Average Error: 40.0 → 0.1
Time: 15.6s
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 40.0

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

  2. Applied simplify0.1

    \[\leadsto \color{blue}{\sqrt{\frac{1 + e^{x}}{1}}}\]

Runtime

Time bar (total: 15.6s)Debug log

herbie shell --seed '#(1743936871 1855164119 3668777427 1254258049 132811564 1366975197)' 
(FPCore (x)
  :name "NMSE problem 3.4.4"
  :pre (!= x 0)
  (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))))