Average Error: 40.4 → 0.0
Time: 15.3s
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 40.4

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

  2. Applied simplify0.0

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

Runtime

Time bar (total: 15.3s)Debug log

herbie shell --seed '#(212267722 3993171362 1093346726 3605783651 2106536041 3335990851)' 
(FPCore (x)
  :name "sqrtexp (problem 3.4.4)"
  (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))))