Average Error: 31.1 → 31.1
Time: 22.4s
Precision: 64
Internal Precision: 2368
\[{\left(\tan^{-1} \left(a \bmod \left(\sin^{-1} a\right)\right)\right)}^{\left(a \cdot a\right)}\]
↓
\[{\left(\tan^{-1} \left(e^{\log \left(a \bmod \left(\sin^{-1} a\right)\right)}\right)\right)}^{\left(a \cdot a\right)}\]

Error

Bits error versus a

Derivation

  1. Initial program 31.1

    \[{\left(\tan^{-1} \left(a \bmod \left(\sin^{-1} a\right)\right)\right)}^{\left(a \cdot a\right)}\]
  2. Using strategy rm

  3. Applied add-exp-log31.1

    \[\leadsto {\left(\tan^{-1} \color{blue}{\left(e^{\log \left(a \bmod \left(\sin^{-1} a\right)\right)}\right)}\right)}^{\left(a \cdot a\right)}\]

  4. Final simplification31.1

    \[\leadsto {\left(\tan^{-1} \left(e^{\log \left(a \bmod \left(\sin^{-1} a\right)\right)}\right)\right)}^{\left(a \cdot a\right)}\]

Runtime

Time bar (total: 22.4s)Debug logProfile

herbie shell --seed 2018220 +o rules:numerics
(FPCore (a)
  :name "Fuzzer 002"
  (pow (atan (fmod a (asin a))) (* a a)))