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

# Derivation

1. Initial program 57.7

$\left(\left(x + \pi\right) \bmod \left(2 \cdot \pi\right)\right) - \pi$
2. Using strategy rm

$\leadsto \color{blue}{\log \left(e^{\left(\left(x + \pi\right) \bmod \left(2 \cdot \pi\right)\right) - \pi}\right)}$
4. Using strategy rm

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