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 r6280273 = 1.0;
        double r6280274 = /* ERROR: no posit support in C */;
        double r6280275 = x;
        double r6280276 = sqrt(r6280275);
        double r6280277 = r6280274 / r6280276;
        double r6280278 = r6280275 + r6280274;
        double r6280279 = sqrt(r6280278);
        double r6280280 = r6280274 / r6280279;
        double r6280281 = r6280277 - r6280280;
        return r6280281;
}
↓
double f(double x) {
        double r6280282 = 1.0;
        double r6280283 = x;
        double r6280284 = sqrt(r6280283);
        double r6280285 = r6280282 / r6280284;
        double r6280286 = r6280283 + r6280282;
        double r6280287 = sqrt(r6280286);
        double r6280288 = r6280282 / r6280287;
        double r6280289 = r6280285 - r6280288;
        return r6280289;
}

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 2019165 
(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))))))