Average Error: 31.2 → 31.2
Time: 15.1s
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 r95088 = a;
        double r95089 = asin(r95088);
        double r95090 = fmod(r95088, r95089);
        double r95091 = atan(r95090);
        double r95092 = r95088 * r95088;
        double r95093 = pow(r95091, r95092);
        return r95093;
}
↓
double f(double a) {
        double r95094 = a;
        double r95095 = asin(r95094);
        double r95096 = fmod(r95094, r95095);
        double r95097 = atan(r95096);
        double r95098 = r95094 * r95094;
        double r95099 = pow(r95097, r95098);
        return r95099;
}

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 2019235 +o rules:numerics
(FPCore (a)
  :name "Fuzzer 002"
  :precision binary64
  (pow (atan (fmod a (asin a))) (* a a)))