Average Error: 39.9 → 0.0
Time: 34.2s
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 39.9

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

  2. Applied simplify0.0

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

Runtime

Time bar (total: 34.2s)Debug logProfile

herbie shell --seed '#(1063058331 1508344079 3191715834 2470104540 4213459606 1468189912)' 
(FPCore (x)
  :name "sqrtexp (problem 3.4.4)"
  (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))))