Average Error: 0.0 → 0.0
Time: 6.0s
Precision: 64
Internal Precision: 320
\[\frac{2}{e^{x} + e^{-x}}\]
↓
\[\frac{2}{(\left(\sqrt{e^{x}}\right) \cdot \left(\sqrt{e^{x}}\right) + \left(e^{-x}\right))_*}\]

Error

Bits error versus x

Derivation

  1. Initial program 0.0

    \[\frac{2}{e^{x} + e^{-x}}\]
  2. Using strategy rm

  3. Applied add-sqr-sqrt0.0

    \[\leadsto \frac{2}{\color{blue}{\sqrt{e^{x}} \cdot \sqrt{e^{x}}} + e^{-x}}\]

  4. Applied fma-def0.0

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

Runtime

Time bar (total: 6.0s)Debug logProfile

herbie shell --seed '#(1071852389 864846987 1238109217 3425890003 4124793586 650694553)' +o rules:numerics
(FPCore (x)
  :name "Hyperbolic secant"
  (/ 2 (+ (exp x) (exp (- x)))))