Average Error: 31.0 → 31.0
Time: 6.7s
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 r139475 = a;
        double r139476 = asin(r139475);
        double r139477 = fmod(r139475, r139476);
        double r139478 = atan(r139477);
        double r139479 = r139475 * r139475;
        double r139480 = pow(r139478, r139479);
        return r139480;
}
↓
double f(double a) {
        double r139481 = a;
        double r139482 = asin(r139481);
        double r139483 = fmod(r139481, r139482);
        double r139484 = atan(r139483);
        double r139485 = r139481 * r139481;
        double r139486 = pow(r139484, r139485);
        return r139486;
}

Error

Bits error versus a

Derivation

  1. Initial program 31.0

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

  2. Final simplification31.0

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

Reproduce

herbie shell --seed 2020060 +o rules:numerics
(FPCore (a)
  :name "Fuzzer 002"
  :precision binary64
  (pow (atan (fmod a (asin a))) (* a a)))