Average Error: 0.0 → 0.0
Time: 6.2s
Precision: 64
Internal Precision: 384
\[\frac{2}{e^{x} + e^{-x}}\]
↓
\[(e^{\log_* (1 + \frac{2}{e^{x} + e^{-x}})} - 1)^*\]

Error

Bits error versus x

Derivation

  1. Initial program 0.0

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

  3. Applied expm1-log1p-u0.0

    \[\leadsto \color{blue}{(e^{\log_* (1 + \frac{2}{e^{x} + e^{-x}})} - 1)^*}\]

Runtime

Time bar (total: 6.2s)Debug logProfile

herbie shell --seed '#(1070355188 2193211668 3977393919 3454156579 3755371326 1656365382)' +o rules:numerics
(FPCore (x)
  :name "Hyperbolic secant"
  (/ 2 (+ (exp x) (exp (- x)))))