Average Error: 0.0 → 0.1
Time: 1.2m
Precision: 64
Internal Precision: 320
\[\frac{2}{e^{x} + e^{-x}}\]
↓
\[\sqrt[3]{\frac{\frac{8}{e^{-x} + e^{x}}}{\left(e^{-x} + e^{x}\right) \cdot \left(e^{-x} + e^{x}\right)}}\]

Error

Bits error versus x

Derivation

  1. Initial program 0.0

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

  3. Applied add-cbrt-cube0.1

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

  4. Applied simplify0.1

    \[\leadsto \sqrt[3]{\color{blue}{\frac{\frac{8}{e^{-x} + e^{x}}}{\left(e^{-x} + e^{x}\right) \cdot \left(e^{-x} + e^{x}\right)}}}\]

Runtime

Time bar (total: 1.2m)Debug logProfile

herbie shell --seed '#(1071373924 2949776965 1885069702 3247780810 90874544 2263903749)' 
(FPCore (x)
  :name "Hyperbolic secant"
  (/ 2 (+ (exp x) (exp (- x)))))