Average Error: 58.7 → 0.0
Time: 4.6s
Precision: 64
Internal precision: 1408
\[\log \left(\frac{1 - \varepsilon}{1 + \varepsilon}\right)\]
⬇
\[-\left(\frac{2}{3} \cdot {\varepsilon}^{3} + \left(\frac{2}{5} \cdot {\varepsilon}^{5} + 2 \cdot \varepsilon\right)\right)\]

Error

Bits error versus eps

Derivation

  1. Initial program 58.7

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

  2. Applied taylor 0.0

    \[\leadsto -\left(\frac{2}{3} \cdot {\varepsilon}^{3} + \left(\frac{2}{5} \cdot {\varepsilon}^{5} + 2 \cdot \varepsilon\right)\right)\]

  3. Taylor expanded around 0 0.0

    \[\leadsto \color{blue}{-\left(\frac{2}{3} \cdot {\varepsilon}^{3} + \left(\frac{2}{5} \cdot {\varepsilon}^{5} + 2 \cdot \varepsilon\right)\right)}\]
  4. Removed slow pow expressions

Runtime

Time bar (total: 4.6s) Debug log

Please include this information when filing a bug report:

herbie shell --seed '#(3052192724 3812927732 3686175817 630908657 2373248591 511094450)'
(FPCore (eps)
  :name "NMSE problem 3.4.3"
  :pre (< -1 eps 1)
  (log (/ (- 1 eps) (+ 1 eps))))