Average Error: 29.5 → 0.5
Time: 25.9s
Precision: 64
Internal Precision: 1344
\[\sqrt[3]{x + 1} - \sqrt[3]{x}\]
↓
\[\frac{1}{\sqrt[3]{1 + x} \cdot \sqrt[3]{1 + x} + \left(\sqrt[3]{x} + \sqrt[3]{1 + x}\right) \cdot \sqrt[3]{x}}\]

Error

Bits error versus x

Derivation

  1. Initial program 29.5

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

  3. Applied flip3--29.4

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

  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

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

Runtime

Time bar (total: 25.9s)Debug logProfile

herbie shell --seed '#(1071119240 1686926585 3481876196 78132896 2080707795 3185793749)' 
(FPCore (x)
  :name "2cbrt (problem 3.3.4)"
  (- (cbrt (+ x 1)) (cbrt x)))