Average Error: 39.8 → 0.0
Time: 11.4s
Precision: 64
Internal precision: 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 39.8

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

  2. Applied simplify 0.0

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

Runtime

Time bar (total: 11.4s) Debug log

Please include this information when filing a bug report:

herbie --seed '#(3034573705 489225641 1550238035 1148020154 1974297120 2376590436)'
(FPCore (x)
  :name "sqrtexp (problem 3.4.4)"
  (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))))