ \;\;\;\;\sqrt{x} \cdot \frac{0.3333333333333333}{x}\\ \mathbf{elif}\;x \leq 9.5 \cdot 10^{+47}:\\ \;\;\;\;y \cdot \left(3 \cdot \sqrt{x}\right)\\ \mathbf{elif}\;x \leq 9.8 \cdot 10^{+104}:\\ \;\;\;\;\sqrt{x} \cdot -3\\ \mathbf{elif}\;x \leq 4.4 \cdot 10^{+159}:\\ \;\;\;\;\sqrt{x} \cdot \left(y \cdot 3\right)\\ \mathbf{elif}\;x \leq 8.8 \cdot 10^{+184} \lor \neg \left(x \leq 3.3 \cdot 10^{+220}\right):\\ \;\;\;\;\sqrt{x} \cdot -3\\ \mathbf{else}:\\ \;\;\;\;3 \cdot \left(y \cdot \sqrt{x}\right)\\ \end{array} \]

Alternative 5: 60.5% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \sqrt{x} \cdot -3\\ t_1 := 3 \cdot \left(y \cdot \sqrt{x}\right)\\ \mathbf{if}\;x \leq 1.7 \cdot 10^{-90}:\\ \;\;\;\;\sqrt{x} \cdot \frac{0.3333333333333333}{x}\\ \mathbf{elif}\;x \leq 2.3 \cdot 10^{-67}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;x \leq 1.75 \cdot 10^{-21}:\\ \;\;\;\;3 \cdot \left(\frac{0.1111111111111111}{x} \cdot \sqrt{x}\right)\\ \mathbf{elif}\;x \leq 3.2 \cdot 10^{+47}:\\ \;\;\;\;y \cdot \left(3 \cdot \sqrt{x}\right)\\ \mathbf{elif}\;x \leq 5.8 \cdot 10^{+107}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq 4.8 \cdot 10^{+159}:\\ \;\;\;\;\sqrt{x} \cdot \left(y \cdot 3\right)\\ \mathbf{elif}\;x \leq 1.3 \cdot 10^{+185} \lor \neg \left(x \leq 2.3 \cdot 10^{+221}\right):\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (* (sqrt x) -3.0)) (t_1 (* 3.0 (* y (sqrt x)))))
   (if (<= x 1.7e-90)
     (* (sqrt x) (/ 0.3333333333333333 x))
     (if (<= x 2.3e-67)
       t_1
       (if (<= x 1.75e-21)
         (* 3.0 (* (/ 0.1111111111111111 x) (sqrt x)))
         (if (<= x 3.2e+47)
           (* y (* 3.0 (sqrt x)))
           (if (<= x 5.8e+107)
             t_0
             (if (<= x 4.8e+159)
               (* (sqrt x) (* y 3.0))
               (if (or (<= x 1.3e+185) (not (<= x 2.3e+221))) t_0 t_1)))))))))

C

double code(double x, double y) {
	double t_0 = sqrt(x) * -3.0;
	double t_1 = 3.0 * (y * sqrt(x));
	double tmp;
	if (x <= 1.7e-90) {
		tmp = sqrt(x) * (0.3333333333333333 / x);
	} else if (x <= 2.3e-67) {
		tmp = t_1;
	} else if (x <= 1.75e-21) {
		tmp = 3.0 * ((0.1111111111111111 / x) * sqrt(x));
	} else if (x <= 3.2e+47) {
		tmp = y * (3.0 * sqrt(x));
	} else if (x <= 5.8e+107) {
		tmp = t_0;
	} else if (x <= 4.8e+159) {
		tmp = sqrt(x) * (y * 3.0);
	} else if ((x <= 1.3e+185) || !(x <= 2.3e+221)) {
		tmp = t_0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: tmp
    t_0 = sqrt(x) * (-3.0d0)
    t_1 = 3.0d0 * (y * sqrt(x))
    if (x <= 1.7d-90) then
        tmp = sqrt(x) * (0.3333333333333333d0 / x)
    else if (x <= 2.3d-67) then
        tmp = t_1
    else if (x <= 1.75d-21) then
        tmp = 3.0d0 * ((0.1111111111111111d0 / x) * sqrt(x))
    else if (x <= 3.2d+47) then
        tmp = y * (3.0d0 * sqrt(x))
    else if (x <= 5.8d+107) then
        tmp = t_0
    else if (x <= 4.8d+159) then
        tmp = sqrt(x) * (y * 3.0d0)
    else if ((x <= 1.3d+185) .or. (.not. (x <= 2.3d+221))) then
        tmp = t_0
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double t_0 = Math.sqrt(x) * -3.0;
	double t_1 = 3.0 * (y * Math.sqrt(x));
	double tmp;
	if (x <= 1.7e-90) {
		tmp = Math.sqrt(x) * (0.3333333333333333 / x);
	} else if (x <= 2.3e-67) {
		tmp = t_1;
	} else if (x <= 1.75e-21) {
		tmp = 3.0 * ((0.1111111111111111 / x) * Math.sqrt(x));
	} else if (x <= 3.2e+47) {
		tmp = y * (3.0 * Math.sqrt(x));
	} else if (x <= 5.8e+107) {
		tmp = t_0;
	} else if (x <= 4.8e+159) {
		tmp = Math.sqrt(x) * (y * 3.0);
	} else if ((x <= 1.3e+185) || !(x <= 2.3e+221)) {
		tmp = t_0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = math.sqrt(x) * -3.0
	t_1 = 3.0 * (y * math.sqrt(x))
	tmp = 0
	if x <= 1.7e-90:
		tmp = math.sqrt(x) * (0.3333333333333333 / x)
	elif x <= 2.3e-67:
		tmp = t_1
	elif x <= 1.75e-21:
		tmp = 3.0 * ((0.1111111111111111 / x) * math.sqrt(x))
	elif x <= 3.2e+47:
		tmp = y * (3.0 * math.sqrt(x))
	elif x <= 5.8e+107:
		tmp = t_0
	elif x <= 4.8e+159:
		tmp = math.sqrt(x) * (y * 3.0)
	elif (x <= 1.3e+185) or not (x <= 2.3e+221):
		tmp = t_0
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y)
	t_0 = Float64(sqrt(x) * -3.0)
	t_1 = Float64(3.0 * Float64(y * sqrt(x)))
	tmp = 0.0
	if (x <= 1.7e-90)
		tmp = Float64(sqrt(x) * Float64(0.3333333333333333 / x));
	elseif (x <= 2.3e-67)
		tmp = t_1;
	elseif (x <= 1.75e-21)
		tmp = Float64(3.0 * Float64(Float64(0.1111111111111111 / x) * sqrt(x)));
	elseif (x <= 3.2e+47)
		tmp = Float64(y * Float64(3.0 * sqrt(x)));
	elseif (x <= 5.8e+107)
		tmp = t_0;
	elseif (x <= 4.8e+159)
		tmp = Float64(sqrt(x) * Float64(y * 3.0));
	elseif ((x <= 1.3e+185) || !(x <= 2.3e+221))
		tmp = t_0;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = sqrt(x) * -3.0;
	t_1 = 3.0 * (y * sqrt(x));
	tmp = 0.0;
	if (x <= 1.7e-90)
		tmp = sqrt(x) * (0.3333333333333333 / x);
	elseif (x <= 2.3e-67)
		tmp = t_1;
	elseif (x <= 1.75e-21)
		tmp = 3.0 * ((0.1111111111111111 / x) * sqrt(x));
	elseif (x <= 3.2e+47)
		tmp = y * (3.0 * sqrt(x));
	elseif (x <= 5.8e+107)
		tmp = t_0;
	elseif (x <= 4.8e+159)
		tmp = sqrt(x) * (y * 3.0);
	elseif ((x <= 1.3e+185) || ~((x <= 2.3e+221)))
		tmp = t_0;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(N[Sqrt[x], $MachinePrecision] * -3.0), $MachinePrecision]}, Block[{t$95$1 = N[(3.0 * N[(y * N[Sqrt[x], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, 1.7e-90], N[(N[Sqrt[x], $MachinePrecision] * N[(0.3333333333333333 / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 2.3e-67], t$95$1, If[LessEqual[x, 1.75e-21], N[(3.0 * N[(N[(0.1111111111111111 / x), $MachinePrecision] * N[Sqrt[x], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 3.2e+47], N[(y * N[(3.0 * N[Sqrt[x], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 5.8e+107], t$95$0, If[LessEqual[x, 4.8e+159], N[(N[Sqrt[x], $MachinePrecision] * N[(y * 3.0), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[x, 1.3e+185], N[Not[LessEqual[x, 2.3e+221]], $MachinePrecision]], t$95$0, t$95$1]]]]]]]]]

Derivation

1. Split input into 6 regimes

2. if x < 1.69999999999999997e-90

   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. +-commutative 99.2%

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

      2. associate--l+ 99.2%

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

      3. distribute-lft-in 99.2%

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

      4. +-commutative 99.2%

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

      5. *-commutative 99.2%

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

      6. associate-*r* 99.3%

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

      7. cancel-sign-sub 99.3%

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

      8. *-commutative 99.3%

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

      9. associate-*r* 99.4%

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

      10. *-commutative 99.4%

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

      11. distribute-rgt-out-- 99.4%

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

      12. distribute-lft-neg-in 99.4%

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

      13. cancel-sign-sub 99.4%

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

      14. +-commutative 99.4%

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

      15. *-commutative 99.4%

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

      16. distribute-rgt-in 99.4%

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

   3. Simplified 99.4%

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

   4. Taylor expanded in x around 0 82.5%

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

   if 1.69999999999999997e-90 < x < 2.3e-67 or 1.3e185 < x < 2.29999999999999987e221

   1. Initial program 99.4%

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

      1. +-commutative 99.4%

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

      2. associate--l+ 99.4%

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

      3. distribute-lft-in 99.4%

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

      4. +-commutative 99.4%

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

      5. *-commutative 99.4%

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

      6. associate-*r* 99.4%

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

      7. cancel-sign-sub 99.4%

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

      8. *-commutative 99.4%

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

      9. associate-*r* 99.3%

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

      10. *-commutative 99.3%

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

      11. distribute-rgt-out-- 99.3%

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

      12. distribute-lft-neg-in 99.3%

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

      13. cancel-sign-sub 99.3%

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

      14. +-commutative 99.3%

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

      15. *-commutative 99.3%

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

      16. distribute-rgt-in 99.3%

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

   3. Simplified 99.4%

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

   4. Taylor expanded in y around inf 75.0%

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

   if 2.3e-67 < x < 1.7500000000000002e-21

   1. Initial program 99.6%

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

      1. +-commutative 99.6%

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

      2. associate--l+ 99.6%

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

      3. distribute-rgt-in 99.6%

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

      4. remove-double-neg 99.6%

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

      5. distribute-lft-neg-in 99.6%

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

      6. distribute-rgt-neg-in 99.6%

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

      7. mul-1-neg 99.6%

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

      8. metadata-eval 99.6%

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

      9. *-commutative 99.6%

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

      10. associate-/r* 99.6%

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

      11. distribute-neg-frac 99.6%

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

      12. *-commutative 99.6%

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

      13. associate-/r/ 99.4%

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

      14. associate-/l/ 99.4%

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

      15. associate-/r/ 99.6%

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

   3. Simplified 99.6%

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

      1. expm1-log1p-u 99.6%

         \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(3 \cdot \sqrt{x}\right)\right)} \cdot \left(\frac{0.1111111111111111}{x} + \left(y - 1\right)\right) \]

      2. expm1-udef 9.1%

         \[\leadsto \color{blue}{\left(e^{\mathsf{log1p}\left(3 \cdot \sqrt{x}\right)} - 1\right)} \cdot \left(\frac{0.1111111111111111}{x} + \left(y - 1\right)\right) \]

      3. *-commutative 9.1%

         \[\leadsto \left(e^{\mathsf{log1p}\left(\color{blue}{\sqrt{x} \cdot 3}\right)} - 1\right) \cdot \left(\frac{0.1111111111111111}{x} + \left(y - 1\right)\right) \]

      4. metadata-eval 9.1%

         \[\leadsto \left(e^{\mathsf{log1p}\left(\sqrt{x} \cdot \color{blue}{\sqrt{9}}\right)} - 1\right) \cdot \left(\frac{0.1111111111111111}{x} + \left(y - 1\right)\right) \]

      5. sqrt-prod 9.1%

         \[\leadsto \left(e^{\mathsf{log1p}\left(\color{blue}{\sqrt{x \cdot 9}}\right)} - 1\right) \cdot \left(\frac{0.1111111111111111}{x} + \left(y - 1\right)\right) \]

   5. Applied egg-rr 9.1%

      \[\leadsto \color{blue}{\left(e^{\mathsf{log1p}\left(\sqrt{x \cdot 9}\right)} - 1\right)} \cdot \left(\frac{0.1111111111111111}{x} + \left(y - 1\right)\right) \]
   6. Step-by-step derivation

      1. expm1-def 99.7%

         \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\sqrt{x \cdot 9}\right)\right)} \cdot \left(\frac{0.1111111111111111}{x} + \left(y - 1\right)\right) \]

      2. expm1-log1p 99.7%

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

   7. Simplified 99.7%

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

   8. Taylor expanded in y around 0 66.3%

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

      1. sub-neg 66.3%

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

      2. associate-*r/ 66.4%

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

      3. metadata-eval 66.4%

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

      4. metadata-eval 66.4%

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

   10. Simplified 66.4%

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

   11. Taylor expanded in x around 0 66.4%

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

   if 1.7500000000000002e-21 < x < 3.2e47

   1. Initial program 99.4%

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

      1. +-commutative 99.4%

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

      2. associate--l+ 99.4%

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

      3. distribute-lft-in 99.4%

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

      4. +-commutative 99.4%

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

      5. *-commutative 99.4%

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

      6. associate-*r* 99.4%

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

      7. cancel-sign-sub 99.4%

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

      8. *-commutative 99.4%

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

      9. associate-*r* 99.4%

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

      10. *-commutative 99.4%

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

      11. distribute-rgt-out-- 99.4%

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

      12. distribute-lft-neg-in 99.4%

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

      13. cancel-sign-sub 99.4%

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

      14. +-commutative 99.4%

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

      15. *-commutative 99.4%

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

      16. distribute-rgt-in 99.4%

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

   3. Simplified 99.4%

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

   4. Taylor expanded in y around inf 69.8%

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

      1. add-cube-cbrt 69.3%

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

      2. pow3 69.3%

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

      3. associate-*r* 69.1%

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

   6. Applied egg-rr 69.1%

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

      1. rem-cube-cbrt 70.0%

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

      2. *-commutative 70.0%

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

      3. associate-*r* 70.0%

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

   8. Applied egg-rr 70.0%

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

   if 3.2e47 < x < 5.79999999999999975e107 or 4.8e159 < x < 1.3e185 or 2.29999999999999987e221 < x

   1. Initial program 99.5%

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

      1. associate--l+ 99.5%

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

      2. associate-/r* 99.5%

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

   3. Simplified 99.5%

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

   4. Taylor expanded in x around inf 99.5%

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

   5. Taylor expanded in y around 0 64.4%

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

      1. *-commutative 64.4%

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

   7. Simplified 64.4%

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

   if 5.79999999999999975e107 < x < 4.8e159

   1. Initial program 99.4%

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

      1. +-commutative 99.4%

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

      2. associate--l+ 99.4%

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

      3. distribute-lft-in 99.4%

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

      4. +-commutative 99.4%

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

      5. *-commutative 99.4%

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

      6. associate-*r* 99.4%

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

      7. cancel-sign-sub 99.4%

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

      8. *-commutative 99.4%

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

      9. associate-*r* 99.5%

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

      10. *-commutative 99.5%

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

      11. distribute-rgt-out-- 99.5%

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

      12. distribute-lft-neg-in 99.5%

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

      13. cancel-sign-sub 99.5%

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

      14. +-commutative 99.5%

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

      15. *-commutative 99.5%

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

      16. distribute-rgt-in 99.5%

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

   3. Simplified 99.5%

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

   4. Taylor expanded in y around inf 61.8%

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

      1. associate-*r* 62.0%

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

   6. Simplified 62.0%

      \[\leadsto \color{blue}{\left(3 \cdot y\right) \cdot \sqrt{x}} \]
3. Recombined 6 regimes into one program.

4. Final simplification 72.6%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 1.7 \cdot 10^{-90}:\\ \;\;\;\;\sqrt{x} \cdot \frac{0.3333333333333333}{x}\\ \mathbf{elif}\;x \leq 2.3 \cdot 10^{-67}:\\ \;\;\;\;3 \cdot \left(y \cdot \sqrt{x}\right)\\ \mathbf{elif}\;x \leq 1.75 \cdot 10^{-21}:\\ \;\;\;\;3 \cdot \left(\frac{0.1111111111111111}{x} \cdot \sqrt{x}\right)\\ \mathbf{elif}\;x \leq 3.2 \cdot 10^{+47}:\\ \;\;\;\;y \cdot \left(3 \cdot \sqrt{x}\right)\\ \mathbf{elif}\;x \leq 5.8 \cdot 10^{+107}:\\ \;\;\;\;\sqrt{x} \cdot -3\\ \mathbf{elif}\;x \leq 4.8 \cdot 10^{+159}:\\ \;\;\;\;\sqrt{x} \cdot \left(y \cdot 3\right)\\ \mathbf{elif}\;x \leq 1.3 \cdot 10^{+185} \lor \neg \left(x \leq 2.3 \cdot 10^{+221}\right):\\ \;\;\;\;\sqrt{x} \cdot -3\\ \mathbf{else}:\\ \;\;\;\;3 \cdot \left(y \cdot \sqrt{x}\right)\\ \end{array} \]

Alternative 6: 85.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 1.7 \cdot 10^{-90}:\\ \;\;\;\;\sqrt{x} \cdot \frac{0.3333333333333333}{x}\\ \mathbf{elif}\;x \leq 2.45 \cdot 10^{-73} \lor \neg \left(x \leq 1.25 \cdot 10^{-21}\right):\\ \;\;\;\;\sqrt{x \cdot 9} \cdot \left(y + -1\right)\\ \mathbf{else}:\\ \;\;\;\;3 \cdot \left(\frac{0.1111111111111111}{x} \cdot \sqrt{x}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x 1.7e-90)
   (* (sqrt x) (/ 0.3333333333333333 x))
   (if (or (<= x 2.45e-73) (not (<= x 1.25e-21)))
     (* (sqrt (* x 9.0)) (+ y -1.0))
     (* 3.0 (* (/ 0.1111111111111111 x) (sqrt x))))))

C

double code(double x, double y) {
	double tmp;
	if (x <= 1.7e-90) {
		tmp = sqrt(x) * (0.3333333333333333 / x);
	} else if ((x <= 2.45e-73) || !(x <= 1.25e-21)) {
		tmp = sqrt((x * 9.0)) * (y + -1.0);
	} else {
		tmp = 3.0 * ((0.1111111111111111 / x) * sqrt(x));
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (x <= 1.7d-90) then
        tmp = sqrt(x) * (0.3333333333333333d0 / x)
    else if ((x <= 2.45d-73) .or. (.not. (x <= 1.25d-21))) then
        tmp = sqrt((x * 9.0d0)) * (y + (-1.0d0))
    else
        tmp = 3.0d0 * ((0.1111111111111111d0 / x) * sqrt(x))
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= 1.7e-90) {
		tmp = Math.sqrt(x) * (0.3333333333333333 / x);
	} else if ((x <= 2.45e-73) || !(x <= 1.25e-21)) {
		tmp = Math.sqrt((x * 9.0)) * (y + -1.0);
	} else {
		tmp = 3.0 * ((0.1111111111111111 / x) * Math.sqrt(x));
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= 1.7e-90:
		tmp = math.sqrt(x) * (0.3333333333333333 / x)
	elif (x <= 2.45e-73) or not (x <= 1.25e-21):
		tmp = math.sqrt((x * 9.0)) * (y + -1.0)
	else:
		tmp = 3.0 * ((0.1111111111111111 / x) * math.sqrt(x))
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= 1.7e-90)
		tmp = Float64(sqrt(x) * Float64(0.3333333333333333 / x));
	elseif ((x <= 2.45e-73) || !(x <= 1.25e-21))
		tmp = Float64(sqrt(Float64(x * 9.0)) * Float64(y + -1.0));
	else
		tmp = Float64(3.0 * Float64(Float64(0.1111111111111111 / x) * sqrt(x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= 1.7e-90)
		tmp = sqrt(x) * (0.3333333333333333 / x);
	elseif ((x <= 2.45e-73) || ~((x <= 1.25e-21)))
		tmp = sqrt((x * 9.0)) * (y + -1.0);
	else
		tmp = 3.0 * ((0.1111111111111111 / x) * sqrt(x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, 1.7e-90], N[(N[Sqrt[x], $MachinePrecision] * N[(0.3333333333333333 / x), $MachinePrecision]), $MachinePrecision], If[Or[LessEqual[x, 2.45e-73], N[Not[LessEqual[x, 1.25e-21]], $MachinePrecision]], N[(N[Sqrt[N[(x * 9.0), $MachinePrecision]], $MachinePrecision] * N[(y + -1.0), $MachinePrecision]), $MachinePrecision], N[(3.0 * N[(N[(0.1111111111111111 / x), $MachinePrecision] * N[Sqrt[x], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if x < 1.69999999999999997e-90

   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. +-commutative 99.2%

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

      2. associate--l+ 99.2%

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

      3. distribute-lft-in 99.2%

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

      4. +-commutative 99.2%

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

      5. *-commutative 99.2%

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

      6. associate-*r* 99.3%

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

      7. cancel-sign-sub 99.3%

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

      8. *-commutative 99.3%

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

      9. associate-*r* 99.4%

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

      10. *-commutative 99.4%

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

      11. distribute-rgt-out-- 99.4%

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

      12. distribute-lft-neg-in 99.4%

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

      13. cancel-sign-sub 99.4%

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

      14. +-commutative 99.4%

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

      15. *-commutative 99.4%

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

      16. distribute-rgt-in 99.4%

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

   3. Simplified 99.4%

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

   4. Taylor expanded in x around 0 82.5%

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

   if 1.69999999999999997e-90 < x < 2.45000000000000014e-73 or 1.24999999999999993e-21 < x

   1. Initial program 99.4%

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

      1. associate--l+ 99.4%

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

      2. associate-/r* 99.4%

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

   3. Simplified 99.4%

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

   4. Taylor expanded in x around inf 98.3%

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

      1. distribute-lft-in 98.3%

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

      2. *-commutative 98.3%

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

      3. metadata-eval 98.3%

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

      4. sqrt-prod 98.4%

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

      5. *-commutative 98.4%

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

      6. metadata-eval 98.4%

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

      7. sqrt-prod 98.5%

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

   6. Applied egg-rr 98.5%

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

      1. distribute-lft-out 98.5%

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

   8. Simplified 98.5%

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

   if 2.45000000000000014e-73 < x < 1.24999999999999993e-21

   1. Initial program 99.6%

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

      1. +-commutative 99.6%

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

      2. associate--l+ 99.6%

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

      3. distribute-rgt-in 99.6%

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

      4. remove-double-neg 99.6%

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

      5. distribute-lft-neg-in 99.6%

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

      6. distribute-rgt-neg-in 99.6%

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

      7. mul-1-neg 99.6%

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

      8. metadata-eval 99.6%

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

      9. *-commutative 99.6%

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

      10. associate-/r* 99.5%

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

      11. distribute-neg-frac 99.5%

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

      12. *-commutative 99.5%

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

      13. associate-/r/ 99.3%

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

      14. associate-/l/ 99.3%

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

      15. associate-/r/ 99.5%

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

   3. Simplified 99.5%

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

      1. expm1-log1p-u 99.5%

         \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(3 \cdot \sqrt{x}\right)\right)} \cdot \left(\frac{0.1111111111111111}{x} + \left(y - 1\right)\right) \]

      2. expm1-udef 7.8%

         \[\leadsto \color{blue}{\left(e^{\mathsf{log1p}\left(3 \cdot \sqrt{x}\right)} - 1\right)} \cdot \left(\frac{0.1111111111111111}{x} + \left(y - 1\right)\right) \]

      3. *-commutative 7.8%

         \[\leadsto \left(e^{\mathsf{log1p}\left(\color{blue}{\sqrt{x} \cdot 3}\right)} - 1\right) \cdot \left(\frac{0.1111111111111111}{x} + \left(y - 1\right)\right) \]

      4. metadata-eval 7.8%

         \[\leadsto \left(e^{\mathsf{log1p}\left(\sqrt{x} \cdot \color{blue}{\sqrt{9}}\right)} - 1\right) \cdot \left(\frac{0.1111111111111111}{x} + \left(y - 1\right)\right) \]

      5. sqrt-prod 7.8%

         \[\leadsto \left(e^{\mathsf{log1p}\left(\color{blue}{\sqrt{x \cdot 9}}\right)} - 1\right) \cdot \left(\frac{0.1111111111111111}{x} + \left(y - 1\right)\right) \]

   5. Applied egg-rr 7.8%

      \[\leadsto \color{blue}{\left(e^{\mathsf{log1p}\left(\sqrt{x \cdot 9}\right)} - 1\right)} \cdot \left(\frac{0.1111111111111111}{x} + \left(y - 1\right)\right) \]
   6. Step-by-step derivation

      1. expm1-def 99.6%

         \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\sqrt{x \cdot 9}\right)\right)} \cdot \left(\frac{0.1111111111111111}{x} + \left(y - 1\right)\right) \]

      2. expm1-log1p 99.6%

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

   7. Simplified 99.6%

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

   8. Taylor expanded in y around 0 63.5%

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

      1. sub-neg 63.5%

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

      2. associate-*r/ 63.6%

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

      3. metadata-eval 63.6%

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

      4. metadata-eval 63.6%

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

   10. Simplified 63.6%

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

   11. Taylor expanded in x around 0 63.6%

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

4. Final simplification 89.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 1.7 \cdot 10^{-90}:\\ \;\;\;\;\sqrt{x} \cdot \frac{0.3333333333333333}{x}\\ \mathbf{elif}\;x \leq 2.45 \cdot 10^{-73} \lor \neg \left(x \leq 1.25 \cdot 10^{-21}\right):\\ \;\;\;\;\sqrt{x \cdot 9} \cdot \left(y + -1\right)\\ \mathbf{else}:\\ \;\;\;\;3 \cdot \left(\frac{0.1111111111111111}{x} \cdot \sqrt{x}\right)\\ \end{array} \]

Alternative 7: 86.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.12 \cdot 10^{+39}:\\ \;\;\;\;3 \cdot \left(y \cdot \sqrt{x}\right)\\ \mathbf{elif}\;y \leq 4.1 \cdot 10^{+14}:\\ \;\;\;\;\sqrt{x} \cdot \left(\frac{0.3333333333333333}{x} + -3\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(3 \cdot \sqrt{x}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -1.12e+39)
   (* 3.0 (* y (sqrt x)))
   (if (<= y 4.1e+14)
     (* (sqrt x) (+ (/ 0.3333333333333333 x) -3.0))
     (* y (* 3.0 (sqrt x))))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -1.12e+39) {
		tmp = 3.0 * (y * sqrt(x));
	} else if (y <= 4.1e+14) {
		tmp = sqrt(x) * ((0.3333333333333333 / x) + -3.0);
	} else {
		tmp = y * (3.0 * sqrt(x));
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (y <= (-1.12d+39)) then
        tmp = 3.0d0 * (y * sqrt(x))
    else if (y <= 4.1d+14) then
        tmp = sqrt(x) * ((0.3333333333333333d0 / x) + (-3.0d0))
    else
        tmp = y * (3.0d0 * sqrt(x))
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (y <= -1.12e+39) {
		tmp = 3.0 * (y * Math.sqrt(x));
	} else if (y <= 4.1e+14) {
		tmp = Math.sqrt(x) * ((0.3333333333333333 / x) + -3.0);
	} else {
		tmp = y * (3.0 * Math.sqrt(x));
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -1.12e+39:
		tmp = 3.0 * (y * math.sqrt(x))
	elif y <= 4.1e+14:
		tmp = math.sqrt(x) * ((0.3333333333333333 / x) + -3.0)
	else:
		tmp = y * (3.0 * math.sqrt(x))
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -1.12e+39)
		tmp = Float64(3.0 * Float64(y * sqrt(x)));
	elseif (y <= 4.1e+14)
		tmp = Float64(sqrt(x) * Float64(Float64(0.3333333333333333 / x) + -3.0));
	else
		tmp = Float64(y * Float64(3.0 * sqrt(x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -1.12e+39)
		tmp = 3.0 * (y * sqrt(x));
	elseif (y <= 4.1e+14)
		tmp = sqrt(x) * ((0.3333333333333333 / x) + -3.0);
	else
		tmp = y * (3.0 * sqrt(x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -1.12e+39], N[(3.0 * N[(y * N[Sqrt[x], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 4.1e+14], N[(N[Sqrt[x], $MachinePrecision] * N[(N[(0.3333333333333333 / x), $MachinePrecision] + -3.0), $MachinePrecision]), $MachinePrecision], N[(y * N[(3.0 * N[Sqrt[x], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.12e39

   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. +-commutative 99.2%

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

      2. associate--l+ 99.2%

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

      3. distribute-lft-in 99.2%

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

      4. +-commutative 99.2%

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

      5. *-commutative 99.2%

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

      6. associate-*r* 99.3%

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

      7. cancel-sign-sub 99.3%

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

      8. *-commutative 99.3%

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

      9. associate-*r* 99.5%

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

      10. *-commutative 99.5%

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

      11. distribute-rgt-out-- 99.5%

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

      12. distribute-lft-neg-in 99.5%

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

      13. cancel-sign-sub 99.5%

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

      14. +-commutative 99.5%

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

      15. *-commutative 99.5%

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

      16. distribute-rgt-in 99.5%

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

   3. Simplified 99.6%

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

   4. Taylor expanded in y around inf 72.3%

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

   if -1.12e39 < y < 4.1e14

   1. Initial program 99.4%

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

      1. +-commutative 99.4%

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

      2. associate--l+ 99.4%

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

      3. distribute-lft-in 99.4%

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

      4. +-commutative 99.4%

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

      5. *-commutative 99.4%

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

      6. associate-*r* 99.4%

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

      7. cancel-sign-sub 99.4%

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

      8. *-commutative 99.4%

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

      9. associate-*r* 99.4%

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

      10. *-commutative 99.4%

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

      11. distribute-rgt-out-- 99.4%

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

      12. distribute-lft-neg-in 99.4%

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

      13. cancel-sign-sub 99.4%

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

      14. +-commutative 99.4%

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

      15. *-commutative 99.4%

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

      16. distribute-rgt-in 99.4%

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

   3. Simplified 99.4%

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

   4. Taylor expanded in y around 0 97.0%

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

      1. *-commutative 97.0%

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

      2. sub-neg 97.0%

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

      3. associate-*r/ 97.0%

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

      4. metadata-eval 97.0%

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

      5. metadata-eval 97.0%

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

   6. Simplified 97.0%

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

   if 4.1e14 < 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. +-commutative 99.4%

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

      2. associate--l+ 99.4%

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

      3. distribute-lft-in 99.4%

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

      4. +-commutative 99.4%

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

      5. *-commutative 99.4%

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

      6. associate-*r* 99.4%

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

      7. cancel-sign-sub 99.4%

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

      8. *-commutative 99.4%

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

      9. associate-*r* 99.3%

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

      10. *-commutative 99.3%

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

      11. distribute-rgt-out-- 99.3%

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

      12. distribute-lft-neg-in 99.3%

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

      13. cancel-sign-sub 99.3%

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

      14. +-commutative 99.3%

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

      15. *-commutative 99.3%

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

      16. distribute-rgt-in 99.3%

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

   3. Simplified 99.3%

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

   4. Taylor expanded in y around inf 81.3%

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

      1. add-cube-cbrt 80.7%

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

      2. pow3 80.7%

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

      3. associate-*r* 80.7%

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

   6. Applied egg-rr 80.7%

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

      1. rem-cube-cbrt 81.3%

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

      2. *-commutative 81.3%

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

      3. associate-*r* 81.4%

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

   8. Applied egg-rr 81.4%

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

4. Final simplification 87.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.12 \cdot 10^{+39}:\\ \;\;\;\;3 \cdot \left(y \cdot \sqrt{x}\right)\\ \mathbf{elif}\;y \leq 4.1 \cdot 10^{+14}:\\ \;\;\;\;\sqrt{x} \cdot \left(\frac{0.3333333333333333}{x} + -3\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(3 \cdot \sqrt{x}\right)\\ \end{array} \]

Alternative 8: 98.2% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 0.11:\\ \;\;\;\;\left(\frac{0.1111111111111111}{x} + y\right) \cdot \left(3 \cdot \sqrt{x}\right)\\ \mathbf{else}:\\ \;\;\;\;\sqrt{x \cdot 9} \cdot \left(y + -1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x 0.11)
   (* (+ (/ 0.1111111111111111 x) y) (* 3.0 (sqrt x)))
   (* (sqrt (* x 9.0)) (+ y -1.0))))

C

double code(double x, double y) {
	double tmp;
	if (x <= 0.11) {
		tmp = ((0.1111111111111111 / x) + y) * (3.0 * sqrt(x));
	} else {
		tmp = sqrt((x * 9.0)) * (y + -1.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (x <= 0.11d0) then
        tmp = ((0.1111111111111111d0 / x) + y) * (3.0d0 * sqrt(x))
    else
        tmp = sqrt((x * 9.0d0)) * (y + (-1.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= 0.11) {
		tmp = ((0.1111111111111111 / x) + y) * (3.0 * Math.sqrt(x));
	} else {
		tmp = Math.sqrt((x * 9.0)) * (y + -1.0);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= 0.11:
		tmp = ((0.1111111111111111 / x) + y) * (3.0 * math.sqrt(x))
	else:
		tmp = math.sqrt((x * 9.0)) * (y + -1.0)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= 0.11)
		tmp = Float64(Float64(Float64(0.1111111111111111 / x) + y) * Float64(3.0 * sqrt(x)));
	else
		tmp = Float64(sqrt(Float64(x * 9.0)) * Float64(y + -1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= 0.11)
		tmp = ((0.1111111111111111 / x) + y) * (3.0 * sqrt(x));
	else
		tmp = sqrt((x * 9.0)) * (y + -1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, 0.11], N[(N[(N[(0.1111111111111111 / x), $MachinePrecision] + y), $MachinePrecision] * N[(3.0 * N[Sqrt[x], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[Sqrt[N[(x * 9.0), $MachinePrecision]], $MachinePrecision] * N[(y + -1.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < 0.110000000000000001

   1. Initial program 99.3%

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

      1. associate--l+ 99.3%

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

      2. associate-/r* 98.6%

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

   3. Simplified 98.6%

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

      1. flip-- 53.8%

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

      2. pow2 53.8%

         \[\leadsto \left(3 \cdot \sqrt{x}\right) \cdot \left(y + \frac{\color{blue}{{\left(\frac{\frac{1}{x}}{9}\right)}^{2}} - 1 \cdot 1}{\frac{\frac{1}{x}}{9} + 1}\right) \]

      3. associate-/r* 53.7%

         \[\leadsto \left(3 \cdot \sqrt{x}\right) \cdot \left(y + \frac{{\color{blue}{\left(\frac{1}{x \cdot 9}\right)}}^{2} - 1 \cdot 1}{\frac{\frac{1}{x}}{9} + 1}\right) \]

      4. inv-pow 53.7%

         \[\leadsto \left(3 \cdot \sqrt{x}\right) \cdot \left(y + \frac{{\color{blue}{\left({\left(x \cdot 9\right)}^{-1}\right)}}^{2} - 1 \cdot 1}{\frac{\frac{1}{x}}{9} + 1}\right) \]

      5. *-commutative 53.7%

         \[\leadsto \left(3 \cdot \sqrt{x}\right) \cdot \left(y + \frac{{\left({\color{blue}{\left(9 \cdot x\right)}}^{-1}\right)}^{2} - 1 \cdot 1}{\frac{\frac{1}{x}}{9} + 1}\right) \]

      6. unpow-prod-down 53.6%

         \[\leadsto \left(3 \cdot \sqrt{x}\right) \cdot \left(y + \frac{{\color{blue}{\left({9}^{-1} \cdot {x}^{-1}\right)}}^{2} - 1 \cdot 1}{\frac{\frac{1}{x}}{9} + 1}\right) \]

      7. metadata-eval 53.6%

         \[\leadsto \left(3 \cdot \sqrt{x}\right) \cdot \left(y + \frac{{\left(\color{blue}{0.1111111111111111} \cdot {x}^{-1}\right)}^{2} - 1 \cdot 1}{\frac{\frac{1}{x}}{9} + 1}\right) \]

      8. inv-pow 53.6%

         \[\leadsto \left(3 \cdot \sqrt{x}\right) \cdot \left(y + \frac{{\left(0.1111111111111111 \cdot \color{blue}{\frac{1}{x}}\right)}^{2} - 1 \cdot 1}{\frac{\frac{1}{x}}{9} + 1}\right) \]

      9. div-inv 53.7%

         \[\leadsto \left(3 \cdot \sqrt{x}\right) \cdot \left(y + \frac{{\color{blue}{\left(\frac{0.1111111111111111}{x}\right)}}^{2} - 1 \cdot 1}{\frac{\frac{1}{x}}{9} + 1}\right) \]

      10. metadata-eval 53.7%

          \[\leadsto \left(3 \cdot \sqrt{x}\right) \cdot \left(y + \frac{{\left(\frac{0.1111111111111111}{x}\right)}^{\color{blue}{\left(1 + 1\right)}} - 1 \cdot 1}{\frac{\frac{1}{x}}{9} + 1}\right) \]

      11. pow-prod-up 53.7%

          \[\leadsto \left(3 \cdot \sqrt{x}\right) \cdot \left(y + \frac{\color{blue}{{\left(\frac{0.1111111111111111}{x}\right)}^{1} \cdot {\left(\frac{0.1111111111111111}{x}\right)}^{1}} - 1 \cdot 1}{\frac{\frac{1}{x}}{9} + 1}\right) \]

      12. pow1 53.7%

          \[\leadsto \left(3 \cdot \sqrt{x}\right) \cdot \left(y + \frac{\color{blue}{\frac{0.1111111111111111}{x}} \cdot {\left(\frac{0.1111111111111111}{x}\right)}^{1} - 1 \cdot 1}{\frac{\frac{1}{x}}{9} + 1}\right) \]

      13. pow1 53.7%

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

      14. frac-times 53.7%

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

      15. metadata-eval 53.7%

          \[\leadsto \left(3 \cdot \sqrt{x}\right) \cdot \left(y + \frac{\frac{\color{blue}{0.012345679012345678}}{x \cdot x} - 1 \cdot 1}{\frac{\frac{1}{x}}{9} + 1}\right) \]

      16. metadata-eval 53.7%

          \[\leadsto \left(3 \cdot \sqrt{x}\right) \cdot \left(y + \frac{\frac{0.012345679012345678}{x \cdot x} - \color{blue}{1}}{\frac{\frac{1}{x}}{9} + 1}\right) \]

      17. associate-/r* 53.7%

          \[\leadsto \left(3 \cdot \sqrt{x}\right) \cdot \left(y + \frac{\frac{0.012345679012345678}{x \cdot x} - 1}{\color{blue}{\frac{1}{x \cdot 9}} + 1}\right) \]

      18. inv-pow 53.7%

          \[\leadsto \left(3 \cdot \sqrt{x}\right) \cdot \left(y + \frac{\frac{0.012345679012345678}{x \cdot x} - 1}{\color{blue}{{\left(x \cdot 9\right)}^{-1}} + 1}\right) \]

      19. *-commutative 53.7%

          \[\leadsto \left(3 \cdot \sqrt{x}\right) \cdot \left(y + \frac{\frac{0.012345679012345678}{x \cdot x} - 1}{{\color{blue}{\left(9 \cdot x\right)}}^{-1} + 1}\right) \]

      20. unpow-prod-down 53.7%

          \[\leadsto \left(3 \cdot \sqrt{x}\right) \cdot \left(y + \frac{\frac{0.012345679012345678}{x \cdot x} - 1}{\color{blue}{{9}^{-1} \cdot {x}^{-1}} + 1}\right) \]

      21. metadata-eval 53.7%

          \[\leadsto \left(3 \cdot \sqrt{x}\right) \cdot \left(y + \frac{\frac{0.012345679012345678}{x \cdot x} - 1}{\color{blue}{0.1111111111111111} \cdot {x}^{-1} + 1}\right) \]

      22. inv-pow 53.7%

          \[\leadsto \left(3 \cdot \sqrt{x}\right) \cdot \left(y + \frac{\frac{0.012345679012345678}{x \cdot x} - 1}{0.1111111111111111 \cdot \color{blue}{\frac{1}{x}} + 1}\right) \]

      23. div-inv 53.8%

          \[\leadsto \left(3 \cdot \sqrt{x}\right) \cdot \left(y + \frac{\frac{0.012345679012345678}{x \cdot x} - 1}{\color{blue}{\frac{0.1111111111111111}{x}} + 1}\right) \]

   5. Applied egg-rr 53.8%

      \[\leadsto \left(3 \cdot \sqrt{x}\right) \cdot \left(y + \color{blue}{\frac{\frac{0.012345679012345678}{x \cdot x} - 1}{\frac{0.1111111111111111}{x} + 1}}\right) \]

   6. Taylor expanded in x around 0 99.3%

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

   if 0.110000000000000001 < x

   1. Initial program 99.5%

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

      1. associate--l+ 99.5%

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

      2. associate-/r* 99.5%

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

   3. Simplified 99.5%

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

   4. Taylor expanded in x around inf 99.0%

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

      1. distribute-lft-in 99.0%

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

      2. *-commutative 99.0%

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

      3. metadata-eval 99.0%

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

      4. sqrt-prod 99.1%

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

      5. *-commutative 99.1%

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

      6. metadata-eval 99.1%

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

      7. sqrt-prod 99.2%

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

   6. Applied egg-rr 99.2%

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

      1. distribute-lft-out 99.2%

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

   8. Simplified 99.2%

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

4. Final simplification 99.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 0.11:\\ \;\;\;\;\left(\frac{0.1111111111111111}{x} + y\right) \cdot \left(3 \cdot \sqrt{x}\right)\\ \mathbf{else}:\\ \;\;\;\;\sqrt{x \cdot 9} \cdot \left(y + -1\right)\\ \end{array} \]

Alternative 9: 99.4% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.4%

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

   1. +-commutative 99.4%

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

   2. associate--l+ 99.4%

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

   3. distribute-rgt-in 99.4%

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

   4. remove-double-neg 99.4%

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

   5. distribute-lft-neg-in 99.4%

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

   6. distribute-rgt-neg-in 99.4%

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

   7. mul-1-neg 99.4%

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

   8. metadata-eval 99.4%

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

   9. *-commutative 99.4%

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

   10. associate-/r* 99.4%

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

   11. distribute-neg-frac 99.4%

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

   12. *-commutative 99.4%

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

   13. associate-/r/ 99.4%

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

   14. associate-/l/ 99.4%

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

   15. associate-/r/ 99.4%

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

3. Simplified 99.4%

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

   1. expm1-log1p-u 96.4%

      \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(3 \cdot \sqrt{x}\right)\right)} \cdot \left(\frac{0.1111111111111111}{x} + \left(y - 1\right)\right) \]

   2. expm1-udef 50.7%

      \[\leadsto \color{blue}{\left(e^{\mathsf{log1p}\left(3 \cdot \sqrt{x}\right)} - 1\right)} \cdot \left(\frac{0.1111111111111111}{x} + \left(y - 1\right)\right) \]

   3. *-commutative 50.7%

      \[\leadsto \left(e^{\mathsf{log1p}\left(\color{blue}{\sqrt{x} \cdot 3}\right)} - 1\right) \cdot \left(\frac{0.1111111111111111}{x} + \left(y - 1\right)\right) \]

   4. metadata-eval 50.7%

      \[\leadsto \left(e^{\mathsf{log1p}\left(\sqrt{x} \cdot \color{blue}{\sqrt{9}}\right)} - 1\right) \cdot \left(\frac{0.1111111111111111}{x} + \left(y - 1\right)\right) \]

   5. sqrt-prod 50.7%

      \[\leadsto \left(e^{\mathsf{log1p}\left(\color{blue}{\sqrt{x \cdot 9}}\right)} - 1\right) \cdot \left(\frac{0.1111111111111111}{x} + \left(y - 1\right)\right) \]

5. Applied egg-rr 50.7%

   \[\leadsto \color{blue}{\left(e^{\mathsf{log1p}\left(\sqrt{x \cdot 9}\right)} - 1\right)} \cdot \left(\frac{0.1111111111111111}{x} + \left(y - 1\right)\right) \]
6. Step-by-step derivation

   1. expm1-def 96.5%

      \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\sqrt{x \cdot 9}\right)\right)} \cdot \left(\frac{0.1111111111111111}{x} + \left(y - 1\right)\right) \]

   2. expm1-log1p 99.5%

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

7. Simplified 99.5%

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

8. Final simplification 99.5%

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

Alternative 10: 61.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -1.66 \cdot 10^{-12} \lor \neg \left(y \leq 0.0013\right):\\ \;\;\;\;3 \cdot \left(y \cdot \sqrt{x}\right)\\ \mathbf{else}:\\ \;\;\;\;\sqrt{x} \cdot -3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= y -1.66e-12) (not (<= y 0.0013)))
   (* 3.0 (* y (sqrt x)))
   (* (sqrt x) -3.0)))

C

double code(double x, double y) {
	double tmp;
	if ((y <= -1.66e-12) || !(y <= 0.0013)) {
		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 <= (-1.66d-12)) .or. (.not. (y <= 0.0013d0))) 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 <= -1.66e-12) || !(y <= 0.0013)) {
		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 <= -1.66e-12) or not (y <= 0.0013):
		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 <= -1.66e-12) || !(y <= 0.0013))
		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 <= -1.66e-12) || ~((y <= 0.0013)))
		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, -1.66e-12], N[Not[LessEqual[y, 0.0013]], $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 < -1.65999999999999999e-12 or 0.0012999999999999999 < 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. +-commutative 99.3%

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

      2. associate--l+ 99.3%

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

      3. distribute-lft-in 99.3%

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

      4. +-commutative 99.3%

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

      5. *-commutative 99.3%

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

      6. associate-*r* 99.4%

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

      7. cancel-sign-sub 99.4%

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

      8. *-commutative 99.4%

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

      9. associate-*r* 99.4%

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

      10. *-commutative 99.4%

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

      11. distribute-rgt-out-- 99.4%

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

      12. distribute-lft-neg-in 99.4%

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

      13. cancel-sign-sub 99.4%

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

      14. +-commutative 99.4%

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

      15. *-commutative 99.4%

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

      16. distribute-rgt-in 99.4%

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

   3. Simplified 99.4%

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

   4. Taylor expanded in y around inf 72.5%

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

   if -1.65999999999999999e-12 < y < 0.0012999999999999999

   1. Initial program 99.4%

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

      1. associate--l+ 99.4%

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

      2. associate-/r* 99.4%

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

   3. Simplified 99.4%

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

   4. Taylor expanded in x around inf 53.8%

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

   5. Taylor expanded in y around 0 53.4%

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

      1. *-commutative 53.4%

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

   7. Simplified 53.4%

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

4. Final simplification 63.8%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.66 \cdot 10^{-12} \lor \neg \left(y \leq 0.0013\right):\\ \;\;\;\;3 \cdot \left(y \cdot \sqrt{x}\right)\\ \mathbf{else}:\\ \;\;\;\;\sqrt{x} \cdot -3\\ \end{array} \]

Alternative 11: 3.3% accurate, 1.1× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

code[x_, y_] := N[Sqrt[N[(x * 9.0), $MachinePrecision]], $MachinePrecision]

Derivation

1. Initial program 99.4%

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

   1. associate--l+ 99.4%

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

   2. associate-/r* 99.0%

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

3. Simplified 99.0%

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

4. Taylor expanded in x around inf 64.4%

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

   1. distribute-lft-in 64.4%

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

   2. *-commutative 64.4%

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

   3. metadata-eval 64.4%

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

   4. sqrt-prod 64.5%

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

   5. *-commutative 64.5%

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

   6. metadata-eval 64.5%

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

   7. sqrt-prod 64.5%

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

6. Applied egg-rr 64.5%

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

   1. distribute-lft-out 64.5%

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

8. Simplified 64.5%

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

9. Taylor expanded in y around 0 25.8%

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

    1. *-commutative 25.8%

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

    2. unpow1 25.8%

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

    3. sqr-pow 0.0%

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

    4. fabs-sqr 0.0%

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

    5. sqr-pow 3.1%

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

    6. unpow1 3.1%

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

    7. fabs-mul 3.1%

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

    8. metadata-eval 3.1%

       \[\leadsto \left|\sqrt{x}\right| \cdot \color{blue}{3} \]

    9. metadata-eval 3.1%

       \[\leadsto \left|\sqrt{x}\right| \cdot \color{blue}{\left|3\right|} \]

    10. fabs-mul 3.1%

        \[\leadsto \color{blue}{\left|\sqrt{x} \cdot 3\right|} \]

    11. rem-square-sqrt 3.1%

        \[\leadsto \left|\color{blue}{\sqrt{\sqrt{x} \cdot 3} \cdot \sqrt{\sqrt{x} \cdot 3}}\right| \]

    12. unpow1/2 3.1%

        \[\leadsto \left|\color{blue}{{\left(\sqrt{x} \cdot 3\right)}^{0.5}} \cdot \sqrt{\sqrt{x} \cdot 3}\right| \]

    13. metadata-eval 3.1%

        \[\leadsto \left|{\left(\sqrt{x} \cdot 3\right)}^{\color{blue}{\left(2 \cdot 0.25\right)}} \cdot \sqrt{\sqrt{x} \cdot 3}\right| \]

    14. pow-sqr 3.1%

        \[\leadsto \left|\color{blue}{\left({\left(\sqrt{x} \cdot 3\right)}^{0.25} \cdot {\left(\sqrt{x} \cdot 3\right)}^{0.25}\right)} \cdot \sqrt{\sqrt{x} \cdot 3}\right| \]

    15. unpow1/2 3.1%

        \[\leadsto \left|\left({\left(\sqrt{x} \cdot 3\right)}^{0.25} \cdot {\left(\sqrt{x} \cdot 3\right)}^{0.25}\right) \cdot \color{blue}{{\left(\sqrt{x} \cdot 3\right)}^{0.5}}\right| \]

    16. metadata-eval 3.1%

        \[\leadsto \left|\left({\left(\sqrt{x} \cdot 3\right)}^{0.25} \cdot {\left(\sqrt{x} \cdot 3\right)}^{0.25}\right) \cdot {\left(\sqrt{x} \cdot 3\right)}^{\color{blue}{\left(2 \cdot 0.25\right)}}\right| \]

    17. pow-sqr 3.1%

        \[\leadsto \left|\left({\left(\sqrt{x} \cdot 3\right)}^{0.25} \cdot {\left(\sqrt{x} \cdot 3\right)}^{0.25}\right) \cdot \color{blue}{\left({\left(\sqrt{x} \cdot 3\right)}^{0.25} \cdot {\left(\sqrt{x} \cdot 3\right)}^{0.25}\right)}\right| \]

    18. fabs-sqr 3.1%

        \[\leadsto \color{blue}{\left({\left(\sqrt{x} \cdot 3\right)}^{0.25} \cdot {\left(\sqrt{x} \cdot 3\right)}^{0.25}\right) \cdot \left({\left(\sqrt{x} \cdot 3\right)}^{0.25} \cdot {\left(\sqrt{x} \cdot 3\right)}^{0.25}\right)} \]

11. Simplified 3.1%

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

    1. expm1-log1p-u 96.4%

       \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(3 \cdot \sqrt{x}\right)\right)} \cdot \left(\frac{0.1111111111111111}{x} + \left(y - 1\right)\right) \]

    2. expm1-udef 50.7%

       \[\leadsto \color{blue}{\left(e^{\mathsf{log1p}\left(3 \cdot \sqrt{x}\right)} - 1\right)} \cdot \left(\frac{0.1111111111111111}{x} + \left(y - 1\right)\right) \]

    3. *-commutative 50.7%

       \[\leadsto \left(e^{\mathsf{log1p}\left(\color{blue}{\sqrt{x} \cdot 3}\right)} - 1\right) \cdot \left(\frac{0.1111111111111111}{x} + \left(y - 1\right)\right) \]

    4. metadata-eval 50.7%

       \[\leadsto \left(e^{\mathsf{log1p}\left(\sqrt{x} \cdot \color{blue}{\sqrt{9}}\right)} - 1\right) \cdot \left(\frac{0.1111111111111111}{x} + \left(y - 1\right)\right) \]

    5. sqrt-prod 50.7%

       \[\leadsto \left(e^{\mathsf{log1p}\left(\color{blue}{\sqrt{x \cdot 9}}\right)} - 1\right) \cdot \left(\frac{0.1111111111111111}{x} + \left(y - 1\right)\right) \]

13. Applied egg-rr 2.3%

    \[\leadsto \color{blue}{e^{\mathsf{log1p}\left(\sqrt{x \cdot 9}\right)} - 1} \]
14. Step-by-step derivation

    1. expm1-def 96.5%

       \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\sqrt{x \cdot 9}\right)\right)} \cdot \left(\frac{0.1111111111111111}{x} + \left(y - 1\right)\right) \]

    2. expm1-log1p 99.5%

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

15. Simplified 3.1%

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

16. Final simplification 3.1%

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

Alternative 12: 25.5% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \sqrt{x} \cdot -3 \end{array} \]

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.4%

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

   1. associate--l+ 99.4%

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

   2. associate-/r* 99.0%

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

3. Simplified 99.0%

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

4. Taylor expanded in x around inf 64.4%

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

5. Taylor expanded in y around 0 25.8%

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

   1. *-commutative 25.8%

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

7. Simplified 25.8%

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

8. Final simplification 25.8%

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

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 2023238 
(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)))