Average Error: 0.0 → 0.5
Time: 12.3s
Precision: 64
Internal Precision: 320
\[\frac{2}{e^{x} + e^{-x}}\]
↓
\[\frac{\frac{2}{\sqrt{e^{x} + e^{-x}}}}{\sqrt{e^{x} + e^{-x}}}\]

Error

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Results

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Derivation

  1. Initial program 0.0

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

  3. Applied add-sqr-sqrt0.8

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

  4. Applied associate-/r*0.5

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

  5. Final simplification0.5

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

Runtime

Time bar (total: 12.3s)Debug logProfile

BaselineHerbieOracleSpan%
Regimes0.50.50.00.50%
herbie shell --seed 2018285 
(FPCore (x)
  :name "Hyperbolic secant"
  (/ 2 (+ (exp x) (exp (- x)))))