Average Error: 30.8 → 30.8
Time: 5.5s
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 r176302 = a;
        double r176303 = asin(r176302);
        double r176304 = fmod(r176302, r176303);
        double r176305 = atan(r176304);
        double r176306 = r176302 * r176302;
        double r176307 = pow(r176305, r176306);
        return r176307;
}
↓
double f(double a) {
        double r176308 = a;
        double r176309 = asin(r176308);
        double r176310 = fmod(r176308, r176309);
        double r176311 = atan(r176310);
        double r176312 = r176308 * r176308;
        double r176313 = pow(r176311, r176312);
        return r176313;
}

Error

Bits error versus a

Derivation

  1. Initial program 30.8

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

  2. Final simplification30.8

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

Reproduce

herbie shell --seed 2020027 +o rules:numerics
(FPCore (a)
  :name "Fuzzer 002"
  :precision binary64
  (pow (atan (fmod a (asin a))) (* a a)))