Average Error: 31.4 → 31.4
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 r105100 = a;
        double r105101 = asin(r105100);
        double r105102 = fmod(r105100, r105101);
        double r105103 = atan(r105102);
        double r105104 = r105100 * r105100;
        double r105105 = pow(r105103, r105104);
        return r105105;
}
↓
double f(double a) {
        double r105106 = a;
        double r105107 = asin(r105106);
        double r105108 = fmod(r105106, r105107);
        double r105109 = atan(r105108);
        double r105110 = r105106 * r105106;
        double r105111 = pow(r105109, r105110);
        return r105111;
}

Error

Bits error versus a

Derivation

  1. Initial program 31.4

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

  2. Final simplification31.4

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

Reproduce

herbie shell --seed 2020001 +o rules:numerics
(FPCore (a)
  :name "Fuzzer 002"
  :precision binary64
  (pow (atan (fmod a (asin a))) (* a a)))