Error

Derivation

1. Initial program 0.0

   \[\log \left(\frac{1}{x} + \frac{\sqrt{1 - x \cdot x}}{x}\right)\]
2. Using strategy rm

3. Applied add-cube-cbrt0.0

   \[\leadsto \log \left(\color{blue}{\left(\sqrt[3]{\frac{1}{x}} \cdot \sqrt[3]{\frac{1}{x}}\right) \cdot \sqrt[3]{\frac{1}{x}}} + \frac{\sqrt{1 - x \cdot x}}{x}\right)\]

4. Applied fma-def0.0

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

5. Final simplification0.0

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

Runtime

Time bar (total: 13.5s)Debug logProfile

herbie shell --seed 2018274 +o rules:numerics
(FPCore (x)
  :name "Hyperbolic arc-(co)secant"
  (log (+ (/ 1 x) (/ (sqrt (- 1 (* x x))) x))))