Average Error: 31.3 → 31.3
Time: 6.5s
Precision: 64
\[{\left(\tan^{-1} \left(a \bmod \left(\sin^{-1} a\right)\right)\right)}^{\left(a \cdot a\right)}\]
↓
\[{\left(\tan^{-1} \left(a \bmod \left(\sin^{-1} a\right)\right)\right)}^{\left(a \cdot a\right)}\]
{\left(\tan^{-1} \left(a \bmod \left(\sin^{-1} a\right)\right)\right)}^{\left(a \cdot a\right)}
↓
{\left(\tan^{-1} \left(a \bmod \left(\sin^{-1} a\right)\right)\right)}^{\left(a \cdot a\right)}
double f(double a) {
        double r88955 = a;
        double r88956 = asin(r88955);
        double r88957 = fmod(r88955, r88956);
        double r88958 = atan(r88957);
        double r88959 = r88955 * r88955;
        double r88960 = pow(r88958, r88959);
        return r88960;
}
↓
double f(double a) {
        double r88961 = a;
        double r88962 = asin(r88961);
        double r88963 = fmod(r88961, r88962);
        double r88964 = atan(r88963);
        double r88965 = r88961 * r88961;
        double r88966 = pow(r88964, r88965);
        return r88966;
}

Error

Bits error versus a

Derivation

  1. Initial program 31.3

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

  2. Final simplification31.3

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

Reproduce

herbie shell --seed 2020089 +o rules:numerics
(FPCore (a)
  :name "Fuzzer 002"
  :precision binary64
  (pow (atan (fmod a (asin a))) (* a a)))