Error

Derivation

1. Initial program 14.3

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

3. Applied frac-sub13.7

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

4. Applied simplify0.3

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

5. Applied simplify0.3

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

7. Applied add-cube-cbrt1.2

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

9. Applied add-cube-cbrt1.2

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

10. Applied add-cube-cbrt1.2

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

11. Applied times-frac1.2

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

Runtime

Time bar (total: 29.8s)Debug logProfile

herbie shell --seed '#(1070864556 424010669 783715395 1203517814 4070606583 4107618214)' +o rules:numerics
(FPCore (x)
  :name "2frac (problem 3.3.1)"
  (- (/ 1 (+ x 1)) (/ 1 x)))