Average Error: 0.0 → 0.0
Time: 13.4s
Precision: 64
Internal Precision: 320
\[\frac{\pi}{2^{k} \cdot \mathsf{gamma} \left(k + 1\right)}\]
\[\frac{\pi}{\left(\mathsf{gamma} \left(k + 1\right) \cdot \sqrt{2^{k}}\right) \cdot \sqrt{2^{k}}}\]

Error

Bits error versus k

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Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.0

    \[\frac{\pi}{2^{k} \cdot \mathsf{gamma} \left(k + 1\right)}\]
  2. Using strategy rm
  3. Applied add-sqr-sqrt0.0

    \[\leadsto \frac{\pi}{\color{blue}{\left(\sqrt{2^{k}} \cdot \sqrt{2^{k}}\right)} \cdot \mathsf{gamma} \left(k + 1\right)}\]
  4. Applied associate-*l*0.0

    \[\leadsto \frac{\pi}{\color{blue}{\sqrt{2^{k}} \cdot \left(\sqrt{2^{k}} \cdot \mathsf{gamma} \left(k + 1\right)\right)}}\]
  5. Final simplification0.0

    \[\leadsto \frac{\pi}{\left(\mathsf{gamma} \left(k + 1\right) \cdot \sqrt{2^{k}}\right) \cdot \sqrt{2^{k}}}\]

Runtime

Time bar (total: 13.4s)Debug log

herbie shell --seed '#(2775764126 3555076145 3898259844 1891440260 2599947619 1948460636)' 
(FPCore (k)
  :name "PI / (exp2(k) * tgamma(k + 1))"
  (/ PI (* (exp2 k) (tgamma (+ k 1)))))