Average Error: 0.6 → 0.6
Time: 55.8s
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 r8710298 = 1.0;
        double r8710299 = /* ERROR: no posit support in C */;
        double r8710300 = x;
        double r8710301 = sqrt(r8710300);
        double r8710302 = r8710299 / r8710301;
        double r8710303 = r8710300 + r8710299;
        double r8710304 = sqrt(r8710303);
        double r8710305 = r8710299 / r8710304;
        double r8710306 = r8710302 - r8710305;
        return r8710306;
}
↓
double f(double x) {
        double r8710307 = 1.0;
        double r8710308 = x;
        double r8710309 = sqrt(r8710308);
        double r8710310 = r8710307 / r8710309;
        double r8710311 = r8710308 + r8710307;
        double r8710312 = sqrt(r8710311);
        double r8710313 = r8710307 / r8710312;
        double r8710314 = r8710310 - r8710313;
        return r8710314;
}

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 2019134 +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))))))