Fuzzer 002

Average Error: 30.6 → 30.6

Time: 21.2s

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 r4468099 = a;
        double r4468100 = asin(r4468099);
        double r4468101 = fmod(r4468099, r4468100);
        double r4468102 = atan(r4468101);
        double r4468103 = r4468099 * r4468099;
        double r4468104 = pow(r4468102, r4468103);
        return r4468104;
}

↓

double f(double a) {
        double r4468105 = a;
        double r4468106 = asin(r4468105);
        double r4468107 = fmod(r4468105, r4468106);
        double r4468108 = atan(r4468107);
        double r4468109 = r4468105 * r4468105;
        double r4468110 = 2.0;
        double r4468111 = r4468109 / r4468110;
        double r4468112 = pow(r4468108, r4468111);
        double r4468113 = r4468112 * r4468112;
        return r4468113;
}

Error

Bits error versus a

Derivation

1. Initial program 30.6

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

3. Applied sqr-pow 30.6

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

4. Final simplification 30.6

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

Reproduce

herbie shell --seed 2019162 
(FPCore (a)
  :name "Fuzzer 002"
  (pow (atan (fmod a (asin a))) (* a a)))