Average Error: 0.6 → 0.6
Time: 20.2s
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 r3820096 = 1.0;
        double r3820097 = /* ERROR: no posit support in C */;
        double r3820098 = x;
        double r3820099 = sqrt(r3820098);
        double r3820100 = r3820097 / r3820099;
        double r3820101 = r3820098 + r3820097;
        double r3820102 = sqrt(r3820101);
        double r3820103 = r3820097 / r3820102;
        double r3820104 = r3820100 - r3820103;
        return r3820104;
}
↓
double f(double x) {
        double r3820105 = 1.0;
        double r3820106 = x;
        double r3820107 = sqrt(r3820106);
        double r3820108 = r3820105 / r3820107;
        double r3820109 = r3820106 + r3820105;
        double r3820110 = sqrt(r3820109);
        double r3820111 = r3820105 / r3820110;
        double r3820112 = r3820108 - r3820111;
        return r3820112;
}

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 2019121 +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))))))