Average Error: 60.9 → 0.4
Time: 1.5m
Precision: 64
Internal Precision: 1408
\[\frac{\log \left(1 - x\right)}{\log \left(1 + x\right)}\]
↓
\[-\left(\frac{1}{2} \cdot {x}^{2} + \left(1 + x\right)\right)\]

Error

Bits error versus x

Derivation

  1. Initial program 60.9

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

  2. Taylor expanded around 0 0.4

    \[\leadsto \color{blue}{-\left(\frac{1}{2} \cdot {x}^{2} + \left(1 + x\right)\right)}\]

Runtime

Time bar (total: 1.5m)Debug log

herbie shell --seed '#(1743936871 1855164119 3668777427 1254258049 132811564 1366975197)' 
(FPCore (x)
  :name "NMSE example 3.10"
  :pre (< -1 x 1)
  (/ (log (- 1 x)) (log (+ 1 x))))