Average Error: 39.9 → 0.0
Time: 19.0s
Precision: 64
Internal Precision: 1408
\[\sqrt{\frac{e^{2 \cdot x} - 1}{e^{x} - 1}}\]
↓
\[\sqrt{\frac{e^{\log_* (1 + e^{x})}}{1}}\]

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. Using strategy rm

  4. Applied add-exp-log0.0

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

  5. Applied simplify0.0

    \[\leadsto \sqrt{\frac{e^{\color{blue}{\log_* (1 + e^{x})}}}{1}}\]

Runtime

Time bar (total: 19.0s)Debug logProfile

herbie shell --seed '#(1070258749 1877548225 2229079127 1588002776 3179087814 1886870650)' +o rules:numerics
(FPCore (x)
  :name "sqrtexp (problem 3.4.4)"
  (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))))