Error

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Target

Derivation

1. Initial program 61.2

   \[\frac{\log \left(1 - x\right)}{\log \left(1 + x\right)}\]

2. Applied simplify60.2

   \[\leadsto \color{blue}{\frac{\log \left(1 - x\right)}{\log_* (1 + x)}}\]
3. Using strategy rm

4. Applied log1p-expm1-u60.2

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

5. Applied simplify0.0

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

7. Applied add-cbrt-cube41.2

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

8. Applied add-cbrt-cube41.7

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

9. Applied cbrt-undiv41.7

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

10. Applied simplify0.0

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

Runtime

Time bar (total: 47.3s)Debug logProfile

herbie shell --seed 2018199 +o rules:numerics
(FPCore (x)
  :name "qlog (example 3.10)"
  :pre (and (< -1 x) (< x 1))

  :herbie-target
  (- (+ (+ (+ 1 x) (/ (* x x) 2)) (* 5/12 (pow x 3))))

  (/ (log (- 1 x)) (log (+ 1 x))))