Average Error: 30.7 → 30.7
Time: 32.7s
Precision: 64
\[{\left(\tan^{-1} \left(a \bmod \left(\sin^{-1} a\right)\right)\right)}^{\left(a \cdot a\right)}\]
↓
\[{\left(\tan^{-1} \left(\sqrt[3]{\left(a \bmod \left(\sin^{-1} a\right)\right)} \cdot \left(\sqrt[3]{\left(a \bmod \left(\sin^{-1} a\right)\right)} \cdot \sqrt[3]{\left(a \bmod \left(\sin^{-1} a\right)\right)}\right)\right)\right)}^{\left(a \cdot a\right)}\]
{\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)}
double f(double a) {
        double r3829868 = a;
        double r3829869 = asin(r3829868);
        double r3829870 = fmod(r3829868, r3829869);
        double r3829871 = atan(r3829870);
        double r3829872 = r3829868 * r3829868;
        double r3829873 = pow(r3829871, r3829872);
        return r3829873;
}
↓
double f(double a) {
        double r3829874 = a;
        double r3829875 = asin(r3829874);
        double r3829876 = fmod(r3829874, r3829875);
        double r3829877 = cbrt(r3829876);
        double r3829878 = r3829877 * r3829877;
        double r3829879 = r3829877 * r3829878;
        double r3829880 = atan(r3829879);
        double r3829881 = r3829874 * r3829874;
        double r3829882 = pow(r3829880, r3829881);
        return r3829882;
}

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-cbrt30.7

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

  4. Final simplification30.7

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

Reproduce

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