Average Error: 39.6 → 0.0
Time: 6.7s
Precision: 64
Internal Precision: 1344
\[\sqrt{\frac{e^{2 \cdot x} - 1}{e^{x} - 1}}\]
↓
\[\sqrt{1 + e^{x}}\]

Error

Bits error versus x

Derivation

  1. Initial program 39.6

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

  2. Applied simplify0.0

    \[\leadsto \color{blue}{\sqrt{1 + e^{x}}}\]

Runtime

Time bar (total: 6.7s)Debug logProfile

herbie shell --seed '#(1071852389 864846987 1238109217 3425890003 4124793586 650694553)' 
(FPCore (x)
  :name "sqrtexp (problem 3.4.4)"
  (sqrt (/ (- (exp (* 2 x)) 1) (- (exp x) 1))))