Average Error: 0.6 → 0.6
Time: 14.0s
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 r1095540 = 1.0;
        double r1095541 = /* ERROR: no posit support in C */;
        double r1095542 = x;
        double r1095543 = r1095542 + r1095541;
        double r1095544 = r1095541 / r1095543;
        double r1095545 = r1095541 / r1095542;
        double r1095546 = r1095544 - r1095545;
        return r1095546;
}
↓
double f(double x) {
        double r1095547 = 1.0;
        double r1095548 = x;
        double r1095549 = r1095548 + r1095547;
        double r1095550 = r1095547 / r1095549;
        double r1095551 = r1095547 / r1095548;
        double r1095552 = r1095550 - r1095551;
        return r1095552;
}

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 2019156 +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)))