Average Error: 15.0 → 0.1
Time: 2.4m
Precision: 64
Internal Precision: 832
\[\frac{1}{x + 1} - \frac{1}{x}\]
↓
\[\frac{\sqrt[3]{-1} \cdot \sqrt[3]{-1}}{x + 1} \cdot \frac{\sqrt[3]{-1}}{x}\]

Error

Bits error versus x

Derivation

  1. Initial program 15.0

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

  3. Applied frac-sub14.4

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

  4. Applied simplify0.3

    \[\leadsto \frac{\color{blue}{-1}}{\left(x + 1\right) \cdot x}\]
  5. Using strategy rm

  6. Applied add-cube-cbrt0.3

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

  7. Applied times-frac0.1

    \[\leadsto \color{blue}{\frac{\sqrt[3]{-1} \cdot \sqrt[3]{-1}}{x + 1} \cdot \frac{\sqrt[3]{-1}}{x}}\]

Runtime

Time bar (total: 2.4m)Debug logProfile

herbie shell --seed '#(1072330854 3074818769 591214268 3603999196 3863745332 3332387116)' 
(FPCore (x)
  :name "2frac (problem 3.3.1)"
  (- (/ 1 (+ x 1)) (/ 1 x)))