Error

Derivation

1. Initial program 63.3b

   \[\left(\left(n + 1\right) \cdot \log \left(n + 1\right) - n \cdot \log n\right) - 1\]

2. Applied taylor 0.3b

   \[\leadsto \left(\left(n + 1\right) \cdot \log \left(n + 1\right) - -1 \cdot \left(\log n \cdot n\right)\right) - 1\]

3. Taylor expanded around inf 0.3b

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

4. Applied simplify 0.3b

   \[\leadsto \color{blue}{\log \left(n + 1\right) \cdot \left(n + 1\right) - \left(\log n \cdot \left(-n\right) + 1\right)}\]
5. Removed slow pow expressions

Runtime

Total time: 48.8s Debug log

herbie --seed '#(1814942071 347475247 581654128 926166701 3042411603 2884051163)'
(FPCore (n)
  :name "NMSE example 3.8"
  
  :target
  (- (log (+ n 1)) (- (/ 1 (* 2 n)) (- (/ 1 (* 3 (sqr n))) (/ 4 (pow n 3)))))(- (- (* (+ n 1) (log (+ n 1))) (* n (log n))) 1))