Average Error: 0.0 → 0.0
Time: 15.0s
Precision: 64
Internal Precision: 128
\[\frac{2}{e^{x} + e^{-x}}\]
↓
\[\log_* (1 + (e^{\frac{2}{e^{x} + e^{-x}}} - 1)^*)\]

Error

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Results

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Derivation

  1. Initial program 0.0

    \[\frac{2}{e^{x} + e^{-x}}\]

  2. Initial simplification0.0

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

  4. Applied log1p-expm1-u0.0

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

  5. Final simplification0.0

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

Runtime

Time bar (total: 15.0s)Debug logProfile

herbie shell --seed 2018304 +o rules:numerics
(FPCore (x)
  :name "Hyperbolic secant"
  (/ 2 (+ (exp x) (exp (- x)))))