Average Error: 0.6 → 0.6
Time: 18.7s
Precision: 64
\[\left(\frac{\left(1\right)}{\left(\sqrt{x}\right)}\right) - \left(\frac{\left(1\right)}{\left(\sqrt{\left(\frac{x}{\left(1\right)}\right)}\right)}\right)\]
↓
\[\frac{1}{\sqrt{x}} - \frac{1}{\sqrt{x + 1}}\]
\left(\frac{\left(1\right)}{\left(\sqrt{x}\right)}\right) - \left(\frac{\left(1\right)}{\left(\sqrt{\left(\frac{x}{\left(1\right)}\right)}\right)}\right)
↓
\frac{1}{\sqrt{x}} - \frac{1}{\sqrt{x + 1}}
double f(double x) {
        double r7000420 = 1.0;
        double r7000421 = /* ERROR: no posit support in C */;
        double r7000422 = x;
        double r7000423 = sqrt(r7000422);
        double r7000424 = r7000421 / r7000423;
        double r7000425 = r7000422 + r7000421;
        double r7000426 = sqrt(r7000425);
        double r7000427 = r7000421 / r7000426;
        double r7000428 = r7000424 - r7000427;
        return r7000428;
}
↓
double f(double x) {
        double r7000429 = 1.0;
        double r7000430 = x;
        double r7000431 = sqrt(r7000430);
        double r7000432 = r7000429 / r7000431;
        double r7000433 = r7000430 + r7000429;
        double r7000434 = sqrt(r7000433);
        double r7000435 = r7000429 / r7000434;
        double r7000436 = r7000432 - r7000435;
        return r7000436;
}

Error

Bits error versus x

Derivation

  1. Initial program 0.6

    \[\left(\frac{\left(1\right)}{\left(\sqrt{x}\right)}\right) - \left(\frac{\left(1\right)}{\left(\sqrt{\left(\frac{x}{\left(1\right)}\right)}\right)}\right)\]

  2. Final simplification0.6

    \[\leadsto \frac{1}{\sqrt{x}} - \frac{1}{\sqrt{x + 1}}\]

Reproduce

herbie shell --seed 2019125 +o rules:numerics
(FPCore (x)
  :name "2isqrt (example 3.6)"
  (-.p16 (/.p16 (real->posit16 1) (sqrt.p16 x)) (/.p16 (real->posit16 1) (sqrt.p16 (+.p16 x (real->posit16 1))))))