Average Error: 39.7 → 0.0
Time: 16.7s
Precision: 64
Ground Truth: 128
\[\sqrt{\frac{e^{2 \cdot x} - 1}{e^{x} - 1}}\]
⬇
\[\sqrt{\frac{1 + e^{x}}{1}}\]

Error

Bits error versus x

Derivation

  1. Initial program 39.7

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

  2. Applied simplify 0.0

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

Runtime

Total time: 16.7s Debug log

Please include this information when filing a bug report:

herbie --seed '#(3960031271 4190944876 2969215795 4200542520 1454957496 2754512573)'
(FPCore (x)
  :name "NMSE problem 3.4.4"
  (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))))