Average Error: 12.3 → 0
Time: 4.9s
Precision: 64
\[\frac{1}{\frac{{x}^{2} \cdot 1}{\sqrt{x}}}\]
\[{x}^{\left(\frac{1}{2} - 2\right)}\]
\frac{1}{\frac{{x}^{2} \cdot 1}{\sqrt{x}}}
{x}^{\left(\frac{1}{2} - 2\right)}
double f(double x) {
        double r419040 = 1.0;
        double r419041 = x;
        double r419042 = 2.0;
        double r419043 = pow(r419041, r419042);
        double r419044 = r419043 * r419040;
        double r419045 = sqrt(r419041);
        double r419046 = r419044 / r419045;
        double r419047 = r419040 / r419046;
        return r419047;
}

double f(double x) {
        double r419048 = x;
        double r419049 = 0.5;
        double r419050 = 2.0;
        double r419051 = r419049 - r419050;
        double r419052 = pow(r419048, r419051);
        return r419052;
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 12.3

    \[\frac{1}{\frac{{x}^{2} \cdot 1}{\sqrt{x}}}\]
  2. Simplified12.3

    \[\leadsto \color{blue}{\frac{\sqrt{x}}{{x}^{2}}}\]
  3. Using strategy rm
  4. Applied pow1/212.3

    \[\leadsto \frac{\color{blue}{{x}^{\frac{1}{2}}}}{{x}^{2}}\]
  5. Applied pow-div0

    \[\leadsto \color{blue}{{x}^{\left(\frac{1}{2} - 2\right)}}\]
  6. Final simplification0

    \[\leadsto {x}^{\left(\frac{1}{2} - 2\right)}\]

Reproduce

herbie shell --seed 1 
(FPCore (x)
  :name "1/(x^2 * 1/sqrt(x))"
  :precision binary64
  (/ 1 (/ (* (pow x 2) 1) (sqrt x))))