Input Error: 14.9b
Output Error: 0.4b
Time: 8.5s
Precision: 64b
Ground Truth: 128b
\[\tan^{-1} \left(N + 1\right) - \tan^{-1} N\]
⬇
\[\tan^{-1}_* \frac{1 + 0}{\left({N}^2 + N\right) + 1}\]

Error

Bits error versus N

Derivation

  1. Initial program 14.9b

    \[\tan^{-1} \left(N + 1\right) - \tan^{-1} N\]
  2. Using strategy rm

  3. Applied diff-atan 13.8b

    \[\leadsto \color{blue}{\tan^{-1}_* \frac{\left(N + 1\right) - N}{1 + \left(N + 1\right) \cdot N}}\]

  4. Applied simplify 0.4b

    \[\leadsto \tan^{-1}_* \frac{\color{blue}{1 + 0}}{1 + \left(N + 1\right) \cdot N}\]

  5. Applied simplify 0.4b

    \[\leadsto \tan^{-1}_* \frac{1 + 0}{\color{blue}{\left({N}^2 + N\right) + 1}}\]
  6. Removed slow pow expressions

Runtime

Total time: 8.5s Debug log

herbie --seed '#(4146907719 2011765780 2976700490 1406537748 595559077 1589987264)'
(FPCore (N)
  :name "NMSE example 3.5"
  
  :target
  (atan (/ 1 (+ 1 (* N (+ N 1)))))(- (atan (+ N 1)) (atan N)))