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

Percentage Accurate: 99.4% → 99.4%

Time: 9.2s

Alternatives: 15

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

\[\begin{array}{l} \\ {\left(x \cdot 9\right)}^{0.5} \cdot \left(y + \left(\frac{0.1111111111111111}{x} + -1\right)\right) \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (* (pow (* x 9.0) 0.5) (+ y (+ (/ 0.1111111111111111 x) -1.0))))

C

double code(double x, double y) {
	return pow((x * 9.0), 0.5) * (y + ((0.1111111111111111 / x) + -1.0));
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = ((x * 9.0d0) ** 0.5d0) * (y + ((0.1111111111111111d0 / x) + (-1.0d0)))
end function

Java

public static double code(double x, double y) {
	return Math.pow((x * 9.0), 0.5) * (y + ((0.1111111111111111 / x) + -1.0));
}

Python

def code(x, y):
	return math.pow((x * 9.0), 0.5) * (y + ((0.1111111111111111 / x) + -1.0))

Julia

function code(x, y)
	return Float64((Float64(x * 9.0) ^ 0.5) * Float64(y + Float64(Float64(0.1111111111111111 / x) + -1.0)))
end

MATLAB

function tmp = code(x, y)
	tmp = ((x * 9.0) ^ 0.5) * (y + ((0.1111111111111111 / x) + -1.0));
end

Wolfram

code[x_, y_] := N[(N[Power[N[(x * 9.0), $MachinePrecision], 0.5], $MachinePrecision] * N[(y + N[(N[(0.1111111111111111 / x), $MachinePrecision] + -1.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 99.5%

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

   1. associate--l+ 99.5%

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

   2. sub-neg 99.5%

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

   3. *-commutative 99.5%

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

   4. associate-/r* 99.5%

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

   5. metadata-eval 99.5%

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

   6. metadata-eval 99.5%

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

3. Simplified 99.5%

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

   1. *-commutative 99.5%

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

   2. metadata-eval 99.5%

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

   3. sqrt-prod 99.6%

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

   4. pow1/2 99.6%

      \[\leadsto \color{blue}{{\left(x \cdot 9\right)}^{0.5}} \cdot \left(y + \left(\frac{0.1111111111111111}{x} + -1\right)\right) \]

5. Applied egg-rr 99.6%

   \[\leadsto \color{blue}{{\left(x \cdot 9\right)}^{0.5}} \cdot \left(y + \left(\frac{0.1111111111111111}{x} + -1\right)\right) \]

6. Final simplification 99.6%

   \[\leadsto {\left(x \cdot 9\right)}^{0.5} \cdot \left(y + \left(\frac{0.1111111111111111}{x} + -1\right)\right) \]

Alternative 2: 60.0% accurate, 0.9× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \sqrt{\frac{0.1111111111111111}{x} \cdot \frac{x}{x}}\\ t_1 := \sqrt{x} \cdot \left(y \cdot 3\right)\\ t_2 := \sqrt{x} \cdot -3\\ \mathbf{if}\;y \leq -5.7 \cdot 10^{+72}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -2.2 \cdot 10^{+26}:\\ \;\;\;\;0.3333333333333333 \cdot \sqrt{\frac{1}{x}}\\ \mathbf{elif}\;y \leq -4.6 \cdot 10^{-184}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 3.6 \cdot 10^{-201}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 3 \cdot 10^{-102}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 1.55 \cdot 10^{+80}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (sqrt (* (/ 0.1111111111111111 x) (/ x x))))
        (t_1 (* (sqrt x) (* y 3.0)))
        (t_2 (* (sqrt x) -3.0)))
   (if (<= y -5.7e+72)
     t_1
     (if (<= y -2.2e+26)
       (* 0.3333333333333333 (sqrt (/ 1.0 x)))
       (if (<= y -4.6e-184)
         t_2
         (if (<= y 3.6e-201)
           t_0
           (if (<= y 3e-102) t_2 (if (<= y 1.55e+80) t_0 t_1))))))))

C

double code(double x, double y) {
	double t_0 = sqrt(((0.1111111111111111 / x) * (x / x)));
	double t_1 = sqrt(x) * (y * 3.0);
	double t_2 = sqrt(x) * -3.0;
	double tmp;
	if (y <= -5.7e+72) {
		tmp = t_1;
	} else if (y <= -2.2e+26) {
		tmp = 0.3333333333333333 * sqrt((1.0 / x));
	} else if (y <= -4.6e-184) {
		tmp = t_2;
	} else if (y <= 3.6e-201) {
		tmp = t_0;
	} else if (y <= 3e-102) {
		tmp = t_2;
	} else if (y <= 1.55e+80) {
		tmp = t_0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_0 = sqrt(((0.1111111111111111d0 / x) * (x / x)))
    t_1 = sqrt(x) * (y * 3.0d0)
    t_2 = sqrt(x) * (-3.0d0)
    if (y <= (-5.7d+72)) then
        tmp = t_1
    else if (y <= (-2.2d+26)) then
        tmp = 0.3333333333333333d0 * sqrt((1.0d0 / x))
    else if (y <= (-4.6d-184)) then
        tmp = t_2
    else if (y <= 3.6d-201) then
        tmp = t_0
    else if (y <= 3d-102) then
        tmp = t_2
    else if (y <= 1.55d+80) then
        tmp = t_0
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double t_0 = Math.sqrt(((0.1111111111111111 / x) * (x / x)));
	double t_1 = Math.sqrt(x) * (y * 3.0);
	double t_2 = Math.sqrt(x) * -3.0;
	double tmp;
	if (y <= -5.7e+72) {
		tmp = t_1;
	} else if (y <= -2.2e+26) {
		tmp = 0.3333333333333333 * Math.sqrt((1.0 / x));
	} else if (y <= -4.6e-184) {
		tmp = t_2;
	} else if (y <= 3.6e-201) {
		tmp = t_0;
	} else if (y <= 3e-102) {
		tmp = t_2;
	} else if (y <= 1.55e+80) {
		tmp = t_0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = math.sqrt(((0.1111111111111111 / x) * (x / x)))
	t_1 = math.sqrt(x) * (y * 3.0)
	t_2 = math.sqrt(x) * -3.0
	tmp = 0
	if y <= -5.7e+72:
		tmp = t_1
	elif y <= -2.2e+26:
		tmp = 0.3333333333333333 * math.sqrt((1.0 / x))
	elif y <= -4.6e-184:
		tmp = t_2
	elif y <= 3.6e-201:
		tmp = t_0
	elif y <= 3e-102:
		tmp = t_2
	elif y <= 1.55e+80:
		tmp = t_0
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y)
	t_0 = sqrt(Float64(Float64(0.1111111111111111 / x) * Float64(x / x)))
	t_1 = Float64(sqrt(x) * Float64(y * 3.0))
	t_2 = Float64(sqrt(x) * -3.0)
	tmp = 0.0
	if (y <= -5.7e+72)
		tmp = t_1;
	elseif (y <= -2.2e+26)
		tmp = Float64(0.3333333333333333 * sqrt(Float64(1.0 / x)));
	elseif (y <= -4.6e-184)
		tmp = t_2;
	elseif (y <= 3.6e-201)
		tmp = t_0;
	elseif (y <= 3e-102)
		tmp = t_2;
	elseif (y <= 1.55e+80)
		tmp = t_0;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = sqrt(((0.1111111111111111 / x) * (x / x)));
	t_1 = sqrt(x) * (y * 3.0);
	t_2 = sqrt(x) * -3.0;
	tmp = 0.0;
	if (y <= -5.7e+72)
		tmp = t_1;
	elseif (y <= -2.2e+26)
		tmp = 0.3333333333333333 * sqrt((1.0 / x));
	elseif (y <= -4.6e-184)
		tmp = t_2;
	elseif (y <= 3.6e-201)
		tmp = t_0;
	elseif (y <= 3e-102)
		tmp = t_2;
	elseif (y <= 1.55e+80)
		tmp = t_0;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[Sqrt[N[(N[(0.1111111111111111 / x), $MachinePrecision] * N[(x / x), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]}, Block[{t$95$1 = N[(N[Sqrt[x], $MachinePrecision] * N[(y * 3.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[Sqrt[x], $MachinePrecision] * -3.0), $MachinePrecision]}, If[LessEqual[y, -5.7e+72], t$95$1, If[LessEqual[y, -2.2e+26], N[(0.3333333333333333 * N[Sqrt[N[(1.0 / x), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -4.6e-184], t$95$2, If[LessEqual[y, 3.6e-201], t$95$0, If[LessEqual[y, 3e-102], t$95$2, If[LessEqual[y, 1.55e+80], t$95$0, t$95$1]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -5.6999999999999997e72 or 1.54999999999999994e80 < y

   1. Initial program 99.6%

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

      1. *-commutative 99.6%

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

      2. associate-*l* 99.6%

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

      3. +-commutative 99.6%

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

      4. associate--l+ 99.6%

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

      5. +-commutative 99.6%

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

      6. distribute-rgt-in 99.6%

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

      7. *-commutative 99.6%

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

      8. fma-def 99.7%

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

      9. sub-neg 99.7%

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

      10. metadata-eval 99.7%

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

      11. associate-*l/ 99.6%

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

      12. metadata-eval 99.6%

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

      13. *-commutative 99.6%

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

      14. associate-/r* 99.7%

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

      15. metadata-eval 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in y around inf 91.9%

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

      1. associate-*r* 91.9%

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

      2. *-commutative 91.9%

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

      3. associate-*l* 92.0%

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

   6. Simplified 92.0%

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

   if -5.6999999999999997e72 < y < -2.20000000000000007e26

   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. associate--l+ 99.1%

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

      2. sub-neg 99.1%

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

      3. *-commutative 99.1%

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

      4. associate-/r* 99.2%

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

      5. metadata-eval 99.2%

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

      6. metadata-eval 99.2%

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

   3. Simplified 99.2%

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

   4. Taylor expanded in x around 0 99.2%

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

   5. Taylor expanded in y around 0 90.1%

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

   if -2.20000000000000007e26 < y < -4.5999999999999999e-184 or 3.60000000000000031e-201 < y < 3e-102

   1. Initial program 99.6%

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

      1. *-commutative 99.6%

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

      2. associate-*l* 99.6%

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

      3. +-commutative 99.6%

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

      4. associate--l+ 99.6%

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

      5. +-commutative 99.6%

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

      6. distribute-rgt-in 99.6%

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

      7. *-commutative 99.6%

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

      8. fma-def 99.6%

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

      9. sub-neg 99.6%

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

      10. metadata-eval 99.6%

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

      11. associate-*l/ 99.6%

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

      12. metadata-eval 99.6%

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

      13. *-commutative 99.6%

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

      14. associate-/r* 99.6%

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

      15. metadata-eval 99.6%

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

   3. Simplified 99.6%

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

   4. Taylor expanded in y around 0 92.8%

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

      1. sub-neg 92.8%

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

      2. associate-*r/ 92.8%

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

      3. metadata-eval 92.8%

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

      4. metadata-eval 92.8%

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

   6. Simplified 92.8%

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

   7. Taylor expanded in x around inf 62.3%

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

   if -4.5999999999999999e-184 < y < 3.60000000000000031e-201 or 3e-102 < y < 1.54999999999999994e80

   1. Initial program 99.3%

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

      1. *-commutative 99.3%

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

      2. associate-*l* 99.2%

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

      3. +-commutative 99.2%

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

      4. associate--l+ 99.2%

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

      5. +-commutative 99.2%

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

      6. distribute-rgt-in 99.2%

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

      7. *-commutative 99.2%

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

      8. fma-def 99.2%

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

      9. sub-neg 99.2%

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

      10. metadata-eval 99.2%

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

      11. associate-*l/ 99.4%

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

      12. metadata-eval 99.4%

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

      13. *-commutative 99.4%

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

      14. associate-/r* 99.2%

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

      15. metadata-eval 99.2%

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

   3. Simplified 99.2%

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

   4. Taylor expanded in x around 0 59.3%

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

      1. add-sqr-sqrt 59.3%

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

      2. sqrt-unprod 59.3%

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

      3. swap-sqr 35.6%

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

      4. add-sqr-sqrt 35.7%

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

      5. frac-times 35.7%

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

      6. metadata-eval 35.7%

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

   6. Applied egg-rr 35.7%

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

      1. associate-*r/ 37.0%

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

      2. times-frac 59.7%

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

   8. Simplified 59.7%

      \[\leadsto \color{blue}{\sqrt{\frac{x}{x} \cdot \frac{0.1111111111111111}{x}}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 73.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.7 \cdot 10^{+72}:\\ \;\;\;\;\sqrt{x} \cdot \left(y \cdot 3\right)\\ \mathbf{elif}\;y \leq -2.2 \cdot 10^{+26}:\\ \;\;\;\;0.3333333333333333 \cdot \sqrt{\frac{1}{x}}\\ \mathbf{elif}\;y \leq -4.6 \cdot 10^{-184}:\\ \;\;\;\;\sqrt{x} \cdot -3\\ \mathbf{elif}\;y \leq 3.6 \cdot 10^{-201}:\\ \;\;\;\;\sqrt{\frac{0.1111111111111111}{x} \cdot \frac{x}{x}}\\ \mathbf{elif}\;y \leq 3 \cdot 10^{-102}:\\ \;\;\;\;\sqrt{x} \cdot -3\\ \mathbf{elif}\;y \leq 1.55 \cdot 10^{+80}:\\ \;\;\;\;\sqrt{\frac{0.1111111111111111}{x} \cdot \frac{x}{x}}\\ \mathbf{else}:\\ \;\;\;\;\sqrt{x} \cdot \left(y \cdot 3\right)\\ \end{array} \]

Alternative 3: 59.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 0.3333333333333333 \cdot \sqrt{\frac{1}{x}}\\ t_1 := 3 \cdot \left(y \cdot \sqrt{x}\right)\\ t_2 := \sqrt{x} \cdot -3\\ \mathbf{if}\;y \leq -1.9 \cdot 10^{+81}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -2.2 \cdot 10^{+26}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq -1.7 \cdot 10^{-184}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 8.2 \cdot 10^{-202}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 1.3 \cdot 10^{-102}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 9 \cdot 10^{+79}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (* 0.3333333333333333 (sqrt (/ 1.0 x))))
        (t_1 (* 3.0 (* y (sqrt x))))
        (t_2 (* (sqrt x) -3.0)))
   (if (<= y -1.9e+81)
     t_1
     (if (<= y -2.2e+26)
       t_0
       (if (<= y -1.7e-184)
         t_2
         (if (<= y 8.2e-202)
           t_0
           (if (<= y 1.3e-102) t_2 (if (<= y 9e+79) t_0 t_1))))))))

C

double code(double x, double y) {
	double t_0 = 0.3333333333333333 * sqrt((1.0 / x));
	double t_1 = 3.0 * (y * sqrt(x));
	double t_2 = sqrt(x) * -3.0;
	double tmp;
	if (y <= -1.9e+81) {
		tmp = t_1;
	} else if (y <= -2.2e+26) {
		tmp = t_0;
	} else if (y <= -1.7e-184) {
		tmp = t_2;
	} else if (y <= 8.2e-202) {
		tmp = t_0;
	} else if (y <= 1.3e-102) {
		tmp = t_2;
	} else if (y <= 9e+79) {
		tmp = t_0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_0 = 0.3333333333333333d0 * sqrt((1.0d0 / x))
    t_1 = 3.0d0 * (y * sqrt(x))
    t_2 = sqrt(x) * (-3.0d0)
    if (y <= (-1.9d+81)) then
        tmp = t_1
    else if (y <= (-2.2d+26)) then
        tmp = t_0
    else if (y <= (-1.7d-184)) then
        tmp = t_2
    else if (y <= 8.2d-202) then
        tmp = t_0
    else if (y <= 1.3d-102) then
        tmp = t_2
    else if (y <= 9d+79) then
        tmp = t_0
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double t_0 = 0.3333333333333333 * Math.sqrt((1.0 / x));
	double t_1 = 3.0 * (y * Math.sqrt(x));
	double t_2 = Math.sqrt(x) * -3.0;
	double tmp;
	if (y <= -1.9e+81) {
		tmp = t_1;
	} else if (y <= -2.2e+26) {
		tmp = t_0;
	} else if (y <= -1.7e-184) {
		tmp = t_2;
	} else if (y <= 8.2e-202) {
		tmp = t_0;
	} else if (y <= 1.3e-102) {
		tmp = t_2;
	} else if (y <= 9e+79) {
		tmp = t_0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = 0.3333333333333333 * math.sqrt((1.0 / x))
	t_1 = 3.0 * (y * math.sqrt(x))
	t_2 = math.sqrt(x) * -3.0
	tmp = 0
	if y <= -1.9e+81:
		tmp = t_1
	elif y <= -2.2e+26:
		tmp = t_0
	elif y <= -1.7e-184:
		tmp = t_2
	elif y <= 8.2e-202:
		tmp = t_0
	elif y <= 1.3e-102:
		tmp = t_2
	elif y <= 9e+79:
		tmp = t_0
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y)
	t_0 = Float64(0.3333333333333333 * sqrt(Float64(1.0 / x)))
	t_1 = Float64(3.0 * Float64(y * sqrt(x)))
	t_2 = Float64(sqrt(x) * -3.0)
	tmp = 0.0
	if (y <= -1.9e+81)
		tmp = t_1;
	elseif (y <= -2.2e+26)
		tmp = t_0;
	elseif (y <= -1.7e-184)
		tmp = t_2;
	elseif (y <= 8.2e-202)
		tmp = t_0;
	elseif (y <= 1.3e-102)
		tmp = t_2;
	elseif (y <= 9e+79)
		tmp = t_0;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = 0.3333333333333333 * sqrt((1.0 / x));
	t_1 = 3.0 * (y * sqrt(x));
	t_2 = sqrt(x) * -3.0;
	tmp = 0.0;
	if (y <= -1.9e+81)
		tmp = t_1;
	elseif (y <= -2.2e+26)
		tmp = t_0;
	elseif (y <= -1.7e-184)
		tmp = t_2;
	elseif (y <= 8.2e-202)
		tmp = t_0;
	elseif (y <= 1.3e-102)
		tmp = t_2;
	elseif (y <= 9e+79)
		tmp = t_0;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(0.3333333333333333 * N[Sqrt[N[(1.0 / x), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(3.0 * N[(y * N[Sqrt[x], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[Sqrt[x], $MachinePrecision] * -3.0), $MachinePrecision]}, If[LessEqual[y, -1.9e+81], t$95$1, If[LessEqual[y, -2.2e+26], t$95$0, If[LessEqual[y, -1.7e-184], t$95$2, If[LessEqual[y, 8.2e-202], t$95$0, If[LessEqual[y, 1.3e-102], t$95$2, If[LessEqual[y, 9e+79], t$95$0, t$95$1]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -1.9e81 or 8.99999999999999987e79 < y

   1. Initial program 99.6%

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

      1. *-commutative 99.6%

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

      2. associate-*l* 99.6%

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

      3. +-commutative 99.6%

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

      4. associate--l+ 99.6%

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

      5. +-commutative 99.6%

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

      6. distribute-rgt-in 99.6%

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

      7. *-commutative 99.6%

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

      8. fma-def 99.7%

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

      9. sub-neg 99.7%

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

      10. metadata-eval 99.7%

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

      11. associate-*l/ 99.6%

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

      12. metadata-eval 99.6%

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

      13. *-commutative 99.6%

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

      14. associate-/r* 99.7%

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

      15. metadata-eval 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in y around inf 91.9%

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

   if -1.9e81 < y < -2.20000000000000007e26 or -1.70000000000000002e-184 < y < 8.2000000000000008e-202 or 1.29999999999999993e-102 < y < 8.99999999999999987e79

   1. Initial program 99.3%

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

      1. associate--l+ 99.3%

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

      2. sub-neg 99.3%

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

      3. *-commutative 99.3%

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

      4. associate-/r* 99.3%

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

      5. metadata-eval 99.3%

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

      6. metadata-eval 99.3%

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

   3. Simplified 99.3%

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

   4. Taylor expanded in x around 0 65.8%

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

   5. Taylor expanded in y around 0 63.0%

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

   if -2.20000000000000007e26 < y < -1.70000000000000002e-184 or 8.2000000000000008e-202 < y < 1.29999999999999993e-102

   1. Initial program 99.6%

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

      1. *-commutative 99.6%

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

      2. associate-*l* 99.6%

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

      3. +-commutative 99.6%

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

      4. associate--l+ 99.6%

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

      5. +-commutative 99.6%

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

      6. distribute-rgt-in 99.6%

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

      7. *-commutative 99.6%

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

      8. fma-def 99.6%

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

      9. sub-neg 99.6%

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

      10. metadata-eval 99.6%

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

      11. associate-*l/ 99.6%

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

      12. metadata-eval 99.6%

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

      13. *-commutative 99.6%

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

      14. associate-/r* 99.6%

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

      15. metadata-eval 99.6%

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

   3. Simplified 99.6%

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

   4. Taylor expanded in y around 0 92.8%

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

      1. sub-neg 92.8%

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

      2. associate-*r/ 92.8%

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

      3. metadata-eval 92.8%

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

      4. metadata-eval 92.8%

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

   6. Simplified 92.8%

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

   7. Taylor expanded in x around inf 62.3%

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

4. Final simplification 73.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -1.9 \cdot 10^{+81}:\\ \;\;\;\;3 \cdot \left(y \cdot \sqrt{x}\right)\\ \mathbf{elif}\;y \leq -2.2 \cdot 10^{+26}:\\ \;\;\;\;0.3333333333333333 \cdot \sqrt{\frac{1}{x}}\\ \mathbf{elif}\;y \leq -1.7 \cdot 10^{-184}:\\ \;\;\;\;\sqrt{x} \cdot -3\\ \mathbf{elif}\;y \leq 8.2 \cdot 10^{-202}:\\ \;\;\;\;0.3333333333333333 \cdot \sqrt{\frac{1}{x}}\\ \mathbf{elif}\;y \leq 1.3 \cdot 10^{-102}:\\ \;\;\;\;\sqrt{x} \cdot -3\\ \mathbf{elif}\;y \leq 9 \cdot 10^{+79}:\\ \;\;\;\;0.3333333333333333 \cdot \sqrt{\frac{1}{x}}\\ \mathbf{else}:\\ \;\;\;\;3 \cdot \left(y \cdot \sqrt{x}\right)\\ \end{array} \]

Alternative 4: 59.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 0.3333333333333333 \cdot \sqrt{\frac{1}{x}}\\ t_1 := \sqrt{x} \cdot \left(y \cdot 3\right)\\ t_2 := \sqrt{x} \cdot -3\\ \mathbf{if}\;y \leq -3.9 \cdot 10^{+75}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -2.2 \cdot 10^{+26}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq -2.1 \cdot 10^{-184}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 1.32 \cdot 10^{-201}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 9.5 \cdot 10^{-102}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 9 \cdot 10^{+79}:\\ \;\;\;\;t_0\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (* 0.3333333333333333 (sqrt (/ 1.0 x))))
        (t_1 (* (sqrt x) (* y 3.0)))
        (t_2 (* (sqrt x) -3.0)))
   (if (<= y -3.9e+75)
     t_1
     (if (<= y -2.2e+26)
       t_0
       (if (<= y -2.1e-184)
         t_2
         (if (<= y 1.32e-201)
           t_0
           (if (<= y 9.5e-102) t_2 (if (<= y 9e+79) t_0 t_1))))))))

C

double code(double x, double y) {
	double t_0 = 0.3333333333333333 * sqrt((1.0 / x));
	double t_1 = sqrt(x) * (y * 3.0);
	double t_2 = sqrt(x) * -3.0;
	double tmp;
	if (y <= -3.9e+75) {
		tmp = t_1;
	} else if (y <= -2.2e+26) {
		tmp = t_0;
	} else if (y <= -2.1e-184) {
		tmp = t_2;
	} else if (y <= 1.32e-201) {
		tmp = t_0;
	} else if (y <= 9.5e-102) {
		tmp = t_2;
	} else if (y <= 9e+79) {
		tmp = t_0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_0 = 0.3333333333333333d0 * sqrt((1.0d0 / x))
    t_1 = sqrt(x) * (y * 3.0d0)
    t_2 = sqrt(x) * (-3.0d0)
    if (y <= (-3.9d+75)) then
        tmp = t_1
    else if (y <= (-2.2d+26)) then
        tmp = t_0
    else if (y <= (-2.1d-184)) then
        tmp = t_2
    else if (y <= 1.32d-201) then
        tmp = t_0
    else if (y <= 9.5d-102) then
        tmp = t_2
    else if (y <= 9d+79) then
        tmp = t_0
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double t_0 = 0.3333333333333333 * Math.sqrt((1.0 / x));
	double t_1 = Math.sqrt(x) * (y * 3.0);
	double t_2 = Math.sqrt(x) * -3.0;
	double tmp;
	if (y <= -3.9e+75) {
		tmp = t_1;
	} else if (y <= -2.2e+26) {
		tmp = t_0;
	} else if (y <= -2.1e-184) {
		tmp = t_2;
	} else if (y <= 1.32e-201) {
		tmp = t_0;
	} else if (y <= 9.5e-102) {
		tmp = t_2;
	} else if (y <= 9e+79) {
		tmp = t_0;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = 0.3333333333333333 * math.sqrt((1.0 / x))
	t_1 = math.sqrt(x) * (y * 3.0)
	t_2 = math.sqrt(x) * -3.0
	tmp = 0
	if y <= -3.9e+75:
		tmp = t_1
	elif y <= -2.2e+26:
		tmp = t_0
	elif y <= -2.1e-184:
		tmp = t_2
	elif y <= 1.32e-201:
		tmp = t_0
	elif y <= 9.5e-102:
		tmp = t_2
	elif y <= 9e+79:
		tmp = t_0
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y)
	t_0 = Float64(0.3333333333333333 * sqrt(Float64(1.0 / x)))
	t_1 = Float64(sqrt(x) * Float64(y * 3.0))
	t_2 = Float64(sqrt(x) * -3.0)
	tmp = 0.0
	if (y <= -3.9e+75)
		tmp = t_1;
	elseif (y <= -2.2e+26)
		tmp = t_0;
	elseif (y <= -2.1e-184)
		tmp = t_2;
	elseif (y <= 1.32e-201)
		tmp = t_0;
	elseif (y <= 9.5e-102)
		tmp = t_2;
	elseif (y <= 9e+79)
		tmp = t_0;
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = 0.3333333333333333 * sqrt((1.0 / x));
	t_1 = sqrt(x) * (y * 3.0);
	t_2 = sqrt(x) * -3.0;
	tmp = 0.0;
	if (y <= -3.9e+75)
		tmp = t_1;
	elseif (y <= -2.2e+26)
		tmp = t_0;
	elseif (y <= -2.1e-184)
		tmp = t_2;
	elseif (y <= 1.32e-201)
		tmp = t_0;
	elseif (y <= 9.5e-102)
		tmp = t_2;
	elseif (y <= 9e+79)
		tmp = t_0;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(0.3333333333333333 * N[Sqrt[N[(1.0 / x), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(N[Sqrt[x], $MachinePrecision] * N[(y * 3.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[Sqrt[x], $MachinePrecision] * -3.0), $MachinePrecision]}, If[LessEqual[y, -3.9e+75], t$95$1, If[LessEqual[y, -2.2e+26], t$95$0, If[LessEqual[y, -2.1e-184], t$95$2, If[LessEqual[y, 1.32e-201], t$95$0, If[LessEqual[y, 9.5e-102], t$95$2, If[LessEqual[y, 9e+79], t$95$0, t$95$1]]]]]]]]]

Derivation

1. Split input into 3 regimes

2. if y < -3.90000000000000038e75 or 8.99999999999999987e79 < y

   1. Initial program 99.6%

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

      1. *-commutative 99.6%

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

      2. associate-*l* 99.6%

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

      3. +-commutative 99.6%

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

      4. associate--l+ 99.6%

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

      5. +-commutative 99.6%

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

      6. distribute-rgt-in 99.6%

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

      7. *-commutative 99.6%

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

      8. fma-def 99.7%

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

      9. sub-neg 99.7%

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

      10. metadata-eval 99.7%

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

      11. associate-*l/ 99.6%

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

      12. metadata-eval 99.6%

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

      13. *-commutative 99.6%

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

      14. associate-/r* 99.7%

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

      15. metadata-eval 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in y around inf 91.9%

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

      1. associate-*r* 91.9%

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

      2. *-commutative 91.9%

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

      3. associate-*l* 92.0%

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

   6. Simplified 92.0%

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

   if -3.90000000000000038e75 < y < -2.20000000000000007e26 or -2.0999999999999999e-184 < y < 1.31999999999999996e-201 or 9.50000000000000025e-102 < y < 8.99999999999999987e79

   1. Initial program 99.3%

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

      1. associate--l+ 99.3%

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

      2. sub-neg 99.3%

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

      3. *-commutative 99.3%

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

      4. associate-/r* 99.3%

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

      5. metadata-eval 99.3%

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

      6. metadata-eval 99.3%

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

   3. Simplified 99.3%

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

   4. Taylor expanded in x around 0 65.8%

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

   5. Taylor expanded in y around 0 63.0%

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

   if -2.20000000000000007e26 < y < -2.0999999999999999e-184 or 1.31999999999999996e-201 < y < 9.50000000000000025e-102

   1. Initial program 99.6%

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

      1. *-commutative 99.6%

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

      2. associate-*l* 99.6%

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

      3. +-commutative 99.6%

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

      4. associate--l+ 99.6%

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

      5. +-commutative 99.6%

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

      6. distribute-rgt-in 99.6%

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

      7. *-commutative 99.6%

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

      8. fma-def 99.6%

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

      9. sub-neg 99.6%

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

      10. metadata-eval 99.6%

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

      11. associate-*l/ 99.6%

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

      12. metadata-eval 99.6%

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

      13. *-commutative 99.6%

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

      14. associate-/r* 99.6%

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

      15. metadata-eval 99.6%

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

   3. Simplified 99.6%

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

   4. Taylor expanded in y around 0 92.8%

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

      1. sub-neg 92.8%

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

      2. associate-*r/ 92.8%

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

      3. metadata-eval 92.8%

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

      4. metadata-eval 92.8%

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

   6. Simplified 92.8%

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

   7. Taylor expanded in x around inf 62.3%

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

4. Final simplification 73.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -3.9 \cdot 10^{+75}:\\ \;\;\;\;\sqrt{x} \cdot \left(y \cdot 3\right)\\ \mathbf{elif}\;y \leq -2.2 \cdot 10^{+26}:\\ \;\;\;\;0.3333333333333333 \cdot \sqrt{\frac{1}{x}}\\ \mathbf{elif}\;y \leq -2.1 \cdot 10^{-184}:\\ \;\;\;\;\sqrt{x} \cdot -3\\ \mathbf{elif}\;y \leq 1.32 \cdot 10^{-201}:\\ \;\;\;\;0.3333333333333333 \cdot \sqrt{\frac{1}{x}}\\ \mathbf{elif}\;y \leq 9.5 \cdot 10^{-102}:\\ \;\;\;\;\sqrt{x} \cdot -3\\ \mathbf{elif}\;y \leq 9 \cdot 10^{+79}:\\ \;\;\;\;0.3333333333333333 \cdot \sqrt{\frac{1}{x}}\\ \mathbf{else}:\\ \;\;\;\;\sqrt{x} \cdot \left(y \cdot 3\right)\\ \end{array} \]

Alternative 5: 59.9% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := 0.3333333333333333 \cdot \sqrt{\frac{1}{x}}\\ t_1 := \sqrt{x} \cdot \left(y \cdot 3\right)\\ t_2 := \sqrt{x} \cdot -3\\ \mathbf{if}\;y \leq -5.7 \cdot 10^{+72}:\\ \;\;\;\;t_1\\ \mathbf{elif}\;y \leq -2.2 \cdot 10^{+26}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq -4.3 \cdot 10^{-184}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 8.2 \cdot 10^{-201}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq 1.25 \cdot 10^{-101}:\\ \;\;\;\;t_2\\ \mathbf{elif}\;y \leq 9 \cdot 10^{+79}:\\ \;\;\;\;\frac{\sqrt{x} \cdot 0.3333333333333333}{x}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (* 0.3333333333333333 (sqrt (/ 1.0 x))))
        (t_1 (* (sqrt x) (* y 3.0)))
        (t_2 (* (sqrt x) -3.0)))
   (if (<= y -5.7e+72)
     t_1
     (if (<= y -2.2e+26)
       t_0
       (if (<= y -4.3e-184)
         t_2
         (if (<= y 8.2e-201)
           t_0
           (if (<= y 1.25e-101)
             t_2
             (if (<= y 9e+79) (/ (* (sqrt x) 0.3333333333333333) x) t_1))))))))

C

double code(double x, double y) {
	double t_0 = 0.3333333333333333 * sqrt((1.0 / x));
	double t_1 = sqrt(x) * (y * 3.0);
	double t_2 = sqrt(x) * -3.0;
	double tmp;
	if (y <= -5.7e+72) {
		tmp = t_1;
	} else if (y <= -2.2e+26) {
		tmp = t_0;
	} else if (y <= -4.3e-184) {
		tmp = t_2;
	} else if (y <= 8.2e-201) {
		tmp = t_0;
	} else if (y <= 1.25e-101) {
		tmp = t_2;
	} else if (y <= 9e+79) {
		tmp = (sqrt(x) * 0.3333333333333333) / x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: t_0
    real(8) :: t_1
    real(8) :: t_2
    real(8) :: tmp
    t_0 = 0.3333333333333333d0 * sqrt((1.0d0 / x))
    t_1 = sqrt(x) * (y * 3.0d0)
    t_2 = sqrt(x) * (-3.0d0)
    if (y <= (-5.7d+72)) then
        tmp = t_1
    else if (y <= (-2.2d+26)) then
        tmp = t_0
    else if (y <= (-4.3d-184)) then
        tmp = t_2
    else if (y <= 8.2d-201) then
        tmp = t_0
    else if (y <= 1.25d-101) then
        tmp = t_2
    else if (y <= 9d+79) then
        tmp = (sqrt(x) * 0.3333333333333333d0) / x
    else
        tmp = t_1
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double t_0 = 0.3333333333333333 * Math.sqrt((1.0 / x));
	double t_1 = Math.sqrt(x) * (y * 3.0);
	double t_2 = Math.sqrt(x) * -3.0;
	double tmp;
	if (y <= -5.7e+72) {
		tmp = t_1;
	} else if (y <= -2.2e+26) {
		tmp = t_0;
	} else if (y <= -4.3e-184) {
		tmp = t_2;
	} else if (y <= 8.2e-201) {
		tmp = t_0;
	} else if (y <= 1.25e-101) {
		tmp = t_2;
	} else if (y <= 9e+79) {
		tmp = (Math.sqrt(x) * 0.3333333333333333) / x;
	} else {
		tmp = t_1;
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = 0.3333333333333333 * math.sqrt((1.0 / x))
	t_1 = math.sqrt(x) * (y * 3.0)
	t_2 = math.sqrt(x) * -3.0
	tmp = 0
	if y <= -5.7e+72:
		tmp = t_1
	elif y <= -2.2e+26:
		tmp = t_0
	elif y <= -4.3e-184:
		tmp = t_2
	elif y <= 8.2e-201:
		tmp = t_0
	elif y <= 1.25e-101:
		tmp = t_2
	elif y <= 9e+79:
		tmp = (math.sqrt(x) * 0.3333333333333333) / x
	else:
		tmp = t_1
	return tmp

Julia

function code(x, y)
	t_0 = Float64(0.3333333333333333 * sqrt(Float64(1.0 / x)))
	t_1 = Float64(sqrt(x) * Float64(y * 3.0))
	t_2 = Float64(sqrt(x) * -3.0)
	tmp = 0.0
	if (y <= -5.7e+72)
		tmp = t_1;
	elseif (y <= -2.2e+26)
		tmp = t_0;
	elseif (y <= -4.3e-184)
		tmp = t_2;
	elseif (y <= 8.2e-201)
		tmp = t_0;
	elseif (y <= 1.25e-101)
		tmp = t_2;
	elseif (y <= 9e+79)
		tmp = Float64(Float64(sqrt(x) * 0.3333333333333333) / x);
	else
		tmp = t_1;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = 0.3333333333333333 * sqrt((1.0 / x));
	t_1 = sqrt(x) * (y * 3.0);
	t_2 = sqrt(x) * -3.0;
	tmp = 0.0;
	if (y <= -5.7e+72)
		tmp = t_1;
	elseif (y <= -2.2e+26)
		tmp = t_0;
	elseif (y <= -4.3e-184)
		tmp = t_2;
	elseif (y <= 8.2e-201)
		tmp = t_0;
	elseif (y <= 1.25e-101)
		tmp = t_2;
	elseif (y <= 9e+79)
		tmp = (sqrt(x) * 0.3333333333333333) / x;
	else
		tmp = t_1;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(0.3333333333333333 * N[Sqrt[N[(1.0 / x), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]}, Block[{t$95$1 = N[(N[Sqrt[x], $MachinePrecision] * N[(y * 3.0), $MachinePrecision]), $MachinePrecision]}, Block[{t$95$2 = N[(N[Sqrt[x], $MachinePrecision] * -3.0), $MachinePrecision]}, If[LessEqual[y, -5.7e+72], t$95$1, If[LessEqual[y, -2.2e+26], t$95$0, If[LessEqual[y, -4.3e-184], t$95$2, If[LessEqual[y, 8.2e-201], t$95$0, If[LessEqual[y, 1.25e-101], t$95$2, If[LessEqual[y, 9e+79], N[(N[(N[Sqrt[x], $MachinePrecision] * 0.3333333333333333), $MachinePrecision] / x), $MachinePrecision], t$95$1]]]]]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -5.6999999999999997e72 or 8.99999999999999987e79 < y

   1. Initial program 99.6%

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

      1. *-commutative 99.6%

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

      2. associate-*l* 99.6%

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

      3. +-commutative 99.6%

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

      4. associate--l+ 99.6%

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

      5. +-commutative 99.6%

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

      6. distribute-rgt-in 99.6%

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

      7. *-commutative 99.6%

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

      8. fma-def 99.7%

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

      9. sub-neg 99.7%

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

      10. metadata-eval 99.7%

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

      11. associate-*l/ 99.6%

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

      12. metadata-eval 99.6%

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

      13. *-commutative 99.6%

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

      14. associate-/r* 99.7%

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

      15. metadata-eval 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in y around inf 91.9%

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

      1. associate-*r* 91.9%

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

      2. *-commutative 91.9%

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

      3. associate-*l* 92.0%

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

   6. Simplified 92.0%

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

   if -5.6999999999999997e72 < y < -2.20000000000000007e26 or -4.30000000000000007e-184 < y < 8.20000000000000003e-201

   1. Initial program 99.2%

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

      1. associate--l+ 99.2%

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

      2. sub-neg 99.2%

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

      3. *-commutative 99.2%

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

      4. associate-/r* 99.3%

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

      5. metadata-eval 99.3%

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

      6. metadata-eval 99.3%

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

   3. Simplified 99.3%

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

   4. Taylor expanded in x around 0 67.1%

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

   5. Taylor expanded in y around 0 65.4%

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

   if -2.20000000000000007e26 < y < -4.30000000000000007e-184 or 8.20000000000000003e-201 < y < 1.25e-101

   1. Initial program 99.6%

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

      1. *-commutative 99.6%

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

      2. associate-*l* 99.6%

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

      3. +-commutative 99.6%

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

      4. associate--l+ 99.6%

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

      5. +-commutative 99.6%

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

      6. distribute-rgt-in 99.6%

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

      7. *-commutative 99.6%

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

      8. fma-def 99.6%

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

      9. sub-neg 99.6%

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

      10. metadata-eval 99.6%

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

      11. associate-*l/ 99.6%

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

      12. metadata-eval 99.6%

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

      13. *-commutative 99.6%

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

      14. associate-/r* 99.6%

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

      15. metadata-eval 99.6%

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

   3. Simplified 99.6%

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

   4. Taylor expanded in y around 0 92.8%

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

      1. sub-neg 92.8%

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

      2. associate-*r/ 92.8%

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

      3. metadata-eval 92.8%

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

      4. metadata-eval 92.8%

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

   6. Simplified 92.8%

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

   7. Taylor expanded in x around inf 62.3%

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

   if 1.25e-101 < y < 8.99999999999999987e79

   1. Initial program 99.4%

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

      1. *-commutative 99.4%

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

      2. associate-*l* 99.2%

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

      3. +-commutative 99.2%

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

      4. associate--l+ 99.2%

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

      5. +-commutative 99.2%

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

      6. distribute-rgt-in 99.2%

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

      7. *-commutative 99.2%

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

      8. fma-def 99.2%

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

      9. sub-neg 99.2%

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

      10. metadata-eval 99.2%

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

      11. associate-*l/ 99.4%

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

      12. metadata-eval 99.4%

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

      13. *-commutative 99.4%

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

      14. associate-/r* 99.3%

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

      15. metadata-eval 99.3%

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

   3. Simplified 99.3%

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

   4. Taylor expanded in x around 0 58.0%

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

      1. associate-*r/ 58.2%

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

   6. Applied egg-rr 58.2%

      \[\leadsto \color{blue}{\frac{\sqrt{x} \cdot 0.3333333333333333}{x}} \]
3. Recombined 4 regimes into one program.

4. Final simplification 73.3%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.7 \cdot 10^{+72}:\\ \;\;\;\;\sqrt{x} \cdot \left(y \cdot 3\right)\\ \mathbf{elif}\;y \leq -2.2 \cdot 10^{+26}:\\ \;\;\;\;0.3333333333333333 \cdot \sqrt{\frac{1}{x}}\\ \mathbf{elif}\;y \leq -4.3 \cdot 10^{-184}:\\ \;\;\;\;\sqrt{x} \cdot -3\\ \mathbf{elif}\;y \leq 8.2 \cdot 10^{-201}:\\ \;\;\;\;0.3333333333333333 \cdot \sqrt{\frac{1}{x}}\\ \mathbf{elif}\;y \leq 1.25 \cdot 10^{-101}:\\ \;\;\;\;\sqrt{x} \cdot -3\\ \mathbf{elif}\;y \leq 9 \cdot 10^{+79}:\\ \;\;\;\;\frac{\sqrt{x} \cdot 0.3333333333333333}{x}\\ \mathbf{else}:\\ \;\;\;\;\sqrt{x} \cdot \left(y \cdot 3\right)\\ \end{array} \]

Alternative 6: 84.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \sqrt{x} \cdot \left(y \cdot 3\right)\\ \mathbf{if}\;y \leq -5.7 \cdot 10^{+72}:\\ \;\;\;\;t_0\\ \mathbf{elif}\;y \leq -5.9 \cdot 10^{+32}:\\ \;\;\;\;0.3333333333333333 \cdot \sqrt{\frac{1}{x}}\\ \mathbf{elif}\;y \leq -9.5 \cdot 10^{-12}:\\ \;\;\;\;\sqrt{x} \cdot \left(y \cdot 3 + -3\right)\\ \mathbf{elif}\;y \leq 9 \cdot 10^{+79}:\\ \;\;\;\;\sqrt{x} \cdot \left(-3 + \frac{0.3333333333333333}{x}\right)\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (* (sqrt x) (* y 3.0))))
   (if (<= y -5.7e+72)
     t_0
     (if (<= y -5.9e+32)
       (* 0.3333333333333333 (sqrt (/ 1.0 x)))
       (if (<= y -9.5e-12)
         (* (sqrt x) (+ (* y 3.0) -3.0))
         (if (<= y 9e+79)
           (* (sqrt x) (+ -3.0 (/ 0.3333333333333333 x)))
           t_0))))))

C

double code(double x, double y) {
	double t_0 = sqrt(x) * (y * 3.0);
	double tmp;
	if (y <= -5.7e+72) {
		tmp = t_0;
	} else if (y <= -5.9e+32) {
		tmp = 0.3333333333333333 * sqrt((1.0 / x));
	} else if (y <= -9.5e-12) {
		tmp = sqrt(x) * ((y * 3.0) + -3.0);
	} else if (y <= 9e+79) {
		tmp = sqrt(x) * (-3.0 + (0.3333333333333333 / x));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: t_0
    real(8) :: tmp
    t_0 = sqrt(x) * (y * 3.0d0)
    if (y <= (-5.7d+72)) then
        tmp = t_0
    else if (y <= (-5.9d+32)) then
        tmp = 0.3333333333333333d0 * sqrt((1.0d0 / x))
    else if (y <= (-9.5d-12)) then
        tmp = sqrt(x) * ((y * 3.0d0) + (-3.0d0))
    else if (y <= 9d+79) then
        tmp = sqrt(x) * ((-3.0d0) + (0.3333333333333333d0 / x))
    else
        tmp = t_0
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double t_0 = Math.sqrt(x) * (y * 3.0);
	double tmp;
	if (y <= -5.7e+72) {
		tmp = t_0;
	} else if (y <= -5.9e+32) {
		tmp = 0.3333333333333333 * Math.sqrt((1.0 / x));
	} else if (y <= -9.5e-12) {
		tmp = Math.sqrt(x) * ((y * 3.0) + -3.0);
	} else if (y <= 9e+79) {
		tmp = Math.sqrt(x) * (-3.0 + (0.3333333333333333 / x));
	} else {
		tmp = t_0;
	}
	return tmp;
}

Python

def code(x, y):
	t_0 = math.sqrt(x) * (y * 3.0)
	tmp = 0
	if y <= -5.7e+72:
		tmp = t_0
	elif y <= -5.9e+32:
		tmp = 0.3333333333333333 * math.sqrt((1.0 / x))
	elif y <= -9.5e-12:
		tmp = math.sqrt(x) * ((y * 3.0) + -3.0)
	elif y <= 9e+79:
		tmp = math.sqrt(x) * (-3.0 + (0.3333333333333333 / x))
	else:
		tmp = t_0
	return tmp

Julia

function code(x, y)
	t_0 = Float64(sqrt(x) * Float64(y * 3.0))
	tmp = 0.0
	if (y <= -5.7e+72)
		tmp = t_0;
	elseif (y <= -5.9e+32)
		tmp = Float64(0.3333333333333333 * sqrt(Float64(1.0 / x)));
	elseif (y <= -9.5e-12)
		tmp = Float64(sqrt(x) * Float64(Float64(y * 3.0) + -3.0));
	elseif (y <= 9e+79)
		tmp = Float64(sqrt(x) * Float64(-3.0 + Float64(0.3333333333333333 / x)));
	else
		tmp = t_0;
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	t_0 = sqrt(x) * (y * 3.0);
	tmp = 0.0;
	if (y <= -5.7e+72)
		tmp = t_0;
	elseif (y <= -5.9e+32)
		tmp = 0.3333333333333333 * sqrt((1.0 / x));
	elseif (y <= -9.5e-12)
		tmp = sqrt(x) * ((y * 3.0) + -3.0);
	elseif (y <= 9e+79)
		tmp = sqrt(x) * (-3.0 + (0.3333333333333333 / x));
	else
		tmp = t_0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := Block[{t$95$0 = N[(N[Sqrt[x], $MachinePrecision] * N[(y * 3.0), $MachinePrecision]), $MachinePrecision]}, If[LessEqual[y, -5.7e+72], t$95$0, If[LessEqual[y, -5.9e+32], N[(0.3333333333333333 * N[Sqrt[N[(1.0 / x), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -9.5e-12], N[(N[Sqrt[x], $MachinePrecision] * N[(N[(y * 3.0), $MachinePrecision] + -3.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 9e+79], N[(N[Sqrt[x], $MachinePrecision] * N[(-3.0 + N[(0.3333333333333333 / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], t$95$0]]]]]

Derivation

1. Split input into 4 regimes

2. if y < -5.6999999999999997e72 or 8.99999999999999987e79 < y

   1. Initial program 99.6%

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

      1. *-commutative 99.6%

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

      2. associate-*l* 99.6%

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

      3. +-commutative 99.6%

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

      4. associate--l+ 99.6%

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

      5. +-commutative 99.6%

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

      6. distribute-rgt-in 99.6%

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

      7. *-commutative 99.6%

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

      8. fma-def 99.7%

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

      9. sub-neg 99.7%

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

      10. metadata-eval 99.7%

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

      11. associate-*l/ 99.6%

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

      12. metadata-eval 99.6%

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

      13. *-commutative 99.6%

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

      14. associate-/r* 99.7%

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

      15. metadata-eval 99.7%

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

   3. Simplified 99.7%

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

   4. Taylor expanded in y around inf 91.9%

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

      1. associate-*r* 91.9%

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

      2. *-commutative 91.9%

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

      3. associate-*l* 92.0%

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

   6. Simplified 92.0%

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

   if -5.6999999999999997e72 < y < -5.89999999999999965e32

   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. associate--l+ 99.1%

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

      2. sub-neg 99.1%

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

      3. *-commutative 99.1%

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

      4. associate-/r* 99.2%

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

      5. metadata-eval 99.2%

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

      6. metadata-eval 99.2%

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

   3. Simplified 99.2%

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

   4. Taylor expanded in x around 0 99.2%

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

   5. Taylor expanded in y around 0 90.1%

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

   if -5.89999999999999965e32 < y < -9.4999999999999995e-12

   1. Initial program 99.3%

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

      1. *-commutative 99.3%

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

      2. associate-*l* 99.8%

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

      3. +-commutative 99.8%

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

      4. associate--l+ 99.8%

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

      5. +-commutative 99.8%

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

      6. distribute-rgt-in 99.8%

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

      7. *-commutative 99.8%

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

      8. fma-def 99.8%

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

      9. sub-neg 99.8%

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

      10. metadata-eval 99.8%

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

      11. associate-*l/ 99.8%

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

      12. metadata-eval 99.8%

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

      13. *-commutative 99.8%

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

      14. associate-/r* 99.8%

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

      15. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in x around inf 99.8%

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

      1. sub-neg 99.8%

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

      2. metadata-eval 99.8%

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

      3. distribute-lft-in 99.6%

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

      4. metadata-eval 99.6%

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

   6. Simplified 99.6%

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

   if -9.4999999999999995e-12 < y < 8.99999999999999987e79

   1. Initial program 99.4%

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

      1. *-commutative 99.4%

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

      2. associate-*l* 99.4%

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

      3. +-commutative 99.4%

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

      4. associate--l+ 99.4%

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

      5. +-commutative 99.4%

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

      6. distribute-rgt-in 99.4%

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

      7. *-commutative 99.4%

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

      8. fma-def 99.4%

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

      9. sub-neg 99.4%

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

      10. metadata-eval 99.4%

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

      11. associate-*l/ 99.5%

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

      12. metadata-eval 99.5%

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

      13. *-commutative 99.5%

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

      14. associate-/r* 99.4%

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

      15. metadata-eval 99.4%

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

   3. Simplified 99.4%

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

   4. Taylor expanded in y around 0 97.1%

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

      1. sub-neg 97.1%

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

      2. associate-*r/ 97.1%

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

      3. metadata-eval 97.1%

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

      4. metadata-eval 97.1%

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

   6. Simplified 97.1%

      \[\leadsto \color{blue}{\sqrt{x} \cdot \left(\frac{0.3333333333333333}{x} + -3\right)} \]
3. Recombined 4 regimes into one program.

4. Final simplification 95.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.7 \cdot 10^{+72}:\\ \;\;\;\;\sqrt{x} \cdot \left(y \cdot 3\right)\\ \mathbf{elif}\;y \leq -5.9 \cdot 10^{+32}:\\ \;\;\;\;0.3333333333333333 \cdot \sqrt{\frac{1}{x}}\\ \mathbf{elif}\;y \leq -9.5 \cdot 10^{-12}:\\ \;\;\;\;\sqrt{x} \cdot \left(y \cdot 3 + -3\right)\\ \mathbf{elif}\;y \leq 9 \cdot 10^{+79}:\\ \;\;\;\;\sqrt{x} \cdot \left(-3 + \frac{0.3333333333333333}{x}\right)\\ \mathbf{else}:\\ \;\;\;\;\sqrt{x} \cdot \left(y \cdot 3\right)\\ \end{array} \]

Alternative 7: 84.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;y \leq -5.7 \cdot 10^{+72}:\\ \;\;\;\;\sqrt{x} \cdot \left(y \cdot 3\right)\\ \mathbf{elif}\;y \leq -3.5 \cdot 10^{+28}:\\ \;\;\;\;0.3333333333333333 \cdot \sqrt{\frac{1}{x}}\\ \mathbf{elif}\;y \leq -1.02 \cdot 10^{-11}:\\ \;\;\;\;\sqrt{x} \cdot \left(y \cdot 3 + -3\right)\\ \mathbf{elif}\;y \leq 9 \cdot 10^{+79}:\\ \;\;\;\;\sqrt{x} \cdot \left(-3 + \frac{0.3333333333333333}{x}\right)\\ \mathbf{else}:\\ \;\;\;\;\sqrt{x \cdot 9} \cdot \left(y + -1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= y -5.7e+72)
   (* (sqrt x) (* y 3.0))
   (if (<= y -3.5e+28)
     (* 0.3333333333333333 (sqrt (/ 1.0 x)))
     (if (<= y -1.02e-11)
       (* (sqrt x) (+ (* y 3.0) -3.0))
       (if (<= y 9e+79)
         (* (sqrt x) (+ -3.0 (/ 0.3333333333333333 x)))
         (* (sqrt (* x 9.0)) (+ y -1.0)))))))

C

double code(double x, double y) {
	double tmp;
	if (y <= -5.7e+72) {
		tmp = sqrt(x) * (y * 3.0);
	} else if (y <= -3.5e+28) {
		tmp = 0.3333333333333333 * sqrt((1.0 / x));
	} else if (y <= -1.02e-11) {
		tmp = sqrt(x) * ((y * 3.0) + -3.0);
	} else if (y <= 9e+79) {
		tmp = sqrt(x) * (-3.0 + (0.3333333333333333 / x));
	} else {
		tmp = sqrt((x * 9.0)) * (y + -1.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (y <= (-5.7d+72)) then
        tmp = sqrt(x) * (y * 3.0d0)
    else if (y <= (-3.5d+28)) then
        tmp = 0.3333333333333333d0 * sqrt((1.0d0 / x))
    else if (y <= (-1.02d-11)) then
        tmp = sqrt(x) * ((y * 3.0d0) + (-3.0d0))
    else if (y <= 9d+79) then
        tmp = sqrt(x) * ((-3.0d0) + (0.3333333333333333d0 / x))
    else
        tmp = sqrt((x * 9.0d0)) * (y + (-1.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (y <= -5.7e+72) {
		tmp = Math.sqrt(x) * (y * 3.0);
	} else if (y <= -3.5e+28) {
		tmp = 0.3333333333333333 * Math.sqrt((1.0 / x));
	} else if (y <= -1.02e-11) {
		tmp = Math.sqrt(x) * ((y * 3.0) + -3.0);
	} else if (y <= 9e+79) {
		tmp = Math.sqrt(x) * (-3.0 + (0.3333333333333333 / x));
	} else {
		tmp = Math.sqrt((x * 9.0)) * (y + -1.0);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if y <= -5.7e+72:
		tmp = math.sqrt(x) * (y * 3.0)
	elif y <= -3.5e+28:
		tmp = 0.3333333333333333 * math.sqrt((1.0 / x))
	elif y <= -1.02e-11:
		tmp = math.sqrt(x) * ((y * 3.0) + -3.0)
	elif y <= 9e+79:
		tmp = math.sqrt(x) * (-3.0 + (0.3333333333333333 / x))
	else:
		tmp = math.sqrt((x * 9.0)) * (y + -1.0)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (y <= -5.7e+72)
		tmp = Float64(sqrt(x) * Float64(y * 3.0));
	elseif (y <= -3.5e+28)
		tmp = Float64(0.3333333333333333 * sqrt(Float64(1.0 / x)));
	elseif (y <= -1.02e-11)
		tmp = Float64(sqrt(x) * Float64(Float64(y * 3.0) + -3.0));
	elseif (y <= 9e+79)
		tmp = Float64(sqrt(x) * Float64(-3.0 + Float64(0.3333333333333333 / x)));
	else
		tmp = Float64(sqrt(Float64(x * 9.0)) * Float64(y + -1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (y <= -5.7e+72)
		tmp = sqrt(x) * (y * 3.0);
	elseif (y <= -3.5e+28)
		tmp = 0.3333333333333333 * sqrt((1.0 / x));
	elseif (y <= -1.02e-11)
		tmp = sqrt(x) * ((y * 3.0) + -3.0);
	elseif (y <= 9e+79)
		tmp = sqrt(x) * (-3.0 + (0.3333333333333333 / x));
	else
		tmp = sqrt((x * 9.0)) * (y + -1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[y, -5.7e+72], N[(N[Sqrt[x], $MachinePrecision] * N[(y * 3.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -3.5e+28], N[(0.3333333333333333 * N[Sqrt[N[(1.0 / x), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], If[LessEqual[y, -1.02e-11], N[(N[Sqrt[x], $MachinePrecision] * N[(N[(y * 3.0), $MachinePrecision] + -3.0), $MachinePrecision]), $MachinePrecision], If[LessEqual[y, 9e+79], N[(N[Sqrt[x], $MachinePrecision] * N[(-3.0 + N[(0.3333333333333333 / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[Sqrt[N[(x * 9.0), $MachinePrecision]], $MachinePrecision] * N[(y + -1.0), $MachinePrecision]), $MachinePrecision]]]]]

Derivation

1. Split input into 5 regimes

2. if y < -5.6999999999999997e72

   1. Initial program 99.6%

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

      1. *-commutative 99.6%

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

      2. associate-*l* 99.6%

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

      3. +-commutative 99.6%

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

      4. associate--l+ 99.6%

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

      5. +-commutative 99.6%

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

      6. distribute-rgt-in 99.6%

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

      7. *-commutative 99.6%

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

      8. fma-def 99.6%

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

      9. sub-neg 99.6%

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

      10. metadata-eval 99.6%

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

      11. associate-*l/ 99.6%

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

      12. metadata-eval 99.6%

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

      13. *-commutative 99.6%

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

      14. associate-/r* 99.6%

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

      15. metadata-eval 99.6%

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

   3. Simplified 99.6%

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

   4. Taylor expanded in y around inf 95.6%

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

      1. associate-*r* 95.7%

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

      2. *-commutative 95.7%

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

      3. associate-*l* 95.8%

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

   6. Simplified 95.8%

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

   if -5.6999999999999997e72 < y < -3.5e28

   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. associate--l+ 99.1%

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

      2. sub-neg 99.1%

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

      3. *-commutative 99.1%

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

      4. associate-/r* 99.2%

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

      5. metadata-eval 99.2%

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

      6. metadata-eval 99.2%

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

   3. Simplified 99.2%

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

   4. Taylor expanded in x around 0 99.2%

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

   5. Taylor expanded in y around 0 90.1%

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

   if -3.5e28 < y < -1.01999999999999994e-11

   1. Initial program 99.3%

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

      1. *-commutative 99.3%

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

      2. associate-*l* 99.8%

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

      3. +-commutative 99.8%

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

      4. associate--l+ 99.8%

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

      5. +-commutative 99.8%

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

      6. distribute-rgt-in 99.8%

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

      7. *-commutative 99.8%

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

      8. fma-def 99.8%

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

      9. sub-neg 99.8%

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

      10. metadata-eval 99.8%

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

      11. associate-*l/ 99.8%

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

      12. metadata-eval 99.8%

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

      13. *-commutative 99.8%

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

      14. associate-/r* 99.8%

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

      15. metadata-eval 99.8%

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

   3. Simplified 99.8%

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

   4. Taylor expanded in x around inf 99.8%

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

      1. sub-neg 99.8%

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

      2. metadata-eval 99.8%

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

      3. distribute-lft-in 99.6%

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

      4. metadata-eval 99.6%

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

   6. Simplified 99.6%

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

   if -1.01999999999999994e-11 < y < 8.99999999999999987e79

   1. Initial program 99.4%

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

      1. *-commutative 99.4%

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

      2. associate-*l* 99.4%

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

      3. +-commutative 99.4%

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

      4. associate--l+ 99.4%

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

      5. +-commutative 99.4%

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

      6. distribute-rgt-in 99.4%

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

      7. *-commutative 99.4%

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

      8. fma-def 99.4%

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

      9. sub-neg 99.4%

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

      10. metadata-eval 99.4%

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

      11. associate-*l/ 99.5%

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

      12. metadata-eval 99.5%

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

      13. *-commutative 99.5%

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

      14. associate-/r* 99.4%

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

      15. metadata-eval 99.4%

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

   3. Simplified 99.4%

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

   4. Taylor expanded in y around 0 97.1%

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

      1. sub-neg 97.1%

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

      2. associate-*r/ 97.1%

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

      3. metadata-eval 97.1%

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

      4. metadata-eval 97.1%

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

   6. Simplified 97.1%

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

   if 8.99999999999999987e79 < y

   1. Initial program 99.5%

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

      1. associate--l+ 99.5%

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

      2. sub-neg 99.5%

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

      3. *-commutative 99.5%

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

      4. associate-/r* 99.5%

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

      5. metadata-eval 99.5%

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

      6. metadata-eval 99.5%

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

   3. Simplified 99.5%

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

      1. *-commutative 99.5%

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

      2. metadata-eval 99.5%

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

      3. sqrt-prod 99.7%

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

      4. pow1/2 99.7%

         \[\leadsto \color{blue}{{\left(x \cdot 9\right)}^{0.5}} \cdot \left(y + \left(\frac{0.1111111111111111}{x} + -1\right)\right) \]

   5. Applied egg-rr 99.7%

      \[\leadsto \color{blue}{{\left(x \cdot 9\right)}^{0.5}} \cdot \left(y + \left(\frac{0.1111111111111111}{x} + -1\right)\right) \]
   6. Step-by-step derivation

      1. unpow1/2 99.7%

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

   7. Simplified 99.7%

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

   8. Taylor expanded in x around inf 87.5%

      \[\leadsto \sqrt{x \cdot 9} \cdot \left(y + \color{blue}{-1}\right) \]
3. Recombined 5 regimes into one program.

4. Final simplification 95.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \leq -5.7 \cdot 10^{+72}:\\ \;\;\;\;\sqrt{x} \cdot \left(y \cdot 3\right)\\ \mathbf{elif}\;y \leq -3.5 \cdot 10^{+28}:\\ \;\;\;\;0.3333333333333333 \cdot \sqrt{\frac{1}{x}}\\ \mathbf{elif}\;y \leq -1.02 \cdot 10^{-11}:\\ \;\;\;\;\sqrt{x} \cdot \left(y \cdot 3 + -3\right)\\ \mathbf{elif}\;y \leq 9 \cdot 10^{+79}:\\ \;\;\;\;\sqrt{x} \cdot \left(-3 + \frac{0.3333333333333333}{x}\right)\\ \mathbf{else}:\\ \;\;\;\;\sqrt{x \cdot 9} \cdot \left(y + -1\right)\\ \end{array} \]

Alternative 8: 98.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 0.1:\\ \;\;\;\;3 \cdot \left(\sqrt{x} \cdot \left(y + \frac{0.1111111111111111}{x}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;{\left(x \cdot 9\right)}^{0.5} \cdot \left(y + -1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x 0.1)
   (* 3.0 (* (sqrt x) (+ y (/ 0.1111111111111111 x))))
   (* (pow (* x 9.0) 0.5) (+ y -1.0))))

C

double code(double x, double y) {
	double tmp;
	if (x <= 0.1) {
		tmp = 3.0 * (sqrt(x) * (y + (0.1111111111111111 / x)));
	} else {
		tmp = pow((x * 9.0), 0.5) * (y + -1.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (x <= 0.1d0) then
        tmp = 3.0d0 * (sqrt(x) * (y + (0.1111111111111111d0 / x)))
    else
        tmp = ((x * 9.0d0) ** 0.5d0) * (y + (-1.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= 0.1) {
		tmp = 3.0 * (Math.sqrt(x) * (y + (0.1111111111111111 / x)));
	} else {
		tmp = Math.pow((x * 9.0), 0.5) * (y + -1.0);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= 0.1:
		tmp = 3.0 * (math.sqrt(x) * (y + (0.1111111111111111 / x)))
	else:
		tmp = math.pow((x * 9.0), 0.5) * (y + -1.0)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= 0.1)
		tmp = Float64(3.0 * Float64(sqrt(x) * Float64(y + Float64(0.1111111111111111 / x))));
	else
		tmp = Float64((Float64(x * 9.0) ^ 0.5) * Float64(y + -1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= 0.1)
		tmp = 3.0 * (sqrt(x) * (y + (0.1111111111111111 / x)));
	else
		tmp = ((x * 9.0) ^ 0.5) * (y + -1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, 0.1], N[(3.0 * N[(N[Sqrt[x], $MachinePrecision] * N[(y + N[(0.1111111111111111 / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[Power[N[(x * 9.0), $MachinePrecision], 0.5], $MachinePrecision] * N[(y + -1.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < 0.10000000000000001

   1. Initial program 99.3%

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

      1. associate-*l* 99.3%

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

      2. associate--l+ 99.3%

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

      3. sub-neg 99.3%

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

      4. *-commutative 99.3%

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

      5. associate-/r* 99.3%

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

      6. metadata-eval 99.3%

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

      7. metadata-eval 99.3%

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

   3. Simplified 99.3%

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

   4. Taylor expanded in x around 0 97.4%

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

   if 0.10000000000000001 < 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. associate--l+ 99.6%

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

      2. sub-neg 99.6%

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

      3. *-commutative 99.6%

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

      4. associate-/r* 99.6%

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

      5. metadata-eval 99.6%

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

      6. metadata-eval 99.6%

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

   3. Simplified 99.6%

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

      1. *-commutative 99.6%

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

      2. metadata-eval 99.6%

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

      3. sqrt-prod 99.8%

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

      4. pow1/2 99.8%

         \[\leadsto \color{blue}{{\left(x \cdot 9\right)}^{0.5}} \cdot \left(y + \left(\frac{0.1111111111111111}{x} + -1\right)\right) \]

   5. Applied egg-rr 99.8%

      \[\leadsto \color{blue}{{\left(x \cdot 9\right)}^{0.5}} \cdot \left(y + \left(\frac{0.1111111111111111}{x} + -1\right)\right) \]

   6. Taylor expanded in x around inf 99.2%

      \[\leadsto {\left(x \cdot 9\right)}^{0.5} \cdot \left(y + \color{blue}{-1}\right) \]
3. Recombined 2 regimes into one program.

4. Final simplification 98.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 0.1:\\ \;\;\;\;3 \cdot \left(\sqrt{x} \cdot \left(y + \frac{0.1111111111111111}{x}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;{\left(x \cdot 9\right)}^{0.5} \cdot \left(y + -1\right)\\ \end{array} \]

Alternative 9: 98.4% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 0.1:\\ \;\;\;\;\sqrt{x \cdot 9} \cdot \left(y + \frac{0.1111111111111111}{x}\right)\\ \mathbf{else}:\\ \;\;\;\;{\left(x \cdot 9\right)}^{0.5} \cdot \left(y + -1\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x 0.1)
   (* (sqrt (* x 9.0)) (+ y (/ 0.1111111111111111 x)))
   (* (pow (* x 9.0) 0.5) (+ y -1.0))))

C

double code(double x, double y) {
	double tmp;
	if (x <= 0.1) {
		tmp = sqrt((x * 9.0)) * (y + (0.1111111111111111 / x));
	} else {
		tmp = pow((x * 9.0), 0.5) * (y + -1.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (x <= 0.1d0) then
        tmp = sqrt((x * 9.0d0)) * (y + (0.1111111111111111d0 / x))
    else
        tmp = ((x * 9.0d0) ** 0.5d0) * (y + (-1.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= 0.1) {
		tmp = Math.sqrt((x * 9.0)) * (y + (0.1111111111111111 / x));
	} else {
		tmp = Math.pow((x * 9.0), 0.5) * (y + -1.0);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= 0.1:
		tmp = math.sqrt((x * 9.0)) * (y + (0.1111111111111111 / x))
	else:
		tmp = math.pow((x * 9.0), 0.5) * (y + -1.0)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= 0.1)
		tmp = Float64(sqrt(Float64(x * 9.0)) * Float64(y + Float64(0.1111111111111111 / x)));
	else
		tmp = Float64((Float64(x * 9.0) ^ 0.5) * Float64(y + -1.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= 0.1)
		tmp = sqrt((x * 9.0)) * (y + (0.1111111111111111 / x));
	else
		tmp = ((x * 9.0) ^ 0.5) * (y + -1.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, 0.1], N[(N[Sqrt[N[(x * 9.0), $MachinePrecision]], $MachinePrecision] * N[(y + N[(0.1111111111111111 / x), $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[Power[N[(x * 9.0), $MachinePrecision], 0.5], $MachinePrecision] * N[(y + -1.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < 0.10000000000000001

   1. Initial program 99.3%

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

      1. associate--l+ 99.3%

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

      2. sub-neg 99.3%

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

      3. *-commutative 99.3%

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

      4. associate-/r* 99.3%

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

      5. metadata-eval 99.3%

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

      6. metadata-eval 99.3%

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

   3. Simplified 99.3%

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

   4. Taylor expanded in x around 0 97.3%

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

      1. *-commutative 99.3%

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

      2. metadata-eval 99.3%

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

      3. sqrt-prod 99.4%

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

      4. pow1/2 99.4%

         \[\leadsto \color{blue}{{\left(x \cdot 9\right)}^{0.5}} \cdot \left(y + \left(\frac{0.1111111111111111}{x} + -1\right)\right) \]

   6. Applied egg-rr 97.4%

      \[\leadsto \color{blue}{{\left(x \cdot 9\right)}^{0.5}} \cdot \left(y + \frac{0.1111111111111111}{x}\right) \]
   7. Step-by-step derivation

      1. unpow1/2 99.4%

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

   8. Simplified 97.4%

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

   if 0.10000000000000001 < 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. associate--l+ 99.6%

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

      2. sub-neg 99.6%

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

      3. *-commutative 99.6%

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

      4. associate-/r* 99.6%

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

      5. metadata-eval 99.6%

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

      6. metadata-eval 99.6%

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

   3. Simplified 99.6%

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

      1. *-commutative 99.6%

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

      2. metadata-eval 99.6%

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

      3. sqrt-prod 99.8%

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

      4. pow1/2 99.8%

         \[\leadsto \color{blue}{{\left(x \cdot 9\right)}^{0.5}} \cdot \left(y + \left(\frac{0.1111111111111111}{x} + -1\right)\right) \]

   5. Applied egg-rr 99.8%

      \[\leadsto \color{blue}{{\left(x \cdot 9\right)}^{0.5}} \cdot \left(y + \left(\frac{0.1111111111111111}{x} + -1\right)\right) \]

   6. Taylor expanded in x around inf 99.2%

      \[\leadsto {\left(x \cdot 9\right)}^{0.5} \cdot \left(y + \color{blue}{-1}\right) \]
3. Recombined 2 regimes into one program.

4. Final simplification 98.4%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 0.1:\\ \;\;\;\;\sqrt{x \cdot 9} \cdot \left(y + \frac{0.1111111111111111}{x}\right)\\ \mathbf{else}:\\ \;\;\;\;{\left(x \cdot 9\right)}^{0.5} \cdot \left(y + -1\right)\\ \end{array} \]

Alternative 10: 99.4% accurate, 1.0× speedup

Math

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

FPCore

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

C

double code(double x, double y) {
	return 3.0 * ((y + ((0.1111111111111111 / x) + -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 + ((0.1111111111111111d0 / x) + (-1.0d0))) * sqrt(x))
end function

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.5%

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

   1. associate-*l* 99.5%

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

   2. associate--l+ 99.5%

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

   3. sub-neg 99.5%

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

   4. *-commutative 99.5%

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

   5. associate-/r* 99.5%

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

   6. metadata-eval 99.5%

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

   7. metadata-eval 99.5%

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

3. Simplified 99.5%

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

4. Final simplification 99.5%

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

Alternative 11: 99.4% accurate, 1.0× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.5%

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

   1. associate--l+ 99.5%

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

   2. sub-neg 99.5%

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

   3. *-commutative 99.5%

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

   4. associate-/r* 99.5%

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

   5. metadata-eval 99.5%

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

   6. metadata-eval 99.5%

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

3. Simplified 99.5%

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

   1. *-commutative 99.5%

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

   2. metadata-eval 99.5%

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

   3. sqrt-prod 99.6%

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

   4. pow1/2 99.6%

      \[\leadsto \color{blue}{{\left(x \cdot 9\right)}^{0.5}} \cdot \left(y + \left(\frac{0.1111111111111111}{x} + -1\right)\right) \]

5. Applied egg-rr 99.6%

   \[\leadsto \color{blue}{{\left(x \cdot 9\right)}^{0.5}} \cdot \left(y + \left(\frac{0.1111111111111111}{x} + -1\right)\right) \]
6. Step-by-step derivation

   1. unpow1/2 99.6%

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

7. Simplified 99.6%

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

8. Final simplification 99.6%

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

Alternative 12: 86.1% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 4 \cdot 10^{-27}:\\ \;\;\;\;\sqrt{\frac{0.1111111111111111}{x} \cdot \frac{x}{x}}\\ \mathbf{else}:\\ \;\;\;\;\sqrt{x} \cdot \left(y \cdot 3 + -3\right)\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x 4e-27)
   (sqrt (* (/ 0.1111111111111111 x) (/ x x)))
   (* (sqrt x) (+ (* y 3.0) -3.0))))

C

double code(double x, double y) {
	double tmp;
	if (x <= 4e-27) {
		tmp = sqrt(((0.1111111111111111 / x) * (x / x)));
	} else {
		tmp = sqrt(x) * ((y * 3.0) + -3.0);
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (x <= 4d-27) then
        tmp = sqrt(((0.1111111111111111d0 / x) * (x / x)))
    else
        tmp = sqrt(x) * ((y * 3.0d0) + (-3.0d0))
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= 4e-27) {
		tmp = Math.sqrt(((0.1111111111111111 / x) * (x / x)));
	} else {
		tmp = Math.sqrt(x) * ((y * 3.0) + -3.0);
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= 4e-27:
		tmp = math.sqrt(((0.1111111111111111 / x) * (x / x)))
	else:
		tmp = math.sqrt(x) * ((y * 3.0) + -3.0)
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= 4e-27)
		tmp = sqrt(Float64(Float64(0.1111111111111111 / x) * Float64(x / x)));
	else
		tmp = Float64(sqrt(x) * Float64(Float64(y * 3.0) + -3.0));
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= 4e-27)
		tmp = sqrt(((0.1111111111111111 / x) * (x / x)));
	else
		tmp = sqrt(x) * ((y * 3.0) + -3.0);
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, 4e-27], N[Sqrt[N[(N[(0.1111111111111111 / x), $MachinePrecision] * N[(x / x), $MachinePrecision]), $MachinePrecision]], $MachinePrecision], N[(N[Sqrt[x], $MachinePrecision] * N[(N[(y * 3.0), $MachinePrecision] + -3.0), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < 4.0000000000000002e-27

   1. Initial program 99.3%

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

      1. *-commutative 99.3%

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

      2. associate-*l* 99.3%

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

      3. +-commutative 99.3%

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

      4. associate--l+ 99.3%

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

      5. +-commutative 99.3%

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

      6. distribute-rgt-in 99.3%

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

      7. *-commutative 99.3%

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

      8. fma-def 99.3%

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

      9. sub-neg 99.3%

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

      10. metadata-eval 99.3%

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

      11. associate-*l/ 99.4%

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

      12. metadata-eval 99.4%

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

      13. *-commutative 99.4%

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

      14. associate-/r* 99.3%

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

      15. metadata-eval 99.3%

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

   3. Simplified 99.3%

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

   4. Taylor expanded in x around 0 77.4%

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

      1. add-sqr-sqrt 77.2%

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

      2. sqrt-unprod 77.4%

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

      3. swap-sqr 41.0%

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

      4. add-sqr-sqrt 41.2%

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

      5. frac-times 41.2%

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

      6. metadata-eval 41.2%

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

   6. Applied egg-rr 41.2%

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

      1. associate-*r/ 42.5%

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

      2. times-frac 77.9%

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

   8. Simplified 77.9%

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

   if 4.0000000000000002e-27 < x

   1. Initial program 99.6%

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

      1. *-commutative 99.6%

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

      2. associate-*l* 99.6%

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

      3. +-commutative 99.6%

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

      4. associate--l+ 99.6%

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

      5. +-commutative 99.6%

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

      6. distribute-rgt-in 99.6%

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

      7. *-commutative 99.6%

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

      8. fma-def 99.6%

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

      9. sub-neg 99.6%

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

      10. metadata-eval 99.6%

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

      11. associate-*l/ 99.6%

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

      12. metadata-eval 99.6%

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

      13. *-commutative 99.6%

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

      14. associate-/r* 99.6%

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

      15. metadata-eval 99.6%

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

   3. Simplified 99.6%

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

   4. Taylor expanded in x around inf 94.6%

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

      1. sub-neg 94.6%

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

      2. metadata-eval 94.6%

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

      3. distribute-lft-in 94.6%

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

      4. metadata-eval 94.6%

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

   6. Simplified 94.6%

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

4. Final simplification 88.0%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 4 \cdot 10^{-27}:\\ \;\;\;\;\sqrt{\frac{0.1111111111111111}{x} \cdot \frac{x}{x}}\\ \mathbf{else}:\\ \;\;\;\;\sqrt{x} \cdot \left(y \cdot 3 + -3\right)\\ \end{array} \]

Alternative 13: 61.3% accurate, 1.1× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} \mathbf{if}\;x \leq 2.6:\\ \;\;\;\;0.3333333333333333 \cdot \sqrt{\frac{1}{x}}\\ \mathbf{else}:\\ \;\;\;\;\sqrt{x} \cdot -3\\ \end{array} \end{array} \]

FPCore

(FPCore (x y)
 :precision binary64
 (if (<= x 2.6) (* 0.3333333333333333 (sqrt (/ 1.0 x))) (* (sqrt x) -3.0)))

C

double code(double x, double y) {
	double tmp;
	if (x <= 2.6) {
		tmp = 0.3333333333333333 * sqrt((1.0 / x));
	} else {
		tmp = sqrt(x) * -3.0;
	}
	return tmp;
}

Fortran

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    real(8) :: tmp
    if (x <= 2.6d0) then
        tmp = 0.3333333333333333d0 * sqrt((1.0d0 / x))
    else
        tmp = sqrt(x) * (-3.0d0)
    end if
    code = tmp
end function

Java

public static double code(double x, double y) {
	double tmp;
	if (x <= 2.6) {
		tmp = 0.3333333333333333 * Math.sqrt((1.0 / x));
	} else {
		tmp = Math.sqrt(x) * -3.0;
	}
	return tmp;
}

Python

def code(x, y):
	tmp = 0
	if x <= 2.6:
		tmp = 0.3333333333333333 * math.sqrt((1.0 / x))
	else:
		tmp = math.sqrt(x) * -3.0
	return tmp

Julia

function code(x, y)
	tmp = 0.0
	if (x <= 2.6)
		tmp = Float64(0.3333333333333333 * sqrt(Float64(1.0 / x)));
	else
		tmp = Float64(sqrt(x) * -3.0);
	end
	return tmp
end

MATLAB

function tmp_2 = code(x, y)
	tmp = 0.0;
	if (x <= 2.6)
		tmp = 0.3333333333333333 * sqrt((1.0 / x));
	else
		tmp = sqrt(x) * -3.0;
	end
	tmp_2 = tmp;
end

Wolfram

code[x_, y_] := If[LessEqual[x, 2.6], N[(0.3333333333333333 * N[Sqrt[N[(1.0 / x), $MachinePrecision]], $MachinePrecision]), $MachinePrecision], N[(N[Sqrt[x], $MachinePrecision] * -3.0), $MachinePrecision]]

Derivation

1. Split input into 2 regimes

2. if x < 2.60000000000000009

   1. Initial program 99.3%

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

      1. associate--l+ 99.3%

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

      2. sub-neg 99.3%

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

      3. *-commutative 99.3%

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

      4. associate-/r* 99.3%

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

      5. metadata-eval 99.3%

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

      6. metadata-eval 99.3%

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

   3. Simplified 99.3%

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

   4. Taylor expanded in x around 0 97.4%

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

   5. Taylor expanded in y around 0 71.8%

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

   if 2.60000000000000009 < x

   1. Initial program 99.6%

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

      1. *-commutative 99.6%

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

      2. associate-*l* 99.6%

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

      3. +-commutative 99.6%

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

      4. associate--l+ 99.6%

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

      5. +-commutative 99.6%

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

      6. distribute-rgt-in 99.6%

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

      7. *-commutative 99.6%

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

      8. fma-def 99.6%

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

      9. sub-neg 99.6%

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

      10. metadata-eval 99.6%

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

      11. associate-*l/ 99.6%

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

      12. metadata-eval 99.6%

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

      13. *-commutative 99.6%

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

      14. associate-/r* 99.6%

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

      15. metadata-eval 99.6%

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

   3. Simplified 99.6%

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

   4. Taylor expanded in y around 0 54.5%

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

      1. sub-neg 54.5%

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

      2. associate-*r/ 54.5%

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

      3. metadata-eval 54.5%

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

      4. metadata-eval 54.5%

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

   6. Simplified 54.5%

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

   7. Taylor expanded in x around inf 53.9%

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

4. Final simplification 62.1%

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq 2.6:\\ \;\;\;\;0.3333333333333333 \cdot \sqrt{\frac{1}{x}}\\ \mathbf{else}:\\ \;\;\;\;\sqrt{x} \cdot -3\\ \end{array} \]

Alternative 14: 3.3% accurate, 1.1× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Derivation

1. Initial program 99.5%

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

   1. *-commutative 99.5%

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

   2. associate-*l* 99.5%

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

   3. +-commutative 99.5%

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

   4. associate--l+ 99.5%

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

   5. +-commutative 99.5%

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

   6. distribute-rgt-in 99.5%

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

   7. *-commutative 99.5%

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

   8. fma-def 99.5%

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

   9. sub-neg 99.5%

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

   10. metadata-eval 99.5%

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

   11. associate-*l/ 99.5%

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

   12. metadata-eval 99.5%

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

   13. *-commutative 99.5%

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

   14. associate-/r* 99.5%

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

   15. metadata-eval 99.5%

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

3. Simplified 99.5%

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

4. Taylor expanded in y around 0 63.2%

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

   1. sub-neg 63.2%

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

   2. associate-*r/ 63.2%

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

   3. metadata-eval 63.2%

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

   4. metadata-eval 63.2%

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

6. Simplified 63.2%

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

7. Taylor expanded in x around inf 30.1%

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

   1. add-sqr-sqrt 0.0%

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

   2. sqrt-unprod 3.4%

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

   3. swap-sqr 3.4%

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

   4. add-sqr-sqrt 3.4%

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

   5. metadata-eval 3.4%

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

9. Applied egg-rr 3.4%

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

10. Final simplification 3.4%

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

Alternative 15: 24.9% 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 99.5%

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

   1. *-commutative 99.5%

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

   2. associate-*l* 99.5%

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

   3. +-commutative 99.5%

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

   4. associate--l+ 99.5%

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

   5. +-commutative 99.5%

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

   6. distribute-rgt-in 99.5%

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

   7. *-commutative 99.5%

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

   8. fma-def 99.5%

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

   9. sub-neg 99.5%

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

   10. metadata-eval 99.5%

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

   11. associate-*l/ 99.5%

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

   12. metadata-eval 99.5%

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

   13. *-commutative 99.5%

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

   14. associate-/r* 99.5%

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

   15. metadata-eval 99.5%

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

3. Simplified 99.5%

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

4. Taylor expanded in y around 0 63.2%

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

   1. sub-neg 63.2%

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

   2. associate-*r/ 63.2%

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

   3. metadata-eval 63.2%

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

   4. metadata-eval 63.2%

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

6. Simplified 63.2%

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

7. Taylor expanded in x around inf 30.1%

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

8. Final simplification 30.1%

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

Developer target: 99.4% accurate, 0.5× speedup

Math

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

FPCore

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

C

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

Fortran

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

Java

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

Python

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

Julia

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

MATLAB

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

Wolfram

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

Reproduce

herbie shell --seed 2023290 
(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)))