Average Error: 30.1 → 29.8
Time: 9.3s
Precision: 64
Internal precision: 1408
\[{\left(x + 1\right)}^{\left(\frac{1}{3}\right)} - {x}^{\left(\frac{1}{3}\right)}\]
⬇
\[\sqrt[3]{{\left(\sqrt[3]{x + 1} - {x}^{\left(\frac{1}{3}\right)}\right)}^3}\]

Error

Bits error versus x

Derivation

  1. Initial program 30.1

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

  3. Applied add-exp-log 30.3

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

  4. Applied pow-exp 30.3

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

  5. Applied simplify 30.0

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

  7. Applied add-cbrt-cube 30.0

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

  8. Applied simplify 29.8

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

Runtime

Time bar (total: 9.3s) Debug logProfile

Please include this information when filing a bug report:

herbie shell --seed '#(1067773715 2765207660 218871639 3688798924 2755544087 2054563380)'
(FPCore (x)
  :name "2cbrt (problem 3.3.4)"
  (- (pow (+ x 1) (/ 1 3)) (pow x (/ 1 3))))