Average Error: 12.3 → 0
Time: 16.2s
Precision: 64
\[\frac{1}{\frac{\left(x \cdot x\right) \cdot 1}{\sqrt{x}}}\]
\[{x}^{\frac{-3}{2}}\]
\frac{1}{\frac{\left(x \cdot x\right) \cdot 1}{\sqrt{x}}}
{x}^{\frac{-3}{2}}
double f(double x) {
        double r421319 = 1.0;
        double r421320 = x;
        double r421321 = r421320 * r421320;
        double r421322 = r421321 * r421319;
        double r421323 = sqrt(r421320);
        double r421324 = r421322 / r421323;
        double r421325 = r421319 / r421324;
        return r421325;
}

double f(double x) {
        double r421326 = x;
        double r421327 = -1.5;
        double r421328 = pow(r421326, r421327);
        return r421328;
}

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

    \[\frac{1}{\frac{\left(x \cdot x\right) \cdot 1}{\sqrt{x}}}\]
  2. Simplified0.3

    \[\leadsto \color{blue}{\frac{\frac{\sqrt{x}}{x}}{x}}\]
  3. Using strategy rm
  4. Applied pow10.3

    \[\leadsto \frac{\frac{\sqrt{x}}{x}}{\color{blue}{{x}^{1}}}\]
  5. Applied pow10.3

    \[\leadsto \frac{\frac{\sqrt{x}}{\color{blue}{{x}^{1}}}}{{x}^{1}}\]
  6. Applied pow1/20.3

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

    \[\leadsto \frac{\color{blue}{{x}^{\left(\frac{1}{2} - 1\right)}}}{{x}^{1}}\]
  8. Applied pow-div0

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

    \[\leadsto {x}^{\color{blue}{\frac{-3}{2}}}\]
  10. Final simplification0

    \[\leadsto {x}^{\frac{-3}{2}}\]

Reproduce

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