Error: 59.3 → 0.1
Time: 11.1s
Precision: 64
Ground Truth: 128
\[e^{x} - 1\]
⬇
\[x + {x}^2 \cdot \left(x \cdot \frac{1}{6} + \frac{1}{2}\right)\]

Error

Bits error versus x

Derivation

  1. Initial program 59.3

    \[e^{x} - 1\]

  2. Applied taylor 0.1

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

  3. Taylor expanded around 0 0.1

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

  4. Applied simplify 0.1

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

Runtime

Total time: 11.1s Debug log

Please report a bug with the following info:

herbie --seed '#(546438834 4203122477 2293052706 1340793650 2178604898 2539932767)'
(FPCore (x)
  :name "NMSE example 3.7"
  
  :target
  (* x (+ (+ 1 (/ x 2)) (/ (sqr x) 6)))(- (exp x) 1))