Average Error: 30.6 → 30.6
Time: 5.3s
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 r86025 = a;
        double r86026 = asin(r86025);
        double r86027 = fmod(r86025, r86026);
        double r86028 = atan(r86027);
        double r86029 = r86025 * r86025;
        double r86030 = pow(r86028, r86029);
        return r86030;
}
↓
double f(double a) {
        double r86031 = a;
        double r86032 = asin(r86031);
        double r86033 = fmod(r86031, r86032);
        double r86034 = atan(r86033);
        double r86035 = r86031 * r86031;
        double r86036 = pow(r86034, r86035);
        return r86036;
}

Error

Bits error versus a

Derivation

  1. Initial program 30.6

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

  2. Final simplification30.6

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

Reproduce

herbie shell --seed 2019354 +o rules:numerics
(FPCore (a)
  :name "Fuzzer 002"
  :precision binary64
  (pow (atan (fmod a (asin a))) (* a a)))