Average Error: 31.1 → 31.1
Time: 20.8s
Precision: 64
Internal Precision: 2368
\[{\left(\tan^{-1} \left(a \bmod \left(\sin^{-1} a\right)\right)\right)}^{\left(a \cdot a\right)}\]
↓
\[{\left(\tan^{-1} \left((e^{\log_* (1 + \left(a \bmod \left(\sin^{-1} a\right)\right))} - 1)^*\right)\right)}^{\left(a \cdot a\right)}\]

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 expm1-log1p-u31.1

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

  4. Final simplification31.1

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

Runtime

Time bar (total: 20.8s)Debug logProfile

BaselineHerbieOracleSpan%
Regimes31.131.131.10.0100%
herbie shell --seed 2018296 +o rules:numerics
(FPCore (a)
  :name "Fuzzer 002"
  (pow (atan (fmod a (asin a))) (* a a)))