Average Error: 0.6 → 0.6
Time: 23.0s
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 r8009348 = 1.0;
        double r8009349 = /* ERROR: no posit support in C */;
        double r8009350 = x;
        double r8009351 = r8009350 + r8009349;
        double r8009352 = r8009349 / r8009351;
        double r8009353 = r8009349 / r8009350;
        double r8009354 = r8009352 - r8009353;
        return r8009354;
}
↓
double f(double x) {
        double r8009355 = 1.0;
        double r8009356 = x;
        double r8009357 = r8009356 + r8009355;
        double r8009358 = r8009355 / r8009357;
        double r8009359 = r8009355 / r8009356;
        double r8009360 = r8009358 - r8009359;
        return r8009360;
}

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 2019158 +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)))