Fuzzer 002

Average Error: 31.0 → 31.0

Time: 20.2s

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 r127946 = a;
        double r127947 = asin(r127946);
        double r127948 = fmod(r127946, r127947);
        double r127949 = atan(r127948);
        double r127950 = r127946 * r127946;
        double r127951 = pow(r127949, r127950);
        return r127951;
}

↓

double f(double a) {
        double r127952 = a;
        double r127953 = asin(r127952);
        double r127954 = fmod(r127952, r127953);
        double r127955 = atan(r127954);
        double r127956 = r127952 * r127952;
        double r127957 = 2.0;
        double r127958 = r127956 / r127957;
        double r127959 = pow(r127955, r127958);
        double r127960 = r127959 * r127959;
        return r127960;
}

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. Using strategy rm

3. Applied sqr-pow 31.0

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

4. Final simplification 31.0

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

Reproduce

herbie shell --seed 2019212 
(FPCore (a)
  :name "Fuzzer 002"
  :precision binary64
  (pow (atan (fmod a (asin a))) (* a a)))