Average Error: 39.3 → 0.1
Time: 4.9s
Precision: 64
Internal precision: 1408
\[\sqrt{\frac{e^{2 \cdot x} - 1}{e^{x} - 1}}\]
⬇
\[\sqrt{\frac{\frac{1 + {\left(e^{x}\right)}^3}{{\left(e^{x}\right)}^2 + \left(1 - e^{x}\right)}}{1}}\]

Error

Bits error versus x

Derivation

  1. Initial program 39.3

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

  2. Applied simplify 0.0

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

  4. Applied flip3-+ 0.1

    \[\leadsto \sqrt{\frac{\color{blue}{\frac{{1}^{3} + {\left(e^{x}\right)}^{3}}{{1}^2 + \left({\left(e^{x}\right)}^2 - 1 \cdot e^{x}\right)}}}{1}}\]

  5. Applied simplify 0.1

    \[\leadsto \sqrt{\frac{\frac{\color{blue}{1 + {\left(e^{x}\right)}^3}}{{1}^2 + \left({\left(e^{x}\right)}^2 - 1 \cdot e^{x}\right)}}{1}}\]

  6. Applied simplify 0.1

    \[\leadsto \sqrt{\frac{\frac{1 + {\left(e^{x}\right)}^3}{\color{blue}{e^{x} \cdot e^{x} + \left(1 - e^{x}\right)}}}{1}}\]

  7. Applied simplify 0.1

    \[\leadsto \sqrt{\frac{\frac{1 + {\left(e^{x}\right)}^3}{\color{blue}{{\left(e^{x}\right)}^2} + \left(1 - e^{x}\right)}}{1}}\]
  8. Removed slow pow expressions

Runtime

Time bar (total: 4.9s) Debug logProfile

Please include this information when filing a bug report:

herbie shell --seed '#(1066500295 745726447 3908002351 725592315 4114972361 2368915013)'
(FPCore (x)
  :name "sqrtexp (problem 3.4.4)"
  (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))))