Fuzzer 002

Average Error: 31.2 → 31.2

Time: 25.0s

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 r67610 = a;
        double r67611 = asin(r67610);
        double r67612 = fmod(r67610, r67611);
        double r67613 = atan(r67612);
        double r67614 = r67610 * r67610;
        double r67615 = pow(r67613, r67614);
        return r67615;
}

↓

double f(double a) {
        double r67616 = a;
        double r67617 = asin(r67616);
        double r67618 = fmod(r67616, r67617);
        double r67619 = atan(r67618);
        double r67620 = r67616 * r67616;
        double r67621 = 2.0;
        double r67622 = r67620 / r67621;
        double r67623 = pow(r67619, r67622);
        double r67624 = r67623 * r67623;
        return r67624;
}

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 
(FPCore (a)
  :name "Fuzzer 002"
  :precision binary64
  (pow (atan (fmod a (asin a))) (* a a)))