Average Error: 0.0 → 0.0
Time: 23.4s
Precision: 64
Internal Precision: 320
\[\frac{2}{e^{x} + e^{-x}}\]
↓
\[\sqrt[3]{\left(\frac{2}{e^{x} + e^{-x}} \cdot \frac{2}{e^{x} + e^{-x}}\right) \cdot \frac{2}{e^{x} + e^{-x}}}\]

Error

Bits error versus x

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Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.0

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

  3. Applied add-cbrt-cube0.0

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

  4. Final simplification0.0

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

Runtime

Time bar (total: 23.4s)Debug logProfile

herbie shell --seed 2018221 
(FPCore (x)
  :name "Hyperbolic secant"
  (/ 2 (+ (exp x) (exp (- x)))))