Average Error: 30.5 → 15.4
Time: 2.7s
Precision: binary64
\[\sqrt{\left(2 \cdot x\right) \cdot x}\]
↓
\[\begin{array}{l} \mathbf{if}\;x \leq -2.1487218123004 \cdot 10^{-310}:\\ \;\;\;\;\sqrt{x \cdot \left(x \cdot 2\right)}\\ \mathbf{else}:\\ \;\;\;\;\sqrt{x \cdot 2} \cdot \sqrt{x}\\ \end{array}\]
\sqrt{\left(2 \cdot x\right) \cdot x}
↓
\begin{array}{l}
\mathbf{if}\;x \leq -2.1487218123004 \cdot 10^{-310}:\\
\;\;\;\;\sqrt{x \cdot \left(x \cdot 2\right)}\\

\mathbf{else}:\\
\;\;\;\;\sqrt{x \cdot 2} \cdot \sqrt{x}\\

\end{array}
(FPCore (x) :precision binary64 (sqrt (* (* 2.0 x) x)))
↓
(FPCore (x)
 :precision binary64
 (if (<= x -2.1487218123004e-310)
   (sqrt (* x (* x 2.0)))
   (* (sqrt (* x 2.0)) (sqrt x))))
double code(double x) {
	return sqrt((2.0 * x) * x);
}
↓
double code(double x) {
	double tmp;
	if (x <= -2.1487218123004e-310) {
		tmp = sqrt(x * (x * 2.0));
	} else {
		tmp = sqrt(x * 2.0) * sqrt(x);
	}
	return tmp;
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Split input into 2 regimes

  2. if x < -2.148721812300404e-310

    1. Initial program 30.4

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

    if -2.148721812300404e-310 < x

    1. Initial program 30.6

      \[\sqrt{\left(2 \cdot x\right) \cdot x}\]
    2. Using strategy rm

    3. Applied sqrt-prod_binary640.4

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

  4. Final simplification15.4

    \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -2.1487218123004 \cdot 10^{-310}:\\ \;\;\;\;\sqrt{x \cdot \left(x \cdot 2\right)}\\ \mathbf{else}:\\ \;\;\;\;\sqrt{x \cdot 2} \cdot \sqrt{x}\\ \end{array}\]

Reproduce

herbie shell --seed 2020288 
(FPCore (x)
  :name "sqrt B"
  :precision binary64
  (sqrt (* (* 2.0 x) x)))