Fuzzer 002

Average Error: 30.7 → 30.7

Time: 30.6s

Precision: 64

Math

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

↓

\[{\left(\tan^{-1} \left(\sqrt[3]{\left(a \bmod \left(\sin^{-1} a\right)\right)} \cdot \left(\sqrt[3]{\left(a \bmod \left(\sin^{-1} a\right)\right)} \cdot \sqrt[3]{\left(a \bmod \left(\sin^{-1} a\right)\right)}\right)\right)\right)}^{\left(a \cdot a\right)}\]

C

double f(double a) {
        double r3605016 = a;
        double r3605017 = asin(r3605016);
        double r3605018 = fmod(r3605016, r3605017);
        double r3605019 = atan(r3605018);
        double r3605020 = r3605016 * r3605016;
        double r3605021 = pow(r3605019, r3605020);
        return r3605021;
}

↓

double f(double a) {
        double r3605022 = a;
        double r3605023 = asin(r3605022);
        double r3605024 = fmod(r3605022, r3605023);
        double r3605025 = cbrt(r3605024);
        double r3605026 = r3605025 * r3605025;
        double r3605027 = r3605025 * r3605026;
        double r3605028 = atan(r3605027);
        double r3605029 = r3605022 * r3605022;
        double r3605030 = pow(r3605028, r3605029);
        return r3605030;
}

Error

Bits error versus a

Derivation

1. Initial program 30.7

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

3. Applied add-cube-cbrt 30.7

   \[\leadsto {\left(\tan^{-1} \color{blue}{\left(\left(\sqrt[3]{\left(a \bmod \left(\sin^{-1} a\right)\right)} \cdot \sqrt[3]{\left(a \bmod \left(\sin^{-1} a\right)\right)}\right) \cdot \sqrt[3]{\left(a \bmod \left(\sin^{-1} a\right)\right)}\right)}\right)}^{\left(a \cdot a\right)}\]

4. Final simplification 30.7

   \[\leadsto {\left(\tan^{-1} \left(\sqrt[3]{\left(a \bmod \left(\sin^{-1} a\right)\right)} \cdot \left(\sqrt[3]{\left(a \bmod \left(\sin^{-1} a\right)\right)} \cdot \sqrt[3]{\left(a \bmod \left(\sin^{-1} a\right)\right)}\right)\right)\right)}^{\left(a \cdot a\right)}\]

Reproduce

herbie shell --seed 2019168 
(FPCore (a)
  :name "Fuzzer 002"
  (pow (atan (fmod a (asin a))) (* a a)))