Average Error: 30.9 → 1.4
Time: 1.4s
Precision: binary64
\[\sqrt{2 \cdot \left(x \cdot x\right)} \]
↓
\[{\left({2}^{0.3333333333333333}\right)}^{1.5} \cdot {\left({\left(\sqrt[3]{x}\right)}^{2}\right)}^{1.5} \]
(FPCore (x) :precision binary64 (sqrt (* 2.0 (* x x))))
↓
(FPCore (x)
 :precision binary64
 (* (pow (pow 2.0 0.3333333333333333) 1.5) (pow (pow (cbrt x) 2.0) 1.5)))
double code(double x) {
	return sqrt((2.0 * (x * x)));
}
↓
double code(double x) {
	return pow(pow(2.0, 0.3333333333333333), 1.5) * pow(pow(cbrt(x), 2.0), 1.5);
}

public static double code(double x) {
	return Math.sqrt((2.0 * (x * x)));
}
↓
public static double code(double x) {
	return Math.pow(Math.pow(2.0, 0.3333333333333333), 1.5) * Math.pow(Math.pow(Math.cbrt(x), 2.0), 1.5);
}

function code(x)
	return sqrt(Float64(2.0 * Float64(x * x)))
end
↓
function code(x)
	return Float64(((2.0 ^ 0.3333333333333333) ^ 1.5) * ((cbrt(x) ^ 2.0) ^ 1.5))
end

code[x_] := N[Sqrt[N[(2.0 * N[(x * x), $MachinePrecision]), $MachinePrecision]], $MachinePrecision]
↓
code[x_] := N[(N[Power[N[Power[2.0, 0.3333333333333333], $MachinePrecision], 1.5], $MachinePrecision] * N[Power[N[Power[N[Power[x, 1/3], $MachinePrecision], 2.0], $MachinePrecision], 1.5], $MachinePrecision]), $MachinePrecision]

\sqrt{2 \cdot \left(x \cdot x\right)}
↓
{\left({2}^{0.3333333333333333}\right)}^{1.5} \cdot {\left({\left(\sqrt[3]{x}\right)}^{2}\right)}^{1.5}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 30.9

    \[\sqrt{2 \cdot \left(x \cdot x\right)} \]

  2. Applied egg-rr31.3

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

  3. Applied egg-rr1.4

    \[\leadsto \color{blue}{{\left(\sqrt[3]{2}\right)}^{1.5} \cdot {\left({\left(\sqrt[3]{x}\right)}^{2}\right)}^{1.5}} \]

  4. Applied egg-rr1.4

    \[\leadsto {\color{blue}{\left({2}^{0.3333333333333333}\right)}}^{1.5} \cdot {\left({\left(\sqrt[3]{x}\right)}^{2}\right)}^{1.5} \]

  5. Final simplification1.4

    \[\leadsto {\left({2}^{0.3333333333333333}\right)}^{1.5} \cdot {\left({\left(\sqrt[3]{x}\right)}^{2}\right)}^{1.5} \]

Reproduce

herbie shell --seed 2022166 
(FPCore (x)
  :name "sqrt C"
  :precision binary64
  (sqrt (* 2.0 (* x x))))