Average Error: 0.6 → 0.6
Time: 21.5s
Precision: 64
\[\left(\frac{\left(1\right)}{\left(\frac{x}{\left(1\right)}\right)}\right) - \left(\frac{\left(1\right)}{x}\right)\]
↓
\[\frac{1}{x + 1} - \frac{1}{x}\]
\left(\frac{\left(1\right)}{\left(\frac{x}{\left(1\right)}\right)}\right) - \left(\frac{\left(1\right)}{x}\right)
↓
\frac{1}{x + 1} - \frac{1}{x}
double f(double x) {
        double r5919277 = 1.0;
        double r5919278 = /* ERROR: no posit support in C */;
        double r5919279 = x;
        double r5919280 = r5919279 + r5919278;
        double r5919281 = r5919278 / r5919280;
        double r5919282 = r5919278 / r5919279;
        double r5919283 = r5919281 - r5919282;
        return r5919283;
}
↓
double f(double x) {
        double r5919284 = 1.0;
        double r5919285 = x;
        double r5919286 = r5919285 + r5919284;
        double r5919287 = r5919284 / r5919286;
        double r5919288 = r5919284 / r5919285;
        double r5919289 = r5919287 - r5919288;
        return r5919289;
}

Error

Bits error versus x

Derivation

  1. Initial program 0.6

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

  2. Final simplification0.6

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

Reproduce

herbie shell --seed 2019163 +o rules:numerics
(FPCore (x)
  :name "2frac (problem 3.3.1)"
  (-.p16 (/.p16 (real->posit16 1) (+.p16 x (real->posit16 1))) (/.p16 (real->posit16 1) x)))