Average Error: 0.0 → 0.0
Time: 7.3s
Precision: 64
Internal Precision: 576
\[{\left(\sqrt{2}\right)}^{\left(\frac{x}{N}\right)}\]
\[e^{\left(\frac{1}{2} \cdot \frac{x}{N}\right) \cdot \log 2}\]

Error

Bits error versus x

Bits error versus N

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Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.0

    \[{\left(\sqrt{2}\right)}^{\left(\frac{x}{N}\right)}\]
  2. Using strategy rm
  3. Applied pow1/20.0

    \[\leadsto {\color{blue}{\left({2}^{\frac{1}{2}}\right)}}^{\left(\frac{x}{N}\right)}\]
  4. Applied pow-pow0.0

    \[\leadsto \color{blue}{{2}^{\left(\frac{1}{2} \cdot \frac{x}{N}\right)}}\]
  5. Using strategy rm
  6. Applied pow-to-exp0.0

    \[\leadsto \color{blue}{e^{\log 2 \cdot \left(\frac{1}{2} \cdot \frac{x}{N}\right)}}\]
  7. Final simplification0.0

    \[\leadsto e^{\left(\frac{1}{2} \cdot \frac{x}{N}\right) \cdot \log 2}\]

Runtime

Time bar (total: 7.3s)Debug log

herbie shell --seed '#(2775764126 3555076145 3898259844 1891440260 2599947619 1948460636)' 
(FPCore (x N)
  :name "pow(sqrt(2), x/N)"
  (pow (sqrt 2) (/ x N)))