Error

Derivation

1. Initial program 0.0

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

3. Applied add-cube-cbrt0.0

   \[\leadsto \frac{2}{\color{blue}{\left(\sqrt[3]{e^{x}} \cdot \sqrt[3]{e^{x}}\right) \cdot \sqrt[3]{e^{x}}} + e^{-x}}\]

4. Applied fma-def0.0

   \[\leadsto \frac{2}{\color{blue}{(\left(\sqrt[3]{e^{x}} \cdot \sqrt[3]{e^{x}}\right) \cdot \left(\sqrt[3]{e^{x}}\right) + \left(e^{-x}\right))_*}}\]
5. Using strategy rm

6. Applied expm1-log1p-u0.0

   \[\leadsto \color{blue}{(e^{\log_* (1 + \frac{2}{(\left(\sqrt[3]{e^{x}} \cdot \sqrt[3]{e^{x}}\right) \cdot \left(\sqrt[3]{e^{x}}\right) + \left(e^{-x}\right))_*})} - 1)^*}\]

7. Final simplification0.0

   \[\leadsto (e^{\log_* (1 + \frac{2}{(\left(\sqrt[3]{e^{x}} \cdot \sqrt[3]{e^{x}}\right) \cdot \left(\sqrt[3]{e^{x}}\right) + \left(e^{-x}\right))_*})} - 1)^*\]

Reproduce

herbie shell --seed 2019007 +o rules:numerics
(FPCore (x)
  :name "Hyperbolic secant"
  (/ 2 (+ (exp x) (exp (- x)))))

Details

Time bar (total: 6.1s)Debug log