Fuzzer 002

Average Error: 30.7 → 30.7

Time: 16.5s

Precision: 64

Math

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

↓

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

C

double f(double a) {
        double r100998 = a;
        double r100999 = asin(r100998);
        double r101000 = fmod(r100998, r100999);
        double r101001 = atan(r101000);
        double r101002 = r100998 * r100998;
        double r101003 = pow(r101001, r101002);
        return r101003;
}

↓

double f(double a) {
        double r101004 = a;
        double r101005 = asin(r101004);
        double r101006 = fmod(r101004, r101005);
        double r101007 = cbrt(r101006);
        double r101008 = r101007 * r101007;
        double r101009 = r101008 * r101007;
        double r101010 = atan(r101009);
        double r101011 = r101004 * r101004;
        double r101012 = pow(r101010, r101011);
        return r101012;
}

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

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

Reproduce

herbie shell --seed 2019298 
(FPCore (a)
  :name "Fuzzer 002"
  :precision binary64
  (pow (atan (fmod a (asin a))) (* a a)))