Fuzzer 002

Average Error: 31.1 → 31.0

Time: 6.3s

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 r101879 = a;
        double r101880 = asin(r101879);
        double r101881 = fmod(r101879, r101880);
        double r101882 = atan(r101881);
        double r101883 = r101879 * r101879;
        double r101884 = pow(r101882, r101883);
        return r101884;
}

↓

double f(double a) {
        double r101885 = a;
        double r101886 = asin(r101885);
        double r101887 = fmod(r101885, r101886);
        double r101888 = atan(r101887);
        double r101889 = r101885 * r101885;
        double r101890 = 2.0;
        double r101891 = r101889 / r101890;
        double r101892 = pow(r101888, r101891);
        double r101893 = r101892 * r101892;
        return r101893;
}

Error

Bits error versus a

Derivation

1. Initial program 31.1

   \[{\left(\tan^{-1} \left(a \bmod \left(\sin^{-1} a\right)\right)\right)}^{\left(a \cdot a\right)}\]
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 2020065 
(FPCore (a)
  :name "Fuzzer 002"
  :precision binary64
  (pow (atan (fmod a (asin a))) (* a a)))