Average Error: 0.2 → 0.2
Time: 38.4s
Precision: 64
Internal Precision: 576
\[\frac{\pi}{2^{k} \cdot \mathsf{gamma} k}\]
\[\frac{\pi}{\mathsf{gamma} k \cdot 2^{k}}\]

Error

Bits error versus k

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Results

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Derivation

  1. Initial program 0.2

    \[\frac{\pi}{2^{k} \cdot \mathsf{gamma} k}\]
  2. Taylor expanded around inf 0.2

    \[\leadsto \color{blue}{\frac{\pi}{\mathsf{gamma} k \cdot 2^{k}}}\]
  3. Final simplification0.2

    \[\leadsto \frac{\pi}{\mathsf{gamma} k \cdot 2^{k}}\]

Runtime

Time bar (total: 38.4s)Debug log

herbie shell --seed '#(2775764126 3555076145 3898259844 1891440260 2599947619 1948460636)' 
(FPCore (k)
  :name "PI / (exp2(k) * tgamma(k))"
  (/ PI (* (exp2 k) (tgamma k))))