Error

Derivation

1. Split input into 2 regimes

2. if x < -3410.316970094639 or 5789.810905473262 < x

   1. Initial program 60.0

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

   3. Applied flip--60.0

      \[\leadsto \color{blue}{\frac{\sqrt[3]{x + 1} \cdot \sqrt[3]{x + 1} - \sqrt[3]{x} \cdot \sqrt[3]{x}}{\sqrt[3]{x + 1} + \sqrt[3]{x}}}\]

   4. Taylor expanded around inf 33.7

      \[\leadsto \frac{\color{blue}{\left(\frac{4}{81} \cdot {\left(\frac{1}{{x}^{7}}\right)}^{\frac{1}{3}} + \frac{2}{3} \cdot {\left(\frac{1}{x}\right)}^{\frac{1}{3}}\right) - \frac{1}{9} \cdot {\left(\frac{1}{{x}^{4}}\right)}^{\frac{1}{3}}}}{\sqrt[3]{x + 1} + \sqrt[3]{x}}\]

   5. Simplified1.0

      \[\leadsto \frac{\color{blue}{(\frac{-1}{9} \cdot \left(\sqrt[3]{\frac{1}{{x}^{4}}}\right) + \left((\left(\sqrt[3]{\frac{1}{{x}^{7}}}\right) \cdot \frac{4}{81} + \left(\sqrt[3]{\frac{1}{x}} \cdot \frac{2}{3}\right))_*\right))_*}}{\sqrt[3]{x + 1} + \sqrt[3]{x}}\]

   if -3410.316970094639 < x < 5789.810905473262

   1. Initial program 0.1

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

   3. Applied add-cbrt-cube0.1

      \[\leadsto \color{blue}{\sqrt[3]{\left(\sqrt[3]{x + 1} \cdot \sqrt[3]{x + 1}\right) \cdot \sqrt[3]{x + 1}}} - \sqrt[3]{x}\]
3. Recombined 2 regimes into one program.

4. Final simplification0.6

   \[\leadsto \begin{array}{l} \mathbf{if}\;x \le -3410.316970094639 \lor \neg \left(x \le 5789.810905473262\right):\\ \;\;\;\;\frac{(\frac{-1}{9} \cdot \left(\sqrt[3]{\frac{1}{{x}^{4}}}\right) + \left((\left(\sqrt[3]{\frac{1}{{x}^{7}}}\right) \cdot \frac{4}{81} + \left(\sqrt[3]{\frac{1}{x}} \cdot \frac{2}{3}\right))_*\right))_*}{\sqrt[3]{x} + \sqrt[3]{x + 1}}\\ \mathbf{else}:\\ \;\;\;\;\sqrt[3]{\left(\sqrt[3]{x + 1} \cdot \sqrt[3]{x + 1}\right) \cdot \sqrt[3]{x + 1}} - \sqrt[3]{x}\\ \end{array}\]

Runtime

Time bar (total: 17.7s)Debug logProfile

herbie shell --seed 2018285 +o rules:numerics
(FPCore (x)
  :name "2cbrt (problem 3.3.4)"
  (- (cbrt (+ x 1)) (cbrt x)))