Average Error: 40.1 → 0.0
Time: 3.8s
Precision: 64
Internal precision: 1408
\[\sqrt{\frac{e^{2 \cdot x} - 1}{e^{x} - 1}}\]
⬇
\[\sqrt{\frac{1 + e^{x}}{1}}\]

Error

Bits error versus x

Derivation

  1. Initial program 40.1

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

  2. Applied simplify 0.0

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

Runtime

Time bar (total: 3.8s) Debug logProfile

Please include this information when filing a bug report:

herbie shell --seed '#(1067615470 1817955187 3564058462 2385304812 1026693554 2746013648)'
(FPCore (x)
  :name "sqrtexp (problem 3.4.4)"
  (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))))