Average Error: 39.3 → 0.0
Time: 14.3s
Precision: 64
Internal Precision: 1408
\[\sqrt{\frac{e^{2 \cdot x} - 1}{e^{x} - 1}}\]
↓
\[(e^{\log_* (1 + \sqrt{\frac{e^{x} + 1}{1}})} - 1)^*\]

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

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

  4. Applied expm1-log1p-u0.0

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

Runtime

Time bar (total: 14.3s)Debug logProfile

herbie shell --seed '#(1070386091 2509006183 1430610344 1025408621 36622005 1425925650)' +o rules:numerics
(FPCore (x)
  :name "sqrtexp (problem 3.4.4)"
  (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))))