Average Error: 29.8 → 29.7
Time: 12.1s
Precision: 64
Internal precision: 1408
\[{\left(x + 1\right)}^{\left(\frac{1}{3}\right)} - {x}^{\left(\frac{1}{3}\right)}\]
⬇
\[e^{\frac{\log \left(1 + x\right)}{3}} - {x}^{\left(\frac{1}{3}\right)}\]

Error

Bits error versus x

Derivation

  1. Initial program 29.8

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

  3. Applied add-exp-log 30.0

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

  4. Applied pow-exp 30.0

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

  5. Applied simplify 29.7

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

Runtime

Time bar (total: 12.1s) Debug logProfile

Please include this information when filing a bug report:

herbie shell --seed '#(1066372953 114334025 411438303 1288252006 2962405338 2829794477)'
(FPCore (x)
  :name "2cbrt (problem 3.3.4)"
  (- (pow (+ x 1) (/ 1 3)) (pow x (/ 1 3))))