Fuzzer 002

Average Error: 30.7 → 30.7

Time: 19.1s

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 r3092783 = a;
        double r3092784 = asin(r3092783);
        double r3092785 = fmod(r3092783, r3092784);
        double r3092786 = atan(r3092785);
        double r3092787 = r3092783 * r3092783;
        double r3092788 = pow(r3092786, r3092787);
        return r3092788;
}

↓

double f(double a) {
        double r3092789 = a;
        double r3092790 = asin(r3092789);
        double r3092791 = fmod(r3092789, r3092790);
        double r3092792 = cbrt(r3092791);
        double r3092793 = r3092792 * r3092792;
        double r3092794 = r3092792 * r3092793;
        double r3092795 = atan(r3092794);
        double r3092796 = r3092789 * r3092789;
        double r3092797 = pow(r3092795, r3092796);
        return r3092797;
}

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)))