Fuzzer 002

Average Error: 30.6 → 30.6

Time: 8.3s

Precision: 64

Math

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

↓

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

C

double f(double a) {
        double r84764 = a;
        double r84765 = asin(r84764);
        double r84766 = fmod(r84764, r84765);
        double r84767 = atan(r84766);
        double r84768 = r84764 * r84764;
        double r84769 = pow(r84767, r84768);
        return r84769;
}

↓

double f(double a) {
        double r84770 = a;
        double r84771 = asin(r84770);
        double r84772 = fmod(r84770, r84771);
        double r84773 = sqrt(r84772);
        double r84774 = r84773 * r84773;
        double r84775 = atan(r84774);
        double r84776 = r84770 * r84770;
        double r84777 = pow(r84775, r84776);
        return r84777;
}

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 add-sqr-sqrt 30.6

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

4. Final simplification 30.6

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

Reproduce

herbie shell --seed 2020036 +o rules:numerics
(FPCore (a)
  :name "Fuzzer 002"
  :precision binary64
  (pow (atan (fmod a (asin a))) (* a a)))