Average Error: 0.1 → 0
Time: 3.3s
Precision: 64
\[\sqrt{\sqrt{x}}\]
\[{x}^{\frac{1}{4}}\]
\sqrt{\sqrt{x}}
{x}^{\frac{1}{4}}
double f(double x) {
        double r1860402 = x;
        double r1860403 = sqrt(r1860402);
        double r1860404 = sqrt(r1860403);
        return r1860404;
}

double f(double x) {
        double r1860405 = x;
        double r1860406 = 0.25;
        double r1860407 = pow(r1860405, r1860406);
        return r1860407;
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.1

    \[\sqrt{\sqrt{x}}\]
  2. Using strategy rm
  3. Applied pow1/20.1

    \[\leadsto \sqrt{\color{blue}{{x}^{\frac{1}{2}}}}\]
  4. Applied sqrt-pow10

    \[\leadsto \color{blue}{{x}^{\left(\frac{\frac{1}{2}}{2}\right)}}\]
  5. Simplified0

    \[\leadsto {x}^{\color{blue}{\frac{1}{4}}}\]
  6. Final simplification0

    \[\leadsto {x}^{\frac{1}{4}}\]

Reproduce

herbie shell --seed 1 
(FPCore (x)
  :name "sqrt(sqrt(x))"
  :precision binary64
  (sqrt (sqrt x)))