Average Error: 57.7 → 57.7
Time: 7.0s
Precision: 64
Internal Precision: 1344
\[\left(\left(x + \pi\right) \bmod \left(2 \cdot \pi\right)\right) - \pi\]
\[\log \left(\sqrt[3]{\left(e^{\left(\left(\pi + x\right) \bmod \left(2 \cdot \pi\right)\right) - \pi} \cdot e^{\left(\left(\pi + x\right) \bmod \left(2 \cdot \pi\right)\right) - \pi}\right) \cdot e^{\left(\left(\pi + x\right) \bmod \left(2 \cdot \pi\right)\right) - \pi}}\right)\]

Error

Bits error versus x

Derivation

  1. Initial program 57.7

    \[\left(\left(x + \pi\right) \bmod \left(2 \cdot \pi\right)\right) - \pi\]
  2. Using strategy rm
  3. Applied add-log-exp57.7

    \[\leadsto \color{blue}{\log \left(e^{\left(\left(x + \pi\right) \bmod \left(2 \cdot \pi\right)\right) - \pi}\right)}\]
  4. Using strategy rm
  5. Applied add-cbrt-cube57.7

    \[\leadsto \log \color{blue}{\left(\sqrt[3]{\left(e^{\left(\left(x + \pi\right) \bmod \left(2 \cdot \pi\right)\right) - \pi} \cdot e^{\left(\left(x + \pi\right) \bmod \left(2 \cdot \pi\right)\right) - \pi}\right) \cdot e^{\left(\left(x + \pi\right) \bmod \left(2 \cdot \pi\right)\right) - \pi}}\right)}\]
  6. Final simplification57.7

    \[\leadsto \log \left(\sqrt[3]{\left(e^{\left(\left(\pi + x\right) \bmod \left(2 \cdot \pi\right)\right) - \pi} \cdot e^{\left(\left(\pi + x\right) \bmod \left(2 \cdot \pi\right)\right) - \pi}\right) \cdot e^{\left(\left(\pi + x\right) \bmod \left(2 \cdot \pi\right)\right) - \pi}}\right)\]

Runtime

Time bar (total: 7.0s)Debug log

herbie shell --seed '#(2775764126 3555076145 3898259844 1891440260 2599947619 1948460636)' 
(FPCore (x)
  :name "fmod(x + PI, 2*PI) - PI"
  (- (fmod (+ x PI) (* 2 PI)) PI))