Average Error: 0.6 → 0.6
Time: 44.0s
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 r10470963 = 1.0;
        double r10470964 = /* ERROR: no posit support in C */;
        double r10470965 = x;
        double r10470966 = r10470965 + r10470964;
        double r10470967 = r10470964 / r10470966;
        double r10470968 = r10470964 / r10470965;
        double r10470969 = r10470967 - r10470968;
        return r10470969;
}
↓
double f(double x) {
        double r10470970 = 1.0;
        double r10470971 = x;
        double r10470972 = r10470971 + r10470970;
        double r10470973 = r10470970 / r10470972;
        double r10470974 = r10470970 / r10470971;
        double r10470975 = r10470973 - r10470974;
        return r10470975;
}

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 2019133 
(FPCore (x)
  :name "2frac (problem 3.3.1)"
  (-.p16 (/.p16 (real->posit16 1) (+.p16 x (real->posit16 1))) (/.p16 (real->posit16 1) x)))