Average Error: 0.5 → 0.4
Time: 8.4s
Precision: 64
\[\sqrt{x - 1} \cdot \sqrt{x}\]
↓
\[\left(x - \frac{0.125}{x}\right) - 0.5\]
\sqrt{x - 1} \cdot \sqrt{x}
↓
\left(x - \frac{0.125}{x}\right) - 0.5
double f(double x) {
        double r12056 = x;
        double r12057 = 1.0;
        double r12058 = r12056 - r12057;
        double r12059 = sqrt(r12058);
        double r12060 = sqrt(r12056);
        double r12061 = r12059 * r12060;
        return r12061;
}
↓
double f(double x) {
        double r12062 = x;
        double r12063 = 0.125;
        double r12064 = r12063 / r12062;
        double r12065 = r12062 - r12064;
        double r12066 = 0.5;
        double r12067 = r12065 - r12066;
        return r12067;
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.5

    \[\sqrt{x - 1} \cdot \sqrt{x}\]

  2. Taylor expanded around inf 0.4

    \[\leadsto \color{blue}{x - \left(0.125 \cdot \frac{1}{x} + 0.5\right)}\]

  3. Simplified0.4

    \[\leadsto \color{blue}{\left(x - \frac{0.125}{x}\right) - 0.5}\]

  4. Final simplification0.4

    \[\leadsto \left(x - \frac{0.125}{x}\right) - 0.5\]

Reproduce

herbie shell --seed 2019174 +o rules:numerics
(FPCore (x)
  :name "sqrt times"
  (* (sqrt (- x 1.0)) (sqrt x)))