Average Error: 31.2 → 31.2
Time: 5.4s
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 r108314 = a;
        double r108315 = asin(r108314);
        double r108316 = fmod(r108314, r108315);
        double r108317 = atan(r108316);
        double r108318 = r108314 * r108314;
        double r108319 = pow(r108317, r108318);
        return r108319;
}
↓
double f(double a) {
        double r108320 = a;
        double r108321 = asin(r108320);
        double r108322 = fmod(r108320, r108321);
        double r108323 = atan(r108322);
        double r108324 = r108320 * r108320;
        double r108325 = pow(r108323, r108324);
        return r108325;
}

Error

Bits error versus a

Derivation

  1. Initial program 31.2

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

  2. Final simplification31.2

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

Reproduce

herbie shell --seed 2020018 +o rules:numerics
(FPCore (a)
  :name "Fuzzer 002"
  :precision binary64
  (pow (atan (fmod a (asin a))) (* a a)))