Average Error: 0.0 → 0.0
Time: 15.1s
Precision: 64
Internal Precision: 128
\[\frac{2}{e^{x} + e^{-x}}\]
↓
\[\sqrt[3]{\frac{2}{e^{x} + e^{-x}} \cdot \frac{2 \cdot \frac{2}{e^{x} + e^{-x}}}{e^{x} + e^{-x}}}\]

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

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-cbrt-cube0.0

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

  6. Applied associate-*r/0.0

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

  7. Final simplification0.0

    \[\leadsto \sqrt[3]{\frac{2}{e^{x} + e^{-x}} \cdot \frac{2 \cdot \frac{2}{e^{x} + e^{-x}}}{e^{x} + e^{-x}}}\]

Runtime

Time bar (total: 15.1s)Debug logProfile

herbie shell --seed 2018304 
(FPCore (x)
  :name "Hyperbolic secant"
  (/ 2 (+ (exp x) (exp (- x)))))