Average Error: 0.0 → 0.0
Time: 11.0s
Precision: 64
Internal Precision: 320
\[\frac{2}{e^{x} + e^{-x}}\]
↓
\[\frac{\sqrt{\frac{2}{e^{x} + e^{-x}}} \cdot \sqrt{2}}{\sqrt{e^{x} + e^{-x}}}\]

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 add-sqr-sqrt0.0

    \[\leadsto \color{blue}{\sqrt{\frac{2}{e^{x} + e^{-x}}} \cdot \sqrt{\frac{2}{e^{x} + e^{-x}}}}\]
  5. Using strategy rm

  6. Applied sqrt-div0.0

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

  7. Applied associate-*l/0.0

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

  8. Final simplification0.0

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

Runtime

Time bar (total: 11.0s)Debug logProfile

BaselineHerbieOracleSpan%
Regimes0.00.00.00.00%
herbie shell --seed 2018297 +o rules:numerics
(FPCore (x)
  :name "Hyperbolic secant"
  (/ 2 (+ (exp x) (exp (- x)))))