Error

Derivation

1. Initial program 14.7

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

3. Applied frac-sub14.1

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

4. Applied simplify14.1

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

5. Applied simplify14.1

   \[\leadsto \frac{x - \left(x + 1\right)}{\color{blue}{(x \cdot x + x)_*}}\]
6. Using strategy rm

7. Applied add-cube-cbrt14.7

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

8. Applied simplify14.7

   \[\leadsto \color{blue}{\left(\sqrt[3]{\frac{0 - 1}{(x \cdot x + x)_*}} \cdot \sqrt[3]{\frac{0 - 1}{(x \cdot x + x)_*}}\right)} \cdot \sqrt[3]{\frac{x - \left(x + 1\right)}{(x \cdot x + x)_*}}\]

9. Applied simplify1.3

   \[\leadsto \left(\sqrt[3]{\frac{0 - 1}{(x \cdot x + x)_*}} \cdot \sqrt[3]{\frac{0 - 1}{(x \cdot x + x)_*}}\right) \cdot \color{blue}{\sqrt[3]{\frac{0 - 1}{(x \cdot x + x)_*}}}\]
10. Using strategy rm

11. Applied cbrt-div1.2

    \[\leadsto \left(\sqrt[3]{\frac{0 - 1}{(x \cdot x + x)_*}} \cdot \sqrt[3]{\frac{0 - 1}{(x \cdot x + x)_*}}\right) \cdot \color{blue}{\frac{\sqrt[3]{0 - 1}}{\sqrt[3]{(x \cdot x + x)_*}}}\]

12. Applied simplify1.2

    \[\leadsto \left(\sqrt[3]{\frac{0 - 1}{(x \cdot x + x)_*}} \cdot \sqrt[3]{\frac{0 - 1}{(x \cdot x + x)_*}}\right) \cdot \frac{\color{blue}{\sqrt[3]{-1}}}{\sqrt[3]{(x \cdot x + x)_*}}\]

Runtime

Time bar (total: 21.3s)Debug logProfile

herbie shell --seed '#(1070100504 930361288 1279167582 284574201 1450237281 2578255382)' +o rules:numerics
(FPCore (x)
  :name "2frac (problem 3.3.1)"
  (- (/ 1 (+ x 1)) (/ 1 x)))