Fuzzer 002

Average Error: 30.7 → 30.7

Time: 20.4s

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 r3559073 = a;
        double r3559074 = asin(r3559073);
        double r3559075 = fmod(r3559073, r3559074);
        double r3559076 = atan(r3559075);
        double r3559077 = r3559073 * r3559073;
        double r3559078 = pow(r3559076, r3559077);
        return r3559078;
}

↓

double f(double a) {
        double r3559079 = a;
        double r3559080 = asin(r3559079);
        double r3559081 = fmod(r3559079, r3559080);
        double r3559082 = cbrt(r3559081);
        double r3559083 = r3559082 * r3559082;
        double r3559084 = r3559082 * r3559083;
        double r3559085 = atan(r3559084);
        double r3559086 = r3559079 * r3559079;
        double r3559087 = pow(r3559085, r3559086);
        return r3559087;
}

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 +o rules:numerics
(FPCore (a)
  :name "Fuzzer 002"
  (pow (atan (fmod a (asin a))) (* a a)))