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

Percentage Accurate: 99.4% → 99.4%

Time: 10.6s

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

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.4%

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

   1. +-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. add-sqr-sqrt 48.3%

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

   2. pow2 48.3%

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

5. Applied egg-rr 48.3%

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

6. Taylor expanded in y around 0 98.6%

   \[\leadsto \color{blue}{\left(y \cdot {\left(\sqrt{3}\right)}^{2}\right) \cdot \sqrt{x} + \left(\left(0.1111111111111111 \cdot \frac{1}{x} - 1\right) \cdot {\left(\sqrt{3}\right)}^{2}\right) \cdot \sqrt{x}} \]
7. Step-by-step derivation

   1. associate-*l* 98.5%

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

   2. associate-*l* 98.5%

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

   3. distribute-rgt-out 98.6%

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

   4. unpow2 98.6%

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

   5. rem-square-sqrt 99.4%

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

   6. sub-neg 99.4%

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

   7. associate-*r/ 99.4%

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

   8. metadata-eval 99.4%

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

   9. metadata-eval 99.4%

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

   10. associate-*l* 99.5%

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

   11. +-commutative 99.5%

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

   12. metadata-eval 99.5%

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

   13. sub-neg 99.5%

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

   14. associate-+l- 99.5%

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

8. Simplified 99.5%

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

9. Final simplification 99.5%

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

Alternative 2: 61.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 3 \cdot \left(\sqrt{x} \cdot y\right)\\ t_1 := \sqrt{x} \cdot -3\\ t_2 := \sqrt{x} \cdot \frac{0.3333333333333333}{x}\\ \mathbf{if}\;y \leq -1.36 \cdot 10^{+84}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq -2.1 \cdot 10^{+58}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -0.07:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq -3.3 \cdot 10^{-285}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 8.2 \cdot 10^{-204}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 7.2 \cdot 10^{-7}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (* 3.0 (* (sqrt x) y)))
        (t_1 (* (sqrt x) -3.0))
        (t_2 (* (sqrt x) (/ 0.3333333333333333 x))))
   (if (<= y -1.36e+84)
     t_0
     (if (<= y -2.1e+58)
       t_2
       (if (<= y -0.07)
         t_0
         (if (<= y -3.3e-285)
           t_1
           (if (<= y 8.2e-204) t_2 (if (<= y 7.2e-7) t_1 t_0))))))))

C

double code(double x, double y) {
	double t_0 = 3.0 * (sqrt(x) * y);
	double t_1 = sqrt(x) * -3.0;
	double t_2 = sqrt(x) * (0.3333333333333333 / x);
	double tmp;
	if (y <= -1.36e+84) {
		tmp = t_0;
	} else if (y <= -2.1e+58) {
		tmp = t_2;
	} else if (y <= -0.07) {
		tmp = t_0;
	} else if (y <= -3.3e-285) {
		tmp = t_1;
	} else if (y <= 8.2e-204) {
		tmp = t_2;
	} else if (y <= 7.2e-7) {
		tmp = t_1;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_0 = 3.0d0 * (sqrt(x) * y)
    t_1 = sqrt(x) * (-3.0d0)
    t_2 = sqrt(x) * (0.3333333333333333d0 / x)
    if (y <= (-1.36d+84)) then
        tmp = t_0
    else if (y <= (-2.1d+58)) then
        tmp = t_2
    else if (y <= (-0.07d0)) then
        tmp = t_0
    else if (y <= (-3.3d-285)) then
        tmp = t_1
    else if (y <= 8.2d-204) then
        tmp = t_2
    else if (y <= 7.2d-7) then
        tmp = t_1
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double t_0 = 3.0 * (Math.sqrt(x) * y);
	double t_1 = Math.sqrt(x) * -3.0;
	double t_2 = Math.sqrt(x) * (0.3333333333333333 / x);
	double tmp;
	if (y <= -1.36e+84) {
		tmp = t_0;
	} else if (y <= -2.1e+58) {
		tmp = t_2;
	} else if (y <= -0.07) {
		tmp = t_0;
	} else if (y <= -3.3e-285) {
		tmp = t_1;
	} else if (y <= 8.2e-204) {
		tmp = t_2;
	} else if (y <= 7.2e-7) {
		tmp = t_1;
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = 3.0 * (math.sqrt(x) * y)
	t_1 = math.sqrt(x) * -3.0
	t_2 = math.sqrt(x) * (0.3333333333333333 / x)
	tmp = 0
	if y <= -1.36e+84:
		tmp = t_0
	elif y <= -2.1e+58:
		tmp = t_2
	elif y <= -0.07:
		tmp = t_0
	elif y <= -3.3e-285:
		tmp = t_1
	elif y <= 8.2e-204:
		tmp = t_2
	elif y <= 7.2e-7:
		tmp = t_1
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y)
	t_0 = Float64(3.0 * Float64(sqrt(x) * y))
	t_1 = Float64(sqrt(x) * -3.0)
	t_2 = Float64(sqrt(x) * Float64(0.3333333333333333 / x))
	tmp = 0.0
	if (y <= -1.36e+84)
		tmp = t_0;
	elseif (y <= -2.1e+58)
		tmp = t_2;
	elseif (y <= -0.07)
		tmp = t_0;
	elseif (y <= -3.3e-285)
		tmp = t_1;
	elseif (y <= 8.2e-204)
		tmp = t_2;
	elseif (y <= 7.2e-7)
		tmp = t_1;
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = 3.0 * (sqrt(x) * y);
	t_1 = sqrt(x) * -3.0;
	t_2 = sqrt(x) * (0.3333333333333333 / x);
	tmp = 0.0;
	if (y <= -1.36e+84)
		tmp = t_0;
	elseif (y <= -2.1e+58)
		tmp = t_2;
	elseif (y <= -0.07)
		tmp = t_0;
	elseif (y <= -3.3e-285)
		tmp = t_1;
	elseif (y <= 8.2e-204)
		tmp = t_2;
	elseif (y <= 7.2e-7)
		tmp = t_1;
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(3.0 * N[(N[Sqrt[x], $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(N[Sqrt[x], $MachinePrecision] * -3.0), $MachinePrecision]}, Block[{t$95$2 = N[(N[Sqrt[x], $MachinePrecision] * N[(0.3333333333333333 / x), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.36e+84], t$95$0, If[LessEqual[y, -2.1e+58], t$95$2, If[LessEqual[y, -0.07], t$95$0, If[LessEqual[y, -3.3e-285], t$95$1, If[LessEqual[y, 8.2e-204], t$95$2, If[LessEqual[y, 7.2e-7], t$95$1, t$95$0]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.3599999999999999e84 or -2.10000000000000012e58 < y < -0.070000000000000007 or 7.19999999999999989e-7 < 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-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. +-commutative 99.4%

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

      5. fma-def 99.5%

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

      6. remove-double-neg 99.5%

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

      7. fma-neg 99.4%

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

      8. associate-*r* 99.4%

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

      9. *-commutative 99.4%

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

      10. associate-*r* 99.4%

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

      11. distribute-rgt-neg-in 99.4%

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

      12. *-commutative 99.4%

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

      13. associate-/r* 99.4%

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

      14. associate-/r/ 99.4%

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

      15. mul-1-neg 99.4%

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

      16. metadata-eval 99.4%

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

   3. Simplified 99.5%

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

   4. Taylor expanded in y around inf 77.2%

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

   if -1.3599999999999999e84 < y < -2.10000000000000012e58 or -3.29999999999999985e-285 < y < 8.2000000000000002e-204

   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-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. +-commutative 99.4%

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

      5. fma-def 99.4%

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

      6. remove-double-neg 99.4%

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

      7. fma-neg 99.4%

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

      8. associate-*r* 99.4%

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

      9. *-commutative 99.4%

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

      10. associate-*r* 99.3%

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

      11. distribute-rgt-neg-in 99.3%

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

      12. *-commutative 99.3%

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

      13. associate-/r* 99.2%

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

      14. associate-/r/ 99.3%

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

      15. mul-1-neg 99.3%

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

      16. metadata-eval 99.3%

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

   3. Simplified 99.4%

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

   4. Taylor expanded in x around 0 65.0%

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

   if -0.070000000000000007 < y < -3.29999999999999985e-285 or 8.2000000000000002e-204 < y < 7.19999999999999989e-7

   1. Initial program 99.4%

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

   2. Taylor expanded in y around inf 62.1%

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

   3. Taylor expanded in y around 0 61.7%

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

      1. *-commutative 61.7%

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

   5. Simplified 61.7%

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

4. Final simplification 70.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.36 \cdot 10^{+84}:\\ \;\;\;\;3 \cdot \left(\sqrt{x} \cdot y\right)\\ \mathbf{elif}\;y \leq -2.1 \cdot 10^{+58}:\\ \;\;\;\;\sqrt{x} \cdot \frac{0.3333333333333333}{x}\\ \mathbf{elif}\;y \leq -0.07:\\ \;\;\;\;3 \cdot \left(\sqrt{x} \cdot y\right)\\ \mathbf{elif}\;y \leq -3.3 \cdot 10^{-285}:\\ \;\;\;\;\sqrt{x} \cdot -3\\ \mathbf{elif}\;y \leq 8.2 \cdot 10^{-204}:\\ \;\;\;\;\sqrt{x} \cdot \frac{0.3333333333333333}{x}\\ \mathbf{elif}\;y \leq 7.2 \cdot 10^{-7}:\\ \;\;\;\;\sqrt{x} \cdot -3\\ \mathbf{else}:\\ \;\;\;\;3 \cdot \left(\sqrt{x} \cdot y\right)\\ \end{array} \]

Alternative 3: 61.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 3 \cdot \left(\sqrt{x} \cdot y\right)\\ t_1 := \sqrt{x} \cdot -3\\ t_2 := \sqrt{x} \cdot \frac{0.3333333333333333}{x}\\ \mathbf{if}\;y \leq -1.55 \cdot 10^{+84}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq -1.52 \cdot 10^{+57}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq -0.07:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq -1.55 \cdot 10^{-279}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq 1.46 \cdot 10^{-204}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 7.2 \cdot 10^{-7}:\\ \;\;\;\;t_1\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(3 \cdot \sqrt{x}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (* 3.0 (* (sqrt x) y)))
        (t_1 (* (sqrt x) -3.0))
        (t_2 (* (sqrt x) (/ 0.3333333333333333 x))))
   (if (<= y -1.55e+84)
     t_0
     (if (<= y -1.52e+57)
       t_2
       (if (<= y -0.07)
         t_0
         (if (<= y -1.55e-279)
           t_1
           (if (<= y 1.46e-204)
             t_2
             (if (<= y 7.2e-7) t_1 (* y (* 3.0 (sqrt x)))))))))))

C

double code(double x, double y) {
	double t_0 = 3.0 * (sqrt(x) * y);
	double t_1 = sqrt(x) * -3.0;
	double t_2 = sqrt(x) * (0.3333333333333333 / x);
	double tmp;
	if (y <= -1.55e+84) {
		tmp = t_0;
	} else if (y <= -1.52e+57) {
		tmp = t_2;
	} else if (y <= -0.07) {
		tmp = t_0;
	} else if (y <= -1.55e-279) {
		tmp = t_1;
	} else if (y <= 1.46e-204) {
		tmp = t_2;
	} else if (y <= 7.2e-7) {
		tmp = t_1;
	} 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) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_0 = 3.0d0 * (sqrt(x) * y)
    t_1 = sqrt(x) * (-3.0d0)
    t_2 = sqrt(x) * (0.3333333333333333d0 / x)
    if (y <= (-1.55d+84)) then
        tmp = t_0
    else if (y <= (-1.52d+57)) then
        tmp = t_2
    else if (y <= (-0.07d0)) then
        tmp = t_0
    else if (y <= (-1.55d-279)) then
        tmp = t_1
    else if (y <= 1.46d-204) then
        tmp = t_2
    else if (y <= 7.2d-7) then
        tmp = t_1
    else
        tmp = y * (3.0d0 * sqrt(x))
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double t_0 = 3.0 * (Math.sqrt(x) * y);
	double t_1 = Math.sqrt(x) * -3.0;
	double t_2 = Math.sqrt(x) * (0.3333333333333333 / x);
	double tmp;
	if (y <= -1.55e+84) {
		tmp = t_0;
	} else if (y <= -1.52e+57) {
		tmp = t_2;
	} else if (y <= -0.07) {
		tmp = t_0;
	} else if (y <= -1.55e-279) {
		tmp = t_1;
	} else if (y <= 1.46e-204) {
		tmp = t_2;
	} else if (y <= 7.2e-7) {
		tmp = t_1;
	} else {
		tmp = y * (3.0 * Math.sqrt(x));
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = 3.0 * (math.sqrt(x) * y)
	t_1 = math.sqrt(x) * -3.0
	t_2 = math.sqrt(x) * (0.3333333333333333 / x)
	tmp = 0
	if y <= -1.55e+84:
		tmp = t_0
	elif y <= -1.52e+57:
		tmp = t_2
	elif y <= -0.07:
		tmp = t_0
	elif y <= -1.55e-279:
		tmp = t_1
	elif y <= 1.46e-204:
		tmp = t_2
	elif y <= 7.2e-7:
		tmp = t_1
	else:
		tmp = y * (3.0 * math.sqrt(x))
	return tmp

Julia

function code(x, y)
	t_0 = Float64(3.0 * Float64(sqrt(x) * y))
	t_1 = Float64(sqrt(x) * -3.0)
	t_2 = Float64(sqrt(x) * Float64(0.3333333333333333 / x))
	tmp = 0.0
	if (y <= -1.55e+84)
		tmp = t_0;
	elseif (y <= -1.52e+57)
		tmp = t_2;
	elseif (y <= -0.07)
		tmp = t_0;
	elseif (y <= -1.55e-279)
		tmp = t_1;
	elseif (y <= 1.46e-204)
		tmp = t_2;
	elseif (y <= 7.2e-7)
		tmp = t_1;
	else
		tmp = Float64(y * Float64(3.0 * sqrt(x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = 3.0 * (sqrt(x) * y);
	t_1 = sqrt(x) * -3.0;
	t_2 = sqrt(x) * (0.3333333333333333 / x);
	tmp = 0.0;
	if (y <= -1.55e+84)
		tmp = t_0;
	elseif (y <= -1.52e+57)
		tmp = t_2;
	elseif (y <= -0.07)
		tmp = t_0;
	elseif (y <= -1.55e-279)
		tmp = t_1;
	elseif (y <= 1.46e-204)
		tmp = t_2;
	elseif (y <= 7.2e-7)
		tmp = t_1;
	else
		tmp = y * (3.0 * sqrt(x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(3.0 * N[(N[Sqrt[x], $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(N[Sqrt[x], $MachinePrecision] * -3.0), $MachinePrecision]}, Block[{t$95$2 = N[(N[Sqrt[x], $MachinePrecision] * N[(0.3333333333333333 / x), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -1.55e+84], t$95$0, If[LessEqual[y, -1.52e+57], t$95$2, If[LessEqual[y, -0.07], t$95$0, If[LessEqual[y, -1.55e-279], t$95$1, If[LessEqual[y, 1.46e-204], t$95$2, If[LessEqual[y, 7.2e-7], t$95$1, N[(y * N[(3.0 * N[Sqrt[x], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -1.55000000000000001e84 or -1.51999999999999998e57 < y < -0.070000000000000007

   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 99.5%

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

      4. +-commutative 99.5%

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

      5. fma-def 99.5%

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

      6. remove-double-neg 99.5%

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

      7. fma-neg 99.5%

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

      8. associate-*r* 99.4%

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

      9. *-commutative 99.4%

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

      10. associate-*r* 99.4%

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

      11. distribute-rgt-neg-in 99.4%

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

      12. *-commutative 99.4%

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

      13. associate-/r* 99.4%

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

      14. associate-/r/ 99.4%

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

      15. mul-1-neg 99.4%

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

      16. metadata-eval 99.4%

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

   3. Simplified 99.5%

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

   4. Taylor expanded in y around inf 77.8%

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

   if -1.55000000000000001e84 < y < -1.51999999999999998e57 or -1.55e-279 < y < 1.45999999999999998e-204

   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-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. +-commutative 99.4%

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

      5. fma-def 99.4%

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

      6. remove-double-neg 99.4%

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

      7. fma-neg 99.4%

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

      8. associate-*r* 99.4%

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

      9. *-commutative 99.4%

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

      10. associate-*r* 99.3%

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

      11. distribute-rgt-neg-in 99.3%

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

      12. *-commutative 99.3%

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

      13. associate-/r* 99.2%

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

      14. associate-/r/ 99.3%

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

      15. mul-1-neg 99.3%

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

      16. metadata-eval 99.3%

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

   3. Simplified 99.4%

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

   4. Taylor expanded in x around 0 65.0%

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

   if -0.070000000000000007 < y < -1.55e-279 or 1.45999999999999998e-204 < y < 7.19999999999999989e-7

   1. Initial program 99.4%

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

   2. Taylor expanded in y around inf 62.1%

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

   3. Taylor expanded in y around 0 61.7%

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

      1. *-commutative 61.7%

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

   5. Simplified 61.7%

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

   if 7.19999999999999989e-7 < 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-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. +-commutative 99.4%

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

      5. fma-def 99.5%

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

      6. remove-double-neg 99.5%

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

      7. fma-neg 99.4%

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

      8. associate-*r* 99.4%

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

      9. *-commutative 99.4%

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

      10. associate-*r* 99.3%

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

      11. distribute-rgt-neg-in 99.3%

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

      12. *-commutative 99.3%

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

      13. associate-/r* 99.3%

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

      14. associate-/r/ 99.3%

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

      15. mul-1-neg 99.3%

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

      16. metadata-eval 99.3%

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

   3. Simplified 99.4%

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

   4. Taylor expanded in y around inf 76.4%

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

      1. add-sqr-sqrt 76.2%

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

      2. pow2 76.2%

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

      3. *-commutative 76.2%

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

   6. Applied egg-rr 76.2%

      \[\leadsto \color{blue}{{\left(\sqrt{3 \cdot \left(\sqrt{x} \cdot y\right)}\right)}^{2}} \]
   7. Step-by-step derivation

      1. unpow2 76.2%

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

      2. add-sqr-sqrt 76.4%

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

      3. associate-*r* 76.4%

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

   8. Applied egg-rr 76.4%

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

4. Final simplification 70.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.55 \cdot 10^{+84}:\\ \;\;\;\;3 \cdot \left(\sqrt{x} \cdot y\right)\\ \mathbf{elif}\;y \leq -1.52 \cdot 10^{+57}:\\ \;\;\;\;\sqrt{x} \cdot \frac{0.3333333333333333}{x}\\ \mathbf{elif}\;y \leq -0.07:\\ \;\;\;\;3 \cdot \left(\sqrt{x} \cdot y\right)\\ \mathbf{elif}\;y \leq -1.55 \cdot 10^{-279}:\\ \;\;\;\;\sqrt{x} \cdot -3\\ \mathbf{elif}\;y \leq 1.46 \cdot 10^{-204}:\\ \;\;\;\;\sqrt{x} \cdot \frac{0.3333333333333333}{x}\\ \mathbf{elif}\;y \leq 7.2 \cdot 10^{-7}:\\ \;\;\;\;\sqrt{x} \cdot -3\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(3 \cdot \sqrt{x}\right)\\ \end{array} \]

Alternative 4: 86.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 3 \cdot \left(\sqrt{x} \cdot y\right)\\ \mathbf{if}\;y \leq -8.5 \cdot 10^{+83}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq -2.1 \cdot 10^{+59}:\\ \;\;\;\;\sqrt{x} \cdot \frac{0.3333333333333333}{x}\\ \mathbf{elif}\;y \leq -6500000:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 2000000000:\\ \;\;\;\;\sqrt{x} \cdot \left(-3 + \frac{0.3333333333333333}{x}\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(3 \cdot \sqrt{x}\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (* 3.0 (* (sqrt x) y))))
   (if (<= y -8.5e+83)
     t_0
     (if (<= y -2.1e+59)
       (* (sqrt x) (/ 0.3333333333333333 x))
       (if (<= y -6500000.0)
         t_0
         (if (<= y 2000000000.0)
           (* (sqrt x) (+ -3.0 (/ 0.3333333333333333 x)))
           (* y (* 3.0 (sqrt x)))))))))

C

double code(double x, double y) {
	double t_0 = 3.0 * (sqrt(x) * y);
	double tmp;
	if (y <= -8.5e+83) {
		tmp = t_0;
	} else if (y <= -2.1e+59) {
		tmp = sqrt(x) * (0.3333333333333333 / x);
	} else if (y <= -6500000.0) {
		tmp = t_0;
	} else if (y <= 2000000000.0) {
		tmp = sqrt(x) * (-3.0 + (0.3333333333333333 / x));
	} 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) :: t_0
    real(8) :: tmp
    t_0 = 3.0d0 * (sqrt(x) * y)
    if (y <= (-8.5d+83)) then
        tmp = t_0
    else if (y <= (-2.1d+59)) then
        tmp = sqrt(x) * (0.3333333333333333d0 / x)
    else if (y <= (-6500000.0d0)) then
        tmp = t_0
    else if (y <= 2000000000.0d0) then
        tmp = sqrt(x) * ((-3.0d0) + (0.3333333333333333d0 / x))
    else
        tmp = y * (3.0d0 * sqrt(x))
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double t_0 = 3.0 * (Math.sqrt(x) * y);
	double tmp;
	if (y <= -8.5e+83) {
		tmp = t_0;
	} else if (y <= -2.1e+59) {
		tmp = Math.sqrt(x) * (0.3333333333333333 / x);
	} else if (y <= -6500000.0) {
		tmp = t_0;
	} else if (y <= 2000000000.0) {
		tmp = Math.sqrt(x) * (-3.0 + (0.3333333333333333 / x));
	} else {
		tmp = y * (3.0 * Math.sqrt(x));
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = 3.0 * (math.sqrt(x) * y)
	tmp = 0
	if y <= -8.5e+83:
		tmp = t_0
	elif y <= -2.1e+59:
		tmp = math.sqrt(x) * (0.3333333333333333 / x)
	elif y <= -6500000.0:
		tmp = t_0
	elif y <= 2000000000.0:
		tmp = math.sqrt(x) * (-3.0 + (0.3333333333333333 / x))
	else:
		tmp = y * (3.0 * math.sqrt(x))
	return tmp

Julia

function code(x, y)
	t_0 = Float64(3.0 * Float64(sqrt(x) * y))
	tmp = 0.0
	if (y <= -8.5e+83)
		tmp = t_0;
	elseif (y <= -2.1e+59)
		tmp = Float64(sqrt(x) * Float64(0.3333333333333333 / x));
	elseif (y <= -6500000.0)
		tmp = t_0;
	elseif (y <= 2000000000.0)
		tmp = Float64(sqrt(x) * Float64(-3.0 + Float64(0.3333333333333333 / x)));
	else
		tmp = Float64(y * Float64(3.0 * sqrt(x)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = 3.0 * (sqrt(x) * y);
	tmp = 0.0;
	if (y <= -8.5e+83)
		tmp = t_0;
	elseif (y <= -2.1e+59)
		tmp = sqrt(x) * (0.3333333333333333 / x);
	elseif (y <= -6500000.0)
		tmp = t_0;
	elseif (y <= 2000000000.0)
		tmp = sqrt(x) * (-3.0 + (0.3333333333333333 / x));
	else
		tmp = y * (3.0 * sqrt(x));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(3.0 * N[(N[Sqrt[x], $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -8.5e+83], t$95$0, If[LessEqual[y, -2.1e+59], N[(N[Sqrt[x], $MachinePrecision] * N[(0.3333333333333333 / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -6500000.0], t$95$0, If[LessEqual[y, 2000000000.0], N[(N[Sqrt[x], $MachinePrecision] * N[(-3.0 + N[(0.3333333333333333 / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(y * N[(3.0 * N[Sqrt[x], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -8.4999999999999995e83 or -2.09999999999999984e59 < y < -6.5e6

   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-rgt-in 99.5%

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

      4. +-commutative 99.5%

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

      5. fma-def 99.5%

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

      6. remove-double-neg 99.5%

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

      7. fma-neg 99.5%

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

      8. associate-*r* 99.4%

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

      9. *-commutative 99.4%

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

      10. associate-*r* 99.4%

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

      11. distribute-rgt-neg-in 99.4%

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

      12. *-commutative 99.4%

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

      13. associate-/r* 99.4%

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

      14. associate-/r/ 99.4%

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

      15. mul-1-neg 99.4%

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

      16. metadata-eval 99.4%

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

   3. Simplified 99.5%

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

   4. Taylor expanded in y around inf 81.3%

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

   if -8.4999999999999995e83 < y < -2.09999999999999984e59

   1. Initial program 99.1%

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

      1. +-commutative 99.1%

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

      2. associate--l+ 99.1%

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

      3. distribute-rgt-in 99.1%

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

      4. +-commutative 99.1%

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

      5. fma-def 99.1%

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

      6. remove-double-neg 99.1%

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

      7. fma-neg 99.1%

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

      8. associate-*r* 99.3%

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

      9. *-commutative 99.3%

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

      10. associate-*r* 99.6%

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

      11. distribute-rgt-neg-in 99.6%

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

      12. *-commutative 99.6%

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

      13. associate-/r* 99.3%

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

      14. associate-/r/ 98.9%

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

      15. mul-1-neg 98.9%

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

      16. metadata-eval 98.9%

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

   3. Simplified 99.3%

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

   4. Taylor expanded in x around 0 85.5%

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

   if -6.5e6 < y < 2e9

   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. +-commutative 99.4%

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

      5. fma-def 99.4%

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

      6. remove-double-neg 99.4%

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

      7. fma-neg 99.4%

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

      8. associate-*r* 99.4%

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

      9. *-commutative 99.4%

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

      10. associate-*r* 99.5%

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

      11. distribute-rgt-neg-in 99.5%

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

      12. *-commutative 99.5%

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

      13. associate-/r* 99.4%

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

      14. associate-/r/ 99.4%

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

      15. mul-1-neg 99.4%

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

      16. metadata-eval 99.4%

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

   3. Simplified 99.5%

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

   4. Taylor expanded in y around 0 97.7%

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

      1. *-commutative 97.7%

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

      2. associate-*r/ 97.8%

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

      3. metadata-eval 97.8%

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

      4. sub-neg 97.8%

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

      5. metadata-eval 97.8%

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

   6. Simplified 97.8%

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

   if 2e9 < 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-rgt-in 99.5%

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

      4. +-commutative 99.5%

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

      5. fma-def 99.5%

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

      6. remove-double-neg 99.5%

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

      7. fma-neg 99.5%

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

      8. associate-*r* 99.4%

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

      9. *-commutative 99.4%

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

      10. associate-*r* 99.3%

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

      11. distribute-rgt-neg-in 99.3%

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

      12. *-commutative 99.3%

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

      13. associate-/r* 99.3%

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

      14. associate-/r/ 99.3%

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

      15. mul-1-neg 99.3%

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

      16. metadata-eval 99.3%

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

   3. Simplified 99.4%

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

   4. Taylor expanded in y around inf 79.0%

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

      1. add-sqr-sqrt 78.8%

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

      2. pow2 78.8%

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

      3. *-commutative 78.8%

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

   6. Applied egg-rr 78.8%

      \[\leadsto \color{blue}{{\left(\sqrt{3 \cdot \left(\sqrt{x} \cdot y\right)}\right)}^{2}} \]
   7. Step-by-step derivation

      1. unpow2 78.8%

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

      2. add-sqr-sqrt 79.0%

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

      3. associate-*r* 79.0%

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

   8. Applied egg-rr 79.0%

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

4. Final simplification 88.7%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -8.5 \cdot 10^{+83}:\\ \;\;\;\;3 \cdot \left(\sqrt{x} \cdot y\right)\\ \mathbf{elif}\;y \leq -2.1 \cdot 10^{+59}:\\ \;\;\;\;\sqrt{x} \cdot \frac{0.3333333333333333}{x}\\ \mathbf{elif}\;y \leq -6500000:\\ \;\;\;\;3 \cdot \left(\sqrt{x} \cdot y\right)\\ \mathbf{elif}\;y \leq 2000000000:\\ \;\;\;\;\sqrt{x} \cdot \left(-3 + \frac{0.3333333333333333}{x}\right)\\ \mathbf{else}:\\ \;\;\;\;y \cdot \left(3 \cdot \sqrt{x}\right)\\ \end{array} \]

Alternative 5: 83.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 6 \cdot 10^{-131}:\\ \;\;\;\;\sqrt{x} \cdot \frac{0.3333333333333333}{x}\\ \mathbf{elif}\;x \leq 1.15 \cdot 10^{-72}:\\ \;\;\;\;y \cdot \left(3 \cdot \sqrt{x}\right)\\ \mathbf{elif}\;x \leq 1.05 \cdot 10^{-29}:\\ \;\;\;\;3 \cdot \left(\sqrt{x} \cdot \left(\frac{0.1111111111111111}{x} + -1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;3 \cdot \left(\sqrt{x} \cdot \left(y + -1\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x 6e-131)
   (* (sqrt x) (/ 0.3333333333333333 x))
   (if (<= x 1.15e-72)
     (* y (* 3.0 (sqrt x)))
     (if (<= x 1.05e-29)
       (* 3.0 (* (sqrt x) (+ (/ 0.1111111111111111 x) -1.0)))
       (* 3.0 (* (sqrt x) (+ y -1.0)))))))

C

double code(double x, double y) {
	double tmp;
	if (x <= 6e-131) {
		tmp = sqrt(x) * (0.3333333333333333 / x);
	} else if (x <= 1.15e-72) {
		tmp = y * (3.0 * sqrt(x));
	} else if (x <= 1.05e-29) {
		tmp = 3.0 * (sqrt(x) * ((0.1111111111111111 / x) + -1.0));
	} else {
		tmp = 3.0 * (sqrt(x) * (y + -1.0));
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (x <= 6d-131) then
        tmp = sqrt(x) * (0.3333333333333333d0 / x)
    else if (x <= 1.15d-72) then
        tmp = y * (3.0d0 * sqrt(x))
    else if (x <= 1.05d-29) then
        tmp = 3.0d0 * (sqrt(x) * ((0.1111111111111111d0 / x) + (-1.0d0)))
    else
        tmp = 3.0d0 * (sqrt(x) * (y + (-1.0d0)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= 6e-131) {
		tmp = Math.sqrt(x) * (0.3333333333333333 / x);
	} else if (x <= 1.15e-72) {
		tmp = y * (3.0 * Math.sqrt(x));
	} else if (x <= 1.05e-29) {
		tmp = 3.0 * (Math.sqrt(x) * ((0.1111111111111111 / x) + -1.0));
	} else {
		tmp = 3.0 * (Math.sqrt(x) * (y + -1.0));
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= 6e-131:
		tmp = math.sqrt(x) * (0.3333333333333333 / x)
	elif x <= 1.15e-72:
		tmp = y * (3.0 * math.sqrt(x))
	elif x <= 1.05e-29:
		tmp = 3.0 * (math.sqrt(x) * ((0.1111111111111111 / x) + -1.0))
	else:
		tmp = 3.0 * (math.sqrt(x) * (y + -1.0))
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= 6e-131)
		tmp = Float64(sqrt(x) * Float64(0.3333333333333333 / x));
	elseif (x <= 1.15e-72)
		tmp = Float64(y * Float64(3.0 * sqrt(x)));
	elseif (x <= 1.05e-29)
		tmp = Float64(3.0 * Float64(sqrt(x) * Float64(Float64(0.1111111111111111 / x) + -1.0)));
	else
		tmp = Float64(3.0 * Float64(sqrt(x) * Float64(y + -1.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= 6e-131)
		tmp = sqrt(x) * (0.3333333333333333 / x);
	elseif (x <= 1.15e-72)
		tmp = y * (3.0 * sqrt(x));
	elseif (x <= 1.05e-29)
		tmp = 3.0 * (sqrt(x) * ((0.1111111111111111 / x) + -1.0));
	else
		tmp = 3.0 * (sqrt(x) * (y + -1.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, 6e-131], N[(N[Sqrt[x], $MachinePrecision] * N[(0.3333333333333333 / x), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.15e-72], N[(y * N[(3.0 * N[Sqrt[x], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.05e-29], N[(3.0 * N[(N[Sqrt[x], $MachinePrecision] * N[(N[(0.1111111111111111 / x), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(3.0 * N[(N[Sqrt[x], $MachinePrecision] * N[(y + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]

Derivation

1. Split input into 4 regimes

2. if x < 5.99999999999999992e-131

   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-rgt-in 99.3%

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

      4. +-commutative 99.3%

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

      5. fma-def 99.3%

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

      6. remove-double-neg 99.3%

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

      7. fma-neg 99.3%

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

      8. associate-*r* 99.3%

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

      9. *-commutative 99.3%

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

      10. associate-*r* 99.3%

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

      11. distribute-rgt-neg-in 99.3%

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

      12. *-commutative 99.3%

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

      13. associate-/r* 99.2%

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

      14. associate-/r/ 99.1%

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

      15. mul-1-neg 99.1%

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

      16. metadata-eval 99.1%

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

   3. Simplified 99.3%

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

   4. Taylor expanded in x around 0 84.5%

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

   if 5.99999999999999992e-131 < x < 1.14999999999999997e-72

   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-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. +-commutative 99.6%

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

      5. fma-def 99.6%

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

      6. remove-double-neg 99.6%

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

      7. fma-neg 99.6%

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

      8. associate-*r* 99.5%

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

      9. *-commutative 99.5%

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

      10. associate-*r* 99.3%

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

      11. distribute-rgt-neg-in 99.3%

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

      12. *-commutative 99.3%

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

      13. associate-/r* 99.5%

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

      14. associate-/r/ 99.4%

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

      15. mul-1-neg 99.4%

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

      16. metadata-eval 99.4%

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

   3. Simplified 99.6%

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

   4. Taylor expanded in y around inf 64.9%

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

      1. add-sqr-sqrt 29.3%

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

      2. pow2 29.3%

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

      3. *-commutative 29.3%

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

   6. Applied egg-rr 29.3%

      \[\leadsto \color{blue}{{\left(\sqrt{3 \cdot \left(\sqrt{x} \cdot y\right)}\right)}^{2}} \]
   7. Step-by-step derivation

      1. unpow2 29.3%

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

      2. add-sqr-sqrt 64.9%

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

      3. associate-*r* 65.1%

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

   8. Applied egg-rr 65.1%

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

   if 1.14999999999999997e-72 < x < 1.04999999999999995e-29

   1. Initial program 98.7%

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

      1. +-commutative 98.7%

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

      2. associate--l+ 98.7%

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

      3. distribute-rgt-in 98.7%

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

      4. remove-double-neg 98.7%

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

      5. distribute-lft-neg-in 98.7%

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

      6. distribute-rgt-neg-in 98.7%

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

      7. mul-1-neg 98.7%

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

      8. metadata-eval 98.7%

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

      9. *-commutative 98.7%

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

      10. associate-/r* 98.8%

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

      11. distribute-neg-frac 98.8%

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

      12. *-commutative 98.8%

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

      13. associate-/r/ 99.0%

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

      14. associate-/l/ 99.0%

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

      15. associate-/r/ 98.8%

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

   3. Simplified 98.8%

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

      1. add-sqr-sqrt 83.7%

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

      2. pow2 83.7%

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

   5. Applied egg-rr 83.7%

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

   6. Taylor expanded in y around 0 98.3%

      \[\leadsto \color{blue}{\left(y \cdot {\left(\sqrt{3}\right)}^{2}\right) \cdot \sqrt{x} + \left(\left(0.1111111111111111 \cdot \frac{1}{x} - 1\right) \cdot {\left(\sqrt{3}\right)}^{2}\right) \cdot \sqrt{x}} \]
   7. Step-by-step derivation

      1. associate-*l* 98.2%

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

      2. associate-*l* 98.2%

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

      3. distribute-rgt-out 98.2%

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

      4. unpow2 98.2%

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

      5. rem-square-sqrt 98.9%

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

      6. sub-neg 98.9%

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

      7. associate-*r/ 98.8%

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

      8. metadata-eval 98.8%

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

      9. metadata-eval 98.8%

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

      10. associate-*l* 99.4%

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

      11. +-commutative 99.4%

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

      12. metadata-eval 99.4%

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

      13. sub-neg 99.4%

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

      14. associate-+l- 99.4%

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

   8. Simplified 99.4%

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

   9. Taylor expanded in y around 0 70.6%

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

       1. *-commutative 70.6%

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

       2. sub-neg 70.6%

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

       3. associate-*r/ 70.6%

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

       4. metadata-eval 70.6%

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

       5. metadata-eval 70.6%

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

       6. +-commutative 70.6%

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

   11. Simplified 70.6%

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

   if 1.04999999999999995e-29 < x

   1. Initial program 99.6%

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

   2. Taylor expanded in y around inf 97.1%

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

      1. add-cube-cbrt 95.6%

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

      2. pow3 95.6%

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

      3. *-commutative 95.6%

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

      4. *-commutative 95.6%

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

      5. sub-neg 95.6%

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

      6. metadata-eval 95.6%

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

   4. Applied egg-rr 95.6%

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

      1. rem-cube-cbrt 97.1%

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

      2. associate-*r* 97.1%

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

      3. *-commutative 97.1%

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

   6. Applied egg-rr 97.1%

      \[\leadsto \color{blue}{\left(\sqrt{x} \cdot \left(y + -1\right)\right) \cdot 3} \]
3. Recombined 4 regimes into one program.

4. Final simplification 88.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 6 \cdot 10^{-131}:\\ \;\;\;\;\sqrt{x} \cdot \frac{0.3333333333333333}{x}\\ \mathbf{elif}\;x \leq 1.15 \cdot 10^{-72}:\\ \;\;\;\;y \cdot \left(3 \cdot \sqrt{x}\right)\\ \mathbf{elif}\;x \leq 1.05 \cdot 10^{-29}:\\ \;\;\;\;3 \cdot \left(\sqrt{x} \cdot \left(\frac{0.1111111111111111}{x} + -1\right)\right)\\ \mathbf{else}:\\ \;\;\;\;3 \cdot \left(\sqrt{x} \cdot \left(y + -1\right)\right)\\ \end{array} \]

Alternative 6: 83.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \sqrt{x} \cdot \left(-3 + \frac{3}{x \cdot 9}\right)\\ \mathbf{if}\;x \leq 6.2 \cdot 10^{-131}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq 1.15 \cdot 10^{-72}:\\ \;\;\;\;y \cdot \left(3 \cdot \sqrt{x}\right)\\ \mathbf{elif}\;x \leq 1.35 \cdot 10^{-29}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;3 \cdot \left(\sqrt{x} \cdot \left(y + -1\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (* (sqrt x) (+ -3.0 (/ 3.0 (* x 9.0))))))
   (if (<= x 6.2e-131)
     t_0
     (if (<= x 1.15e-72)
       (* y (* 3.0 (sqrt x)))
       (if (<= x 1.35e-29) t_0 (* 3.0 (* (sqrt x) (+ y -1.0))))))))

C

double code(double x, double y) {
	double t_0 = sqrt(x) * (-3.0 + (3.0 / (x * 9.0)));
	double tmp;
	if (x <= 6.2e-131) {
		tmp = t_0;
	} else if (x <= 1.15e-72) {
		tmp = y * (3.0 * sqrt(x));
	} else if (x <= 1.35e-29) {
		tmp = t_0;
	} else {
		tmp = 3.0 * (sqrt(x) * (y + -1.0));
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: t_0
    real(8) :: tmp
    t_0 = sqrt(x) * ((-3.0d0) + (3.0d0 / (x * 9.0d0)))
    if (x <= 6.2d-131) then
        tmp = t_0
    else if (x <= 1.15d-72) then
        tmp = y * (3.0d0 * sqrt(x))
    else if (x <= 1.35d-29) then
        tmp = t_0
    else
        tmp = 3.0d0 * (sqrt(x) * (y + (-1.0d0)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double t_0 = Math.sqrt(x) * (-3.0 + (3.0 / (x * 9.0)));
	double tmp;
	if (x <= 6.2e-131) {
		tmp = t_0;
	} else if (x <= 1.15e-72) {
		tmp = y * (3.0 * Math.sqrt(x));
	} else if (x <= 1.35e-29) {
		tmp = t_0;
	} else {
		tmp = 3.0 * (Math.sqrt(x) * (y + -1.0));
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = math.sqrt(x) * (-3.0 + (3.0 / (x * 9.0)))
	tmp = 0
	if x <= 6.2e-131:
		tmp = t_0
	elif x <= 1.15e-72:
		tmp = y * (3.0 * math.sqrt(x))
	elif x <= 1.35e-29:
		tmp = t_0
	else:
		tmp = 3.0 * (math.sqrt(x) * (y + -1.0))
	return tmp

Julia

function code(x, y)
	t_0 = Float64(sqrt(x) * Float64(-3.0 + Float64(3.0 / Float64(x * 9.0))))
	tmp = 0.0
	if (x <= 6.2e-131)
		tmp = t_0;
	elseif (x <= 1.15e-72)
		tmp = Float64(y * Float64(3.0 * sqrt(x)));
	elseif (x <= 1.35e-29)
		tmp = t_0;
	else
		tmp = Float64(3.0 * Float64(sqrt(x) * Float64(y + -1.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = sqrt(x) * (-3.0 + (3.0 / (x * 9.0)));
	tmp = 0.0;
	if (x <= 6.2e-131)
		tmp = t_0;
	elseif (x <= 1.15e-72)
		tmp = y * (3.0 * sqrt(x));
	elseif (x <= 1.35e-29)
		tmp = t_0;
	else
		tmp = 3.0 * (sqrt(x) * (y + -1.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(N[Sqrt[x], $MachinePrecision] * N[(-3.0 + N[(3.0 / N[(x * 9.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, 6.2e-131], t$95$0, If[LessEqual[x, 1.15e-72], N[(y * N[(3.0 * N[Sqrt[x], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1.35e-29], t$95$0, N[(3.0 * N[(N[Sqrt[x], $MachinePrecision] * N[(y + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if x < 6.20000000000000041e-131 or 1.14999999999999997e-72 < x < 1.35000000000000011e-29

   1. Initial program 99.1%

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

      1. +-commutative 99.1%

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

      2. associate--l+ 99.1%

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

      3. distribute-rgt-in 99.1%

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

      4. remove-double-neg 99.1%

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

      5. distribute-lft-neg-in 99.1%

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

      6. distribute-rgt-neg-in 99.1%

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

      7. mul-1-neg 99.1%

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

      8. metadata-eval 99.1%

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

      9. *-commutative 99.1%

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

      10. associate-/r* 99.0%

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

      11. distribute-neg-frac 99.0%

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

      12. *-commutative 99.0%

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

      13. associate-/r/ 99.1%

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

      14. associate-/l/ 99.1%

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

      15. associate-/r/ 99.0%

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

   3. Simplified 99.0%

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

      1. add-sqr-sqrt 88.5%

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

      2. pow2 88.5%

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

   5. Applied egg-rr 88.5%

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

   6. Taylor expanded in y around 0 80.3%

      \[\leadsto \color{blue}{\left(\left(0.1111111111111111 \cdot \frac{1}{x} - 1\right) \cdot {\left(\sqrt{3}\right)}^{2}\right) \cdot \sqrt{x}} \]
   7. Step-by-step derivation

      1. *-commutative 80.3%

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

      2. *-commutative 80.3%

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

      3. unpow2 80.3%

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

      4. rem-square-sqrt 81.2%

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

      5. sub-neg 81.2%

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

      6. associate-*r/ 81.1%

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

      7. metadata-eval 81.1%

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

      8. metadata-eval 81.1%

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

      9. +-commutative 81.1%

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

      10. distribute-rgt-in 81.1%

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

      11. metadata-eval 81.1%

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

   8. Simplified 81.1%

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

      1. *-commutative 81.1%

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

      2. clear-num 81.1%

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

      3. un-div-inv 81.2%

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

      4. div-inv 81.4%

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

      5. metadata-eval 81.4%

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

   10. Applied egg-rr 81.4%

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

   if 6.20000000000000041e-131 < x < 1.14999999999999997e-72

   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-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. +-commutative 99.6%

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

      5. fma-def 99.6%

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

      6. remove-double-neg 99.6%

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

      7. fma-neg 99.6%

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

      8. associate-*r* 99.5%

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

      9. *-commutative 99.5%

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

      10. associate-*r* 99.3%

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

      11. distribute-rgt-neg-in 99.3%

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

      12. *-commutative 99.3%

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

      13. associate-/r* 99.5%

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

      14. associate-/r/ 99.4%

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

      15. mul-1-neg 99.4%

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

      16. metadata-eval 99.4%

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

   3. Simplified 99.6%

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

   4. Taylor expanded in y around inf 64.9%

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

      1. add-sqr-sqrt 29.3%

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

      2. pow2 29.3%

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

      3. *-commutative 29.3%

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

   6. Applied egg-rr 29.3%

      \[\leadsto \color{blue}{{\left(\sqrt{3 \cdot \left(\sqrt{x} \cdot y\right)}\right)}^{2}} \]
   7. Step-by-step derivation

      1. unpow2 29.3%

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

      2. add-sqr-sqrt 64.9%

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

      3. associate-*r* 65.1%

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

   8. Applied egg-rr 65.1%

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

   if 1.35000000000000011e-29 < x

   1. Initial program 99.6%

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

   2. Taylor expanded in y around inf 97.1%

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

      1. add-cube-cbrt 95.6%

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

      2. pow3 95.6%

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

      3. *-commutative 95.6%

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

      4. *-commutative 95.6%

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

      5. sub-neg 95.6%

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

      6. metadata-eval 95.6%

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

   4. Applied egg-rr 95.6%

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

      1. rem-cube-cbrt 97.1%

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

      2. associate-*r* 97.1%

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

      3. *-commutative 97.1%

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

   6. Applied egg-rr 97.1%

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

4. Final simplification 88.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 6.2 \cdot 10^{-131}:\\ \;\;\;\;\sqrt{x} \cdot \left(-3 + \frac{3}{x \cdot 9}\right)\\ \mathbf{elif}\;x \leq 1.15 \cdot 10^{-72}:\\ \;\;\;\;y \cdot \left(3 \cdot \sqrt{x}\right)\\ \mathbf{elif}\;x \leq 1.35 \cdot 10^{-29}:\\ \;\;\;\;\sqrt{x} \cdot \left(-3 + \frac{3}{x \cdot 9}\right)\\ \mathbf{else}:\\ \;\;\;\;3 \cdot \left(\sqrt{x} \cdot \left(y + -1\right)\right)\\ \end{array} \]

Alternative 7: 83.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \sqrt{x} \cdot \frac{0.3333333333333333}{x}\\ \mathbf{if}\;x \leq 7.2 \cdot 10^{-131}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq 1.05 \cdot 10^{-72}:\\ \;\;\;\;y \cdot \left(3 \cdot \sqrt{x}\right)\\ \mathbf{elif}\;x \leq 7.5 \cdot 10^{-30}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;\sqrt{x} \cdot \left(3 \cdot y - 3\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (* (sqrt x) (/ 0.3333333333333333 x))))
   (if (<= x 7.2e-131)
     t_0
     (if (<= x 1.05e-72)
       (* y (* 3.0 (sqrt x)))
       (if (<= x 7.5e-30) t_0 (* (sqrt x) (- (* 3.0 y) 3.0)))))))

C

double code(double x, double y) {
	double t_0 = sqrt(x) * (0.3333333333333333 / x);
	double tmp;
	if (x <= 7.2e-131) {
		tmp = t_0;
	} else if (x <= 1.05e-72) {
		tmp = y * (3.0 * sqrt(x));
	} else if (x <= 7.5e-30) {
		tmp = t_0;
	} else {
		tmp = sqrt(x) * ((3.0 * y) - 3.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: t_0
    real(8) :: tmp
    t_0 = sqrt(x) * (0.3333333333333333d0 / x)
    if (x <= 7.2d-131) then
        tmp = t_0
    else if (x <= 1.05d-72) then
        tmp = y * (3.0d0 * sqrt(x))
    else if (x <= 7.5d-30) then
        tmp = t_0
    else
        tmp = sqrt(x) * ((3.0d0 * y) - 3.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double t_0 = Math.sqrt(x) * (0.3333333333333333 / x);
	double tmp;
	if (x <= 7.2e-131) {
		tmp = t_0;
	} else if (x <= 1.05e-72) {
		tmp = y * (3.0 * Math.sqrt(x));
	} else if (x <= 7.5e-30) {
		tmp = t_0;
	} else {
		tmp = Math.sqrt(x) * ((3.0 * y) - 3.0);
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = math.sqrt(x) * (0.3333333333333333 / x)
	tmp = 0
	if x <= 7.2e-131:
		tmp = t_0
	elif x <= 1.05e-72:
		tmp = y * (3.0 * math.sqrt(x))
	elif x <= 7.5e-30:
		tmp = t_0
	else:
		tmp = math.sqrt(x) * ((3.0 * y) - 3.0)
	return tmp

Julia

function code(x, y)
	t_0 = Float64(sqrt(x) * Float64(0.3333333333333333 / x))
	tmp = 0.0
	if (x <= 7.2e-131)
		tmp = t_0;
	elseif (x <= 1.05e-72)
		tmp = Float64(y * Float64(3.0 * sqrt(x)));
	elseif (x <= 7.5e-30)
		tmp = t_0;
	else
		tmp = Float64(sqrt(x) * Float64(Float64(3.0 * y) - 3.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = sqrt(x) * (0.3333333333333333 / x);
	tmp = 0.0;
	if (x <= 7.2e-131)
		tmp = t_0;
	elseif (x <= 1.05e-72)
		tmp = y * (3.0 * sqrt(x));
	elseif (x <= 7.5e-30)
		tmp = t_0;
	else
		tmp = sqrt(x) * ((3.0 * y) - 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]}, If[LessEqual[x, 7.2e-131], t$95$0, If[LessEqual[x, 1.05e-72], N[(y * N[(3.0 * N[Sqrt[x], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 7.5e-30], t$95$0, N[(N[Sqrt[x], $MachinePrecision] * N[(N[(3.0 * y), $MachinePrecision] - 3.0), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if x < 7.1999999999999999e-131 or 1.05e-72 < x < 7.5000000000000006e-30

   1. Initial program 99.1%

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

      1. +-commutative 99.1%

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

      2. associate--l+ 99.1%

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

      3. distribute-rgt-in 99.1%

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

      4. +-commutative 99.1%

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

      5. fma-def 99.2%

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

      6. remove-double-neg 99.2%

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

      7. fma-neg 99.1%

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

      8. associate-*r* 99.1%

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

      9. *-commutative 99.1%

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

      10. associate-*r* 99.2%

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

      11. distribute-rgt-neg-in 99.2%

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

      12. *-commutative 99.2%

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

      13. associate-/r* 99.1%

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

      14. associate-/r/ 99.1%

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

      15. mul-1-neg 99.1%

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

      16. metadata-eval 99.1%

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

   3. Simplified 99.2%

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

   4. Taylor expanded in x around 0 81.2%

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

   if 7.1999999999999999e-131 < x < 1.05e-72

   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-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. +-commutative 99.6%

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

      5. fma-def 99.6%

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

      6. remove-double-neg 99.6%

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

      7. fma-neg 99.6%

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

      8. associate-*r* 99.5%

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

      9. *-commutative 99.5%

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

      10. associate-*r* 99.3%

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

      11. distribute-rgt-neg-in 99.3%

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

      12. *-commutative 99.3%

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

      13. associate-/r* 99.5%

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

      14. associate-/r/ 99.4%

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

      15. mul-1-neg 99.4%

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

      16. metadata-eval 99.4%

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

   3. Simplified 99.6%

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

   4. Taylor expanded in y around inf 64.9%

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

      1. add-sqr-sqrt 29.3%

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

      2. pow2 29.3%

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

      3. *-commutative 29.3%

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

   6. Applied egg-rr 29.3%

      \[\leadsto \color{blue}{{\left(\sqrt{3 \cdot \left(\sqrt{x} \cdot y\right)}\right)}^{2}} \]
   7. Step-by-step derivation

      1. unpow2 29.3%

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

      2. add-sqr-sqrt 64.9%

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

      3. associate-*r* 65.1%

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

   8. Applied egg-rr 65.1%

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

   if 7.5000000000000006e-30 < x

   1. Initial program 99.6%

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

      1. +-commutative 99.6%

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

      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. +-commutative 99.6%

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

      5. fma-def 99.6%

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

      6. remove-double-neg 99.6%

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

      7. fma-neg 99.6%

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

      8. associate-*r* 99.5%

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

      9. *-commutative 99.5%

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

      10. associate-*r* 99.6%

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

      11. distribute-rgt-neg-in 99.6%

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

      12. *-commutative 99.6%

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

      13. associate-/r* 99.5%

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

      14. associate-/r/ 99.5%

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

      15. mul-1-neg 99.5%

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

      16. metadata-eval 99.5%

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

   3. Simplified 99.6%

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

   4. Taylor expanded in x around inf 97.1%

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

4. Final simplification 88.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 7.2 \cdot 10^{-131}:\\ \;\;\;\;\sqrt{x} \cdot \frac{0.3333333333333333}{x}\\ \mathbf{elif}\;x \leq 1.05 \cdot 10^{-72}:\\ \;\;\;\;y \cdot \left(3 \cdot \sqrt{x}\right)\\ \mathbf{elif}\;x \leq 7.5 \cdot 10^{-30}:\\ \;\;\;\;\sqrt{x} \cdot \frac{0.3333333333333333}{x}\\ \mathbf{else}:\\ \;\;\;\;\sqrt{x} \cdot \left(3 \cdot y - 3\right)\\ \end{array} \]

Alternative 8: 83.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \sqrt{x} \cdot \frac{0.3333333333333333}{x}\\ t_1 := 3 \cdot \sqrt{x}\\ \mathbf{if}\;x \leq 7.2 \cdot 10^{-131}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq 1.05 \cdot 10^{-72}:\\ \;\;\;\;y \cdot t_1\\ \mathbf{elif}\;x \leq 7 \cdot 10^{-30}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;t_1 \cdot \left(y + -1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (* (sqrt x) (/ 0.3333333333333333 x))) (t_1 (* 3.0 (sqrt x))))
   (if (<= x 7.2e-131)
     t_0
     (if (<= x 1.05e-72) (* y t_1) (if (<= x 7e-30) t_0 (* t_1 (+ y -1.0)))))))

C

double code(double x, double y) {
	double t_0 = sqrt(x) * (0.3333333333333333 / x);
	double t_1 = 3.0 * sqrt(x);
	double tmp;
	if (x <= 7.2e-131) {
		tmp = t_0;
	} else if (x <= 1.05e-72) {
		tmp = y * t_1;
	} else if (x <= 7e-30) {
		tmp = t_0;
	} else {
		tmp = t_1 * (y + -1.0);
	}
	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 * sqrt(x)
    if (x <= 7.2d-131) then
        tmp = t_0
    else if (x <= 1.05d-72) then
        tmp = y * t_1
    else if (x <= 7d-30) then
        tmp = t_0
    else
        tmp = t_1 * (y + (-1.0d0))
    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 * Math.sqrt(x);
	double tmp;
	if (x <= 7.2e-131) {
		tmp = t_0;
	} else if (x <= 1.05e-72) {
		tmp = y * t_1;
	} else if (x <= 7e-30) {
		tmp = t_0;
	} else {
		tmp = t_1 * (y + -1.0);
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = math.sqrt(x) * (0.3333333333333333 / x)
	t_1 = 3.0 * math.sqrt(x)
	tmp = 0
	if x <= 7.2e-131:
		tmp = t_0
	elif x <= 1.05e-72:
		tmp = y * t_1
	elif x <= 7e-30:
		tmp = t_0
	else:
		tmp = t_1 * (y + -1.0)
	return tmp

Julia

function code(x, y)
	t_0 = Float64(sqrt(x) * Float64(0.3333333333333333 / x))
	t_1 = Float64(3.0 * sqrt(x))
	tmp = 0.0
	if (x <= 7.2e-131)
		tmp = t_0;
	elseif (x <= 1.05e-72)
		tmp = Float64(y * t_1);
	elseif (x <= 7e-30)
		tmp = t_0;
	else
		tmp = Float64(t_1 * Float64(y + -1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = sqrt(x) * (0.3333333333333333 / x);
	t_1 = 3.0 * sqrt(x);
	tmp = 0.0;
	if (x <= 7.2e-131)
		tmp = t_0;
	elseif (x <= 1.05e-72)
		tmp = y * t_1;
	elseif (x <= 7e-30)
		tmp = t_0;
	else
		tmp = t_1 * (y + -1.0);
	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[Sqrt[x], $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, 7.2e-131], t$95$0, If[LessEqual[x, 1.05e-72], N[(y * t$95$1), $MachinePrecision], If[LessEqual[x, 7e-30], t$95$0, N[(t$95$1 * N[(y + -1.0), $MachinePrecision]), $MachinePrecision]]]]]]

Derivation

1. Split input into 3 regimes

2. if x < 7.1999999999999999e-131 or 1.05e-72 < x < 7.0000000000000006e-30

   1. Initial program 99.1%

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

      1. +-commutative 99.1%

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

      2. associate--l+ 99.1%

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

      3. distribute-rgt-in 99.1%

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

      4. +-commutative 99.1%

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

      5. fma-def 99.2%

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

      6. remove-double-neg 99.2%

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

      7. fma-neg 99.1%

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

      8. associate-*r* 99.1%

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

      9. *-commutative 99.1%

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

      10. associate-*r* 99.2%

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

      11. distribute-rgt-neg-in 99.2%

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

      12. *-commutative 99.2%

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

      13. associate-/r* 99.1%

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

      14. associate-/r/ 99.1%

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

      15. mul-1-neg 99.1%

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

      16. metadata-eval 99.1%

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

   3. Simplified 99.2%

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

   4. Taylor expanded in x around 0 81.2%

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

   if 7.1999999999999999e-131 < x < 1.05e-72

   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-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. +-commutative 99.6%

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

      5. fma-def 99.6%

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

      6. remove-double-neg 99.6%

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

      7. fma-neg 99.6%

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

      8. associate-*r* 99.5%

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

      9. *-commutative 99.5%

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

      10. associate-*r* 99.3%

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

      11. distribute-rgt-neg-in 99.3%

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

      12. *-commutative 99.3%

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

      13. associate-/r* 99.5%

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

      14. associate-/r/ 99.4%

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

      15. mul-1-neg 99.4%

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

      16. metadata-eval 99.4%

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

   3. Simplified 99.6%

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

   4. Taylor expanded in y around inf 64.9%

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

      1. add-sqr-sqrt 29.3%

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

      2. pow2 29.3%

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

      3. *-commutative 29.3%

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

   6. Applied egg-rr 29.3%

      \[\leadsto \color{blue}{{\left(\sqrt{3 \cdot \left(\sqrt{x} \cdot y\right)}\right)}^{2}} \]
   7. Step-by-step derivation

      1. unpow2 29.3%

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

      2. add-sqr-sqrt 64.9%

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

      3. associate-*r* 65.1%

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

   8. Applied egg-rr 65.1%

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

   if 7.0000000000000006e-30 < x

   1. Initial program 99.6%

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

   2. Taylor expanded in y around inf 97.1%

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

4. Final simplification 88.2%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 7.2 \cdot 10^{-131}:\\ \;\;\;\;\sqrt{x} \cdot \frac{0.3333333333333333}{x}\\ \mathbf{elif}\;x \leq 1.05 \cdot 10^{-72}:\\ \;\;\;\;y \cdot \left(3 \cdot \sqrt{x}\right)\\ \mathbf{elif}\;x \leq 7 \cdot 10^{-30}:\\ \;\;\;\;\sqrt{x} \cdot \frac{0.3333333333333333}{x}\\ \mathbf{else}:\\ \;\;\;\;\left(3 \cdot \sqrt{x}\right) \cdot \left(y + -1\right)\\ \end{array} \]

Alternative 9: 83.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \sqrt{x} \cdot \frac{0.3333333333333333}{x}\\ \mathbf{if}\;x \leq 5.2 \cdot 10^{-131}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq 1.7 \cdot 10^{-72}:\\ \;\;\;\;y \cdot \left(3 \cdot \sqrt{x}\right)\\ \mathbf{elif}\;x \leq 10^{-29}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;3 \cdot \left(\sqrt{x} \cdot \left(y + -1\right)\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (* (sqrt x) (/ 0.3333333333333333 x))))
   (if (<= x 5.2e-131)
     t_0
     (if (<= x 1.7e-72)
       (* y (* 3.0 (sqrt x)))
       (if (<= x 1e-29) t_0 (* 3.0 (* (sqrt x) (+ y -1.0))))))))

C

double code(double x, double y) {
	double t_0 = sqrt(x) * (0.3333333333333333 / x);
	double tmp;
	if (x <= 5.2e-131) {
		tmp = t_0;
	} else if (x <= 1.7e-72) {
		tmp = y * (3.0 * sqrt(x));
	} else if (x <= 1e-29) {
		tmp = t_0;
	} else {
		tmp = 3.0 * (sqrt(x) * (y + -1.0));
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: t_0
    real(8) :: tmp
    t_0 = sqrt(x) * (0.3333333333333333d0 / x)
    if (x <= 5.2d-131) then
        tmp = t_0
    else if (x <= 1.7d-72) then
        tmp = y * (3.0d0 * sqrt(x))
    else if (x <= 1d-29) then
        tmp = t_0
    else
        tmp = 3.0d0 * (sqrt(x) * (y + (-1.0d0)))
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double t_0 = Math.sqrt(x) * (0.3333333333333333 / x);
	double tmp;
	if (x <= 5.2e-131) {
		tmp = t_0;
	} else if (x <= 1.7e-72) {
		tmp = y * (3.0 * Math.sqrt(x));
	} else if (x <= 1e-29) {
		tmp = t_0;
	} else {
		tmp = 3.0 * (Math.sqrt(x) * (y + -1.0));
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = math.sqrt(x) * (0.3333333333333333 / x)
	tmp = 0
	if x <= 5.2e-131:
		tmp = t_0
	elif x <= 1.7e-72:
		tmp = y * (3.0 * math.sqrt(x))
	elif x <= 1e-29:
		tmp = t_0
	else:
		tmp = 3.0 * (math.sqrt(x) * (y + -1.0))
	return tmp

Julia

function code(x, y)
	t_0 = Float64(sqrt(x) * Float64(0.3333333333333333 / x))
	tmp = 0.0
	if (x <= 5.2e-131)
		tmp = t_0;
	elseif (x <= 1.7e-72)
		tmp = Float64(y * Float64(3.0 * sqrt(x)));
	elseif (x <= 1e-29)
		tmp = t_0;
	else
		tmp = Float64(3.0 * Float64(sqrt(x) * Float64(y + -1.0)));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = sqrt(x) * (0.3333333333333333 / x);
	tmp = 0.0;
	if (x <= 5.2e-131)
		tmp = t_0;
	elseif (x <= 1.7e-72)
		tmp = y * (3.0 * sqrt(x));
	elseif (x <= 1e-29)
		tmp = t_0;
	else
		tmp = 3.0 * (sqrt(x) * (y + -1.0));
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(N[Sqrt[x], $MachinePrecision] * N[(0.3333333333333333 / x), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[x, 5.2e-131], t$95$0, If[LessEqual[x, 1.7e-72], N[(y * N[(3.0 * N[Sqrt[x], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], If[LessEqual[x, 1e-29], t$95$0, N[(3.0 * N[(N[Sqrt[x], $MachinePrecision] * N[(y + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 3 regimes

2. if x < 5.19999999999999993e-131 or 1.6999999999999999e-72 < x < 9.99999999999999943e-30

   1. Initial program 99.1%

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

      1. +-commutative 99.1%

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

      2. associate--l+ 99.1%

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

      3. distribute-rgt-in 99.1%

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

      4. +-commutative 99.1%

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

      5. fma-def 99.2%

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

      6. remove-double-neg 99.2%

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

      7. fma-neg 99.1%

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

      8. associate-*r* 99.1%

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

      9. *-commutative 99.1%

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

      10. associate-*r* 99.2%

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

      11. distribute-rgt-neg-in 99.2%

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

      12. *-commutative 99.2%

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

      13. associate-/r* 99.1%

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

      14. associate-/r/ 99.1%

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

      15. mul-1-neg 99.1%

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

      16. metadata-eval 99.1%

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

   3. Simplified 99.2%

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

   4. Taylor expanded in x around 0 81.2%

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

   if 5.19999999999999993e-131 < x < 1.6999999999999999e-72

   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-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. +-commutative 99.6%

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

      5. fma-def 99.6%

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

      6. remove-double-neg 99.6%

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

      7. fma-neg 99.6%

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

      8. associate-*r* 99.5%

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

      9. *-commutative 99.5%

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

      10. associate-*r* 99.3%

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

      11. distribute-rgt-neg-in 99.3%

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

      12. *-commutative 99.3%

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

      13. associate-/r* 99.5%

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

      14. associate-/r/ 99.4%

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

      15. mul-1-neg 99.4%

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

      16. metadata-eval 99.4%

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

   3. Simplified 99.6%

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

   4. Taylor expanded in y around inf 64.9%

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

      1. add-sqr-sqrt 29.3%

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

      2. pow2 29.3%

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

      3. *-commutative 29.3%

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

   6. Applied egg-rr 29.3%

      \[\leadsto \color{blue}{{\left(\sqrt{3 \cdot \left(\sqrt{x} \cdot y\right)}\right)}^{2}} \]
   7. Step-by-step derivation

      1. unpow2 29.3%

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

      2. add-sqr-sqrt 64.9%

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

      3. associate-*r* 65.1%

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

   8. Applied egg-rr 65.1%

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

   if 9.99999999999999943e-30 < x

   1. Initial program 99.6%

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

   2. Taylor expanded in y around inf 97.1%

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

      1. add-cube-cbrt 95.6%

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

      2. pow3 95.6%

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

      3. *-commutative 95.6%

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

      4. *-commutative 95.6%

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

      5. sub-neg 95.6%

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

      6. metadata-eval 95.6%

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

   4. Applied egg-rr 95.6%

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

      1. rem-cube-cbrt 97.1%

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

      2. associate-*r* 97.1%

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

      3. *-commutative 97.1%

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

   6. Applied egg-rr 97.1%

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

4. Final simplification 88.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 5.2 \cdot 10^{-131}:\\ \;\;\;\;\sqrt{x} \cdot \frac{0.3333333333333333}{x}\\ \mathbf{elif}\;x \leq 1.7 \cdot 10^{-72}:\\ \;\;\;\;y \cdot \left(3 \cdot \sqrt{x}\right)\\ \mathbf{elif}\;x \leq 10^{-29}:\\ \;\;\;\;\sqrt{x} \cdot \frac{0.3333333333333333}{x}\\ \mathbf{else}:\\ \;\;\;\;3 \cdot \left(\sqrt{x} \cdot \left(y + -1\right)\right)\\ \end{array} \]

Alternative 10: 62.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -0.07 \lor \neg \left(y \leq 7.2 \cdot 10^{-7}\right):\\ \;\;\;\;3 \cdot \left(\sqrt{x} \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;\sqrt{x} \cdot -3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (or (<= y -0.07) (not (<= y 7.2e-7)))
   (* 3.0 (* (sqrt x) y))
   (* (sqrt x) -3.0)))

C

double code(double x, double y) {
	double tmp;
	if ((y <= -0.07) || !(y <= 7.2e-7)) {
		tmp = 3.0 * (sqrt(x) * y);
	} 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 <= (-0.07d0)) .or. (.not. (y <= 7.2d-7))) then
        tmp = 3.0d0 * (sqrt(x) * y)
    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 <= -0.07) || !(y <= 7.2e-7)) {
		tmp = 3.0 * (Math.sqrt(x) * y);
	} else {
		tmp = Math.sqrt(x) * -3.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if (y <= -0.07) or not (y <= 7.2e-7):
		tmp = 3.0 * (math.sqrt(x) * y)
	else:
		tmp = math.sqrt(x) * -3.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if ((y <= -0.07) || !(y <= 7.2e-7))
		tmp = Float64(3.0 * Float64(sqrt(x) * y));
	else
		tmp = Float64(sqrt(x) * -3.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if ((y <= -0.07) || ~((y <= 7.2e-7)))
		tmp = 3.0 * (sqrt(x) * y);
	else
		tmp = sqrt(x) * -3.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[Or[LessEqual[y, -0.07], N[Not[LessEqual[y, 7.2e-7]], $MachinePrecision]], N[(3.0 * N[(N[Sqrt[x], $MachinePrecision] * y), $MachinePrecision]), $MachinePrecision], N[(N[Sqrt[x], $MachinePrecision] * -3.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if y < -0.070000000000000007 or 7.19999999999999989e-7 < 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-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. +-commutative 99.4%

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

      5. fma-def 99.4%

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

      6. remove-double-neg 99.4%

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

      7. fma-neg 99.4%

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

      8. associate-*r* 99.4%

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

      9. *-commutative 99.4%

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

      10. associate-*r* 99.4%

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

      11. distribute-rgt-neg-in 99.4%

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

      12. *-commutative 99.4%

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

      13. associate-/r* 99.4%

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

      14. associate-/r/ 99.3%

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

      15. mul-1-neg 99.3%

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

      16. metadata-eval 99.3%

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

   3. Simplified 99.4%

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

   4. Taylor expanded in y around inf 74.0%

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

   if -0.070000000000000007 < y < 7.19999999999999989e-7

   1. Initial program 99.4%

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

   2. Taylor expanded in y around inf 56.1%

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

   3. Taylor expanded in y around 0 55.8%

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

      1. *-commutative 55.8%

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

   5. Simplified 55.8%

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

4. Final simplification 65.9%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -0.07 \lor \neg \left(y \leq 7.2 \cdot 10^{-7}\right):\\ \;\;\;\;3 \cdot \left(\sqrt{x} \cdot y\right)\\ \mathbf{else}:\\ \;\;\;\;\sqrt{x} \cdot -3\\ \end{array} \]

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. Taylor expanded in y around inf 67.1%

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

3. Taylor expanded in y around 0 26.7%

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

   1. *-commutative 26.7%

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

5. Simplified 26.7%

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

   1. add-sqr-sqrt 0.0%

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

   2. sqrt-unprod 2.9%

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

   3. swap-sqr 2.9%

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

   4. add-sqr-sqrt 2.9%

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

   5. metadata-eval 2.9%

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

7. Applied egg-rr 2.9%

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

8. Final simplification 2.9%

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

Alternative 12: 25.3% accurate, 1.1× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.4%

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

2. Taylor expanded in y around inf 67.1%

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

3. Taylor expanded in y around 0 26.7%

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

   1. *-commutative 26.7%

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

5. Simplified 26.7%

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

6. Final simplification 26.7%

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

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 2023181 
(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)))