Average Error: 29.5 → 29.4
Time: 12.9s
Precision: 64
Internal precision: 1408
\[{\left(x + 1\right)}^{\left(\frac{1}{3}\right)} - {x}^{\left(\frac{1}{3}\right)}\]
⬇
\[e^{\log \left(\sqrt[3]{x + 1}\right)} - {x}^{\left(\frac{1}{3}\right)}\]

Error

Bits error versus x

Derivation

  1. Initial program 29.5

    \[{\left(x + 1\right)}^{\left(\frac{1}{3}\right)} - {x}^{\left(\frac{1}{3}\right)}\]
  2. Using strategy rm

  3. Applied add-exp-log 29.8

    \[\leadsto {\color{blue}{\left(e^{\log \left(x + 1\right)}\right)}}^{\left(\frac{1}{3}\right)} - {x}^{\left(\frac{1}{3}\right)}\]

  4. Applied pow-exp 29.8

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

  5. Applied simplify 29.5

    \[\leadsto e^{\color{blue}{\frac{\log \left(1 + x\right)}{3}}} - {x}^{\left(\frac{1}{3}\right)}\]
  6. Using strategy rm

  7. Applied add-log-exp 29.5

    \[\leadsto e^{\color{blue}{\log \left(e^{\frac{\log \left(1 + x\right)}{3}}\right)}} - {x}^{\left(\frac{1}{3}\right)}\]

  8. Applied simplify 29.4

    \[\leadsto e^{\log \color{blue}{\left(\sqrt[3]{x + 1}\right)}} - {x}^{\left(\frac{1}{3}\right)}\]
  9. Removed slow pow expressions

Runtime

Time bar (total: 12.9s) Debug logProfile

Please include this information when filing a bug report:

herbie shell --seed '#(1067615470 1817955187 3564058462 2385304812 1026693554 2746013648)'
(FPCore (x)
  :name "2cbrt (problem 3.3.4)"
  (- (pow (+ x 1) (/ 1 3)) (pow x (/ 1 3))))