Fuzzer 002

Average Error: 31.3 → 31.3

Time: 19.1s

Precision: 64

Math

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

↓

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

C

double f(double a) {
        double r1627972 = a;
        double r1627973 = asin(r1627972);
        double r1627974 = fmod(r1627972, r1627973);
        double r1627975 = atan(r1627974);
        double r1627976 = r1627972 * r1627972;
        double r1627977 = pow(r1627975, r1627976);
        return r1627977;
}

↓

double f(double a) {
        double r1627978 = a;
        double r1627979 = asin(r1627978);
        double r1627980 = fmod(r1627978, r1627979);
        double r1627981 = atan(r1627980);
        double r1627982 = r1627978 * r1627978;
        double r1627983 = 2.0;
        double r1627984 = r1627982 / r1627983;
        double r1627985 = pow(r1627981, r1627984);
        double r1627986 = r1627985 * r1627985;
        return r1627986;
}

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-pow 31.3

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

4. Final simplification 31.3

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

Reproduce

herbie shell --seed 2019152 
(FPCore (a)
  :name "Fuzzer 002"
  (pow (atan (fmod a (asin a))) (* a a)))