Error

Derivation

1. Initial program 21.1

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

3. Applied add-cube-cbrt21.1

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

4. Applied fma-def21.1

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

6. Applied log1p-expm1-u21.1

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

8. Applied log1p-expm1-u21.1

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

10. Applied log1p-expm1-u21.1

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

11. Final simplification21.1

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

Runtime

Time bar (total: 20.8s)Debug logProfile

herbie shell --seed 2018255 +o rules:numerics
(FPCore (x)
  :name "Asymptote B"
  (+ (/ 1 (- x 1)) (/ x (+ x 1))))