Fuzzer 002

Average Error: 30.8 → 30.8

Time: 18.8s

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 r3811083 = a;
        double r3811084 = asin(r3811083);
        double r3811085 = fmod(r3811083, r3811084);
        double r3811086 = atan(r3811085);
        double r3811087 = r3811083 * r3811083;
        double r3811088 = pow(r3811086, r3811087);
        return r3811088;
}

↓

double f(double a) {
        double r3811089 = a;
        double r3811090 = asin(r3811089);
        double r3811091 = fmod(r3811089, r3811090);
        double r3811092 = atan(r3811091);
        double r3811093 = r3811089 * r3811089;
        double r3811094 = 2.0;
        double r3811095 = r3811093 / r3811094;
        double r3811096 = pow(r3811092, r3811095);
        double r3811097 = r3811096 * r3811096;
        return r3811097;
}

Error

Bits error versus a

Derivation

1. Initial program 30.8

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

3. Applied sqr-pow 30.8

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

4. Final simplification 30.8

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

Reproduce

herbie shell --seed 2019164 
(FPCore (a)
  :name "Fuzzer 002"
  (pow (atan (fmod a (asin a))) (* a a)))