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

# Try it out

Results

 In Out
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

$\leadsto \frac{\pi}{\color{blue}{\left(\sqrt{2^{k}} \cdot \sqrt{2^{k}}\right)} \cdot \mathsf{gamma} \left(k + 1\right)}$
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)))))