Average Error: 0.2 → 0
Time: 9.4s
Precision: 64
\[\sqrt{x} \cdot x\]
\[{x}^{\frac{3}{2}}\]
\sqrt{x} \cdot x
{x}^{\frac{3}{2}}
double f(double x) {
        double r3477942 = x;
        double r3477943 = sqrt(r3477942);
        double r3477944 = r3477943 * r3477942;
        return r3477944;
}

double f(double x) {
        double r3477945 = x;
        double r3477946 = 1.5;
        double r3477947 = pow(r3477945, r3477946);
        return r3477947;
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.2

    \[\sqrt{x} \cdot x\]
  2. Using strategy rm
  3. Applied pow10.2

    \[\leadsto \sqrt{x} \cdot \color{blue}{{x}^{1}}\]
  4. Applied pow1/20.2

    \[\leadsto \color{blue}{{x}^{\frac{1}{2}}} \cdot {x}^{1}\]
  5. Applied pow-prod-up0

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

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

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

Reproduce

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