Fuzzer 002

Average Error: 31.3 → 31.3

Time: 28.7s

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 r14828081 = a;
        double r14828082 = asin(r14828081);
        double r14828083 = fmod(r14828081, r14828082);
        double r14828084 = atan(r14828083);
        double r14828085 = r14828081 * r14828081;
        double r14828086 = pow(r14828084, r14828085);
        return r14828086;
}

↓

double f(double a) {
        double r14828087 = a;
        double r14828088 = asin(r14828087);
        double r14828089 = fmod(r14828087, r14828088);
        double r14828090 = cbrt(r14828089);
        double r14828091 = r14828090 * r14828090;
        double r14828092 = r14828090 * r14828091;
        double r14828093 = atan(r14828092);
        double r14828094 = r14828087 * r14828087;
        double r14828095 = pow(r14828093, r14828094);
        return r14828095;
}

Error

Bits error versus a

Derivation

1. Initial program 31.3

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

3. Applied add-cube-cbrt 31.3

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

4. Final simplification 31.3

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

Reproduce

herbie shell --seed 2019128 
(FPCore (a)
  :name "Fuzzer 002"
  (pow (atan (fmod a (asin a))) (* a a)))