Average Error: 31.0 → 31.0
Time: 5.6s
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 r85027 = a;
        double r85028 = asin(r85027);
        double r85029 = fmod(r85027, r85028);
        double r85030 = atan(r85029);
        double r85031 = r85027 * r85027;
        double r85032 = pow(r85030, r85031);
        return r85032;
}
↓
double f(double a) {
        double r85033 = a;
        double r85034 = asin(r85033);
        double r85035 = fmod(r85033, r85034);
        double r85036 = atan(r85035);
        double r85037 = r85033 * r85033;
        double r85038 = pow(r85036, r85037);
        return r85038;
}

Error

Bits error versus a

Derivation

  1. Initial program 31.0

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

  2. Final simplification31.0

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

Reproduce

herbie shell --seed 2019346 +o rules:numerics
(FPCore (a)
  :name "Fuzzer 002"
  :precision binary64
  (pow (atan (fmod a (asin a))) (* a a)))