Average Error: 39.9 → 0.0
Time: 5.6s
Precision: 64
Ground Truth: 128
\[\sqrt{\frac{e^{2 \cdot x} - 1}{e^{x} - 1}}\]
⬇
\[\sqrt{\frac{e^{x} + 1}{1}}\]

Error

Bits error versus x

Derivation

  1. Initial program 39.9

    \[\sqrt{\frac{e^{2 \cdot x} - 1}{e^{x} - 1}}\]

  2. Applied simplify 0.0

    \[\leadsto \color{blue}{\sqrt{\frac{e^{x} + 1}{1}}}\]
  3. Removed slow pow expressions

Runtime

Total time: 5.6s Debug log

Please include this information when filing a bug report:

herbie --seed '#(2721477869 3365922910 3119324189 3329655893 655799541 65625004)'
(FPCore (x)
  :name "NMSE problem 3.4.4"
  (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))))