Average Error: 31.3 → 31.2
Time: 14.2s
Precision: 64
\[{\left(\tan^{-1} \left(a \bmod \left(\sin^{-1} a\right)\right)\right)}^{\left(a \cdot a\right)}\]
↓
\[{\left(\tan^{-1} \left(a \bmod \left(\sin^{-1} a\right)\right)\right)}^{\left(2 \cdot \frac{a \cdot a}{2}\right)}\]
{\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(2 \cdot \frac{a \cdot a}{2}\right)}
double f(double a) {
        double r114303 = a;
        double r114304 = asin(r114303);
        double r114305 = fmod(r114303, r114304);
        double r114306 = atan(r114305);
        double r114307 = r114303 * r114303;
        double r114308 = pow(r114306, r114307);
        return r114308;
}
↓
double f(double a) {
        double r114309 = a;
        double r114310 = asin(r114309);
        double r114311 = fmod(r114309, r114310);
        double r114312 = atan(r114311);
        double r114313 = 2.0;
        double r114314 = r114309 * r114309;
        double r114315 = r114314 / r114313;
        double r114316 = r114313 * r114315;
        double r114317 = pow(r114312, r114316);
        return r114317;
}

Error

Bits error versus a

Derivation

  1. Initial program 31.3

    \[{\left(\tan^{-1} \left(a \bmod \left(\sin^{-1} a\right)\right)\right)}^{\left(a \cdot a\right)}\]
  2. Using strategy rm

  3. Applied sqr-pow31.2

    \[\leadsto \color{blue}{{\left(\tan^{-1} \left(a \bmod \left(\sin^{-1} a\right)\right)\right)}^{\left(\frac{a \cdot a}{2}\right)} \cdot {\left(\tan^{-1} \left(a \bmod \left(\sin^{-1} a\right)\right)\right)}^{\left(\frac{a \cdot a}{2}\right)}}\]

  4. Final simplification31.2

    \[\leadsto {\left(\tan^{-1} \left(a \bmod \left(\sin^{-1} a\right)\right)\right)}^{\left(2 \cdot \frac{a \cdot a}{2}\right)}\]

Reproduce

herbie shell --seed 2019303 
(FPCore (a)
  :name "Fuzzer 002"
  :precision binary64
  (pow (atan (fmod a (asin a))) (* a a)))