Average Error: 39.3 → 0.0
Time: 27.7s
Precision: 64
Internal Precision: 1408
\[\sqrt{\frac{e^{2 \cdot x} - 1}{e^{x} - 1}}\]
↓
\[e^{\log \left(\sqrt{\frac{1 + e^{x}}{1}}\right)}\]

Error

Bits error versus x

Derivation

  1. Initial program 39.3

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

  2. Applied simplify0.0

    \[\leadsto \color{blue}{\sqrt{\frac{1 + e^{x}}{1}}}\]
  3. Using strategy rm

  4. Applied add-exp-log0.0

    \[\leadsto \color{blue}{e^{\log \left(\sqrt{\frac{1 + e^{x}}{1}}\right)}}\]
  5. Removed slow pow expressions.

Runtime

Time bar (total: 27.7s)Debug logProfile

herbie shell --seed '#(1063154770 1824007522 645063331 41291047 494775821 1237684644)' 
(FPCore (x)
  :name "sqrtexp (problem 3.4.4)"
  (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))))