Fuzzer 002

Average Error: 30.7 → 30.7

Time: 23.6s

Precision: 64

Math

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

↓

\[{\left(\tan^{-1} \left(a \bmod \left(\sin^{-1} a\right)\right)\right)}^{\left(\frac{a \cdot a}{2}\right)} \cdot {\left(\tan^{-1} \left(a \bmod \left(\sin^{-1} a\right)\right)\right)}^{\left(\frac{a \cdot a}{2}\right)}\]

C

double f(double a) {
        double r4913042 = a;
        double r4913043 = asin(r4913042);
        double r4913044 = fmod(r4913042, r4913043);
        double r4913045 = atan(r4913044);
        double r4913046 = r4913042 * r4913042;
        double r4913047 = pow(r4913045, r4913046);
        return r4913047;
}

↓

double f(double a) {
        double r4913048 = a;
        double r4913049 = asin(r4913048);
        double r4913050 = fmod(r4913048, r4913049);
        double r4913051 = atan(r4913050);
        double r4913052 = r4913048 * r4913048;
        double r4913053 = 2.0;
        double r4913054 = r4913052 / r4913053;
        double r4913055 = pow(r4913051, r4913054);
        double r4913056 = r4913055 * r4913055;
        return r4913056;
}

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 sqr-pow 30.7

   \[\leadsto \color{blue}{{\left(\tan^{-1} \left(a \bmod \left(\sin^{-1} a\right)\right)\right)}^{\left(\frac{a \cdot a}{2}\right)} \cdot {\left(\tan^{-1} \left(a \bmod \left(\sin^{-1} a\right)\right)\right)}^{\left(\frac{a \cdot a}{2}\right)}}\]

4. Final simplification 30.7

   \[\leadsto {\left(\tan^{-1} \left(a \bmod \left(\sin^{-1} a\right)\right)\right)}^{\left(\frac{a \cdot a}{2}\right)} \cdot {\left(\tan^{-1} \left(a \bmod \left(\sin^{-1} a\right)\right)\right)}^{\left(\frac{a \cdot a}{2}\right)}\]

Reproduce

herbie shell --seed 2019146 
(FPCore (a)
  :name "Fuzzer 002"
  (pow (atan (fmod a (asin a))) (* a a)))