Average Error: 59.2 → 0.1
Time: 27.4s
Precision: 64
Internal precision: 1408
\[e^{x} - 1\]
⬇
\[\left(x \cdot x\right) \cdot \left(\frac{1}{2} + \frac{1}{6} \cdot x\right) + x\]

Error

Bits error versus x

Derivation

  1. Initial program 59.2

    \[e^{x} - 1\]

  2. Taylor expanded around 0 0.1

    \[\leadsto \color{blue}{\frac{1}{2} \cdot {x}^{2} + \left(\frac{1}{6} \cdot {x}^{3} + x\right)}\]

  3. Applied simplify 0.1

    \[\leadsto \color{blue}{\left(x \cdot x\right) \cdot \left(\frac{1}{2} + \frac{1}{6} \cdot x\right) + x}\]
  4. Removed slow pow expressions

Runtime

Time bar (total: 27.4s) Debug log

Please include this information when filing a bug report:

herbie shell --seed '#(2329929097 3210370195 3111198779 2406363002 3511342718 2136436390)'
(FPCore (x)
  :name "expm1 (example 3.7)"
  :pre (< -0.00017 x)
  (- (exp x) 1))