Average Error: 14.3 → 1.2
Time: 35.0s
Precision: 64
Internal Precision: 896
\[\frac{1}{x + 1} - \frac{1}{x}\]
↓
\[\left(\sqrt[3]{\frac{-1}{(x \cdot x + x)_*}} \cdot \sqrt[3]{\frac{-1}{(x \cdot x + x)_*}}\right) \cdot \sqrt[3]{\frac{-1}{(x \cdot x + x)_*}}\]

Error

Bits error versus x

Derivation

  1. Initial program 14.3

    \[\frac{1}{x + 1} - \frac{1}{x}\]
  2. Using strategy rm

  3. Applied frac-sub13.7

    \[\leadsto \color{blue}{\frac{1 \cdot x - \left(x + 1\right) \cdot 1}{\left(x + 1\right) \cdot x}}\]

  4. Applied simplify0.3

    \[\leadsto \frac{\color{blue}{-1}}{\left(x + 1\right) \cdot x}\]

  5. Applied simplify0.3

    \[\leadsto \frac{-1}{\color{blue}{(x \cdot x + x)_*}}\]
  6. Using strategy rm

  7. Applied add-cube-cbrt1.2

    \[\leadsto \color{blue}{\left(\sqrt[3]{\frac{-1}{(x \cdot x + x)_*}} \cdot \sqrt[3]{\frac{-1}{(x \cdot x + x)_*}}\right) \cdot \sqrt[3]{\frac{-1}{(x \cdot x + x)_*}}}\]

Runtime

Time bar (total: 35.0s)Debug logProfile

herbie shell --seed '#(1070864556 424010669 783715395 1203517814 4070606583 4107618214)' +o rules:numerics
(FPCore (x)
  :name "2frac (problem 3.3.1)"
  (- (/ 1 (+ x 1)) (/ 1 x)))