Average Error: 0.6 → 0.6
Time: 24.6s
Precision: 64
\[\left(\frac{\left(1\right)}{\left(\frac{x}{\left(1\right)}\right)}\right) - \left(\frac{\left(1\right)}{x}\right)\]
↓
\[\left(\frac{\left(1\right)}{\left(\frac{x}{\left(1\right)}\right)}\right) - \left(\frac{\left(1\right)}{x}\right)\]
\left(\frac{\left(1\right)}{\left(\frac{x}{\left(1\right)}\right)}\right) - \left(\frac{\left(1\right)}{x}\right)
↓
\left(\frac{\left(1\right)}{\left(\frac{x}{\left(1\right)}\right)}\right) - \left(\frac{\left(1\right)}{x}\right)
double f(double x) {
        double r6893162 = 1.0;
        double r6893163 = /* ERROR: no posit support in C */;
        double r6893164 = x;
        double r6893165 = r6893164 + r6893163;
        double r6893166 = r6893163 / r6893165;
        double r6893167 = r6893163 / r6893164;
        double r6893168 = r6893166 - r6893167;
        return r6893168;
}
↓
double f(double x) {
        double r6893169 = 1.0;
        double r6893170 = /* ERROR: no posit support in C */;
        double r6893171 = x;
        double r6893172 = r6893171 + r6893170;
        double r6893173 = r6893170 / r6893172;
        double r6893174 = r6893170 / r6893171;
        double r6893175 = r6893173 - r6893174;
        return r6893175;
}

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

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

Reproduce

herbie shell --seed 2019168 +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)))