Average Error: 0.6 → 0.6
Time: 22.2s
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 r6635365 = 1.0;
        double r6635366 = /* ERROR: no posit support in C */;
        double r6635367 = x;
        double r6635368 = sqrt(r6635367);
        double r6635369 = r6635366 / r6635368;
        double r6635370 = r6635367 + r6635366;
        double r6635371 = sqrt(r6635370);
        double r6635372 = r6635366 / r6635371;
        double r6635373 = r6635369 - r6635372;
        return r6635373;
}
↓
double f(double x) {
        double r6635374 = 1.0;
        double r6635375 = x;
        double r6635376 = sqrt(r6635375);
        double r6635377 = r6635374 / r6635376;
        double r6635378 = r6635375 + r6635374;
        double r6635379 = sqrt(r6635378);
        double r6635380 = r6635374 / r6635379;
        double r6635381 = r6635377 - r6635380;
        return r6635381;
}

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 2019158 
(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))))))