Fuzzer 002

Average Error: 31.2 → 31.1

Time: 24.5s

Precision: 64

Math

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

↓

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

C

double f(double a) {
        double r3051199 = a;
        double r3051200 = asin(r3051199);
        double r3051201 = fmod(r3051199, r3051200);
        double r3051202 = atan(r3051201);
        double r3051203 = r3051199 * r3051199;
        double r3051204 = pow(r3051202, r3051203);
        return r3051204;
}

↓

double f(double a) {
        double r3051205 = a;
        double r3051206 = asin(r3051205);
        double r3051207 = fmod(r3051205, r3051206);
        double r3051208 = atan(r3051207);
        double r3051209 = r3051205 * r3051205;
        double r3051210 = 2.0;
        double r3051211 = r3051209 / r3051210;
        double r3051212 = pow(r3051208, r3051211);
        double r3051213 = r3051212 * r3051212;
        return r3051213;
}

Error

Bits error versus a

Derivation

1. Initial program 31.2

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

3. Applied sqr-pow 31.1

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

4. Final simplification 31.1

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

Reproduce

herbie shell --seed 2019179 +o rules:numerics
(FPCore (a)
  :name "Fuzzer 002"
  (pow (atan (fmod a (asin a))) (* a a)))