Average Error: 29.8 → 0.5
Time: 27.0s
Precision: 64
Internal Precision: 1408
\[\sqrt[3]{x + 1} - \sqrt[3]{x}\]
↓
\[\frac{1}{(\left(\sqrt[3]{x}\right) \cdot \left(\sqrt[3]{x} + \sqrt[3]{1 + x}\right) + \left(\sqrt[3]{1 + x} \cdot \sqrt[3]{1 + x}\right))_*}\]

Error

Bits error versus x

Derivation

  1. Initial program 29.8

    \[\sqrt[3]{x + 1} - \sqrt[3]{x}\]
  2. Using strategy rm

  3. Applied flip3--29.8

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

  4. Applied simplify0.5

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

  5. Applied simplify0.5

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

Runtime

Time bar (total: 27.0s)Debug logProfile

herbie shell --seed '#(1070864556 424010669 783715395 1203517814 4070606583 4107618214)' +o rules:numerics
(FPCore (x)
  :name "2cbrt (problem 3.3.4)"
  (- (cbrt (+ x 1)) (cbrt x)))