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

# Try it out

Results

 In Out
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# 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)))