Average Error: 58.7 → 58.7
Time: 6.3s
Precision: 64
Internal Precision: 2368
\[\left(\left(x + pi\right) \bmod \left(2 \cdot pi\right)\right) - pi\]
\[\left(\sqrt[3]{\left(\left(pi + x\right) \bmod \left(2 \cdot pi\right)\right) - pi} \cdot \sqrt[3]{\left(\left(pi + x\right) \bmod \left(2 \cdot pi\right)\right) - pi}\right) \cdot \sqrt[3]{\left(\left(pi + x\right) \bmod \left(2 \cdot pi\right)\right) - pi}\]

Error

Bits error versus x

Bits error versus pi

Derivation

  1. Initial program 58.7

    \[\left(\left(x + pi\right) \bmod \left(2 \cdot pi\right)\right) - pi\]
  2. Using strategy rm
  3. Applied add-cube-cbrt58.7

    \[\leadsto \color{blue}{\left(\sqrt[3]{\left(\left(x + pi\right) \bmod \left(2 \cdot pi\right)\right) - pi} \cdot \sqrt[3]{\left(\left(x + pi\right) \bmod \left(2 \cdot pi\right)\right) - pi}\right) \cdot \sqrt[3]{\left(\left(x + pi\right) \bmod \left(2 \cdot pi\right)\right) - pi}}\]
  4. Final simplification58.7

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

Runtime

Time bar (total: 6.3s)Debug log

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