Average Error: 0.6 → 0.6
Time: 24.3s
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 r5401019 = 1.0;
        double r5401020 = /* ERROR: no posit support in C */;
        double r5401021 = x;
        double r5401022 = r5401021 + r5401020;
        double r5401023 = r5401020 / r5401022;
        double r5401024 = r5401020 / r5401021;
        double r5401025 = r5401023 - r5401024;
        return r5401025;
}
↓
double f(double x) {
        double r5401026 = 1.0;
        double r5401027 = /* ERROR: no posit support in C */;
        double r5401028 = x;
        double r5401029 = r5401028 + r5401027;
        double r5401030 = r5401027 / r5401029;
        double r5401031 = r5401027 / r5401028;
        double r5401032 = r5401030 - r5401031;
        return r5401032;
}

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