Average Error: 30.9 → 30.9
Time: 15.2s
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 r134076 = a;
        double r134077 = asin(r134076);
        double r134078 = fmod(r134076, r134077);
        double r134079 = atan(r134078);
        double r134080 = r134076 * r134076;
        double r134081 = pow(r134079, r134080);
        return r134081;
}
↓
double f(double a) {
        double r134082 = a;
        double r134083 = asin(r134082);
        double r134084 = fmod(r134082, r134083);
        double r134085 = atan(r134084);
        double r134086 = r134082 * r134082;
        double r134087 = pow(r134085, r134086);
        return r134087;
}

Error

Bits error versus a

Derivation

  1. Initial program 30.9

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

  2. Final simplification30.9

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

Reproduce

herbie shell --seed 2020045 +o rules:numerics
(FPCore (a)
  :name "Fuzzer 002"
  :precision binary64
  (pow (atan (fmod a (asin a))) (* a a)))