Fuzzer 002

Average Error: 31.2 → 31.2

Time: 58.9s

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 r83658 = a;
        double r83659 = asin(r83658);
        double r83660 = fmod(r83658, r83659);
        double r83661 = atan(r83660);
        double r83662 = r83658 * r83658;
        double r83663 = pow(r83661, r83662);
        return r83663;
}

↓

double f(double a) {
        double r83664 = a;
        double r83665 = asin(r83664);
        double r83666 = fmod(r83664, r83665);
        double r83667 = atan(r83666);
        double r83668 = r83664 * r83664;
        double r83669 = 2.0;
        double r83670 = r83668 / r83669;
        double r83671 = pow(r83667, r83670);
        double r83672 = r83671 * r83671;
        return r83672;
}

Error

Bits error versus a

Derivation

1. Initial program 31.2

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

3. Applied sqr-pow 31.2

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

4. Final simplification 31.2

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

Reproduce

herbie shell --seed 2019323 +o rules:numerics
(FPCore (a)
  :name "Fuzzer 002"
  :precision binary64
  (pow (atan (fmod a (asin a))) (* a a)))