Fuzzer 002

Average Error: 31.3 → 31.3

Time: 21.2s

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 r1297462 = a;
        double r1297463 = asin(r1297462);
        double r1297464 = fmod(r1297462, r1297463);
        double r1297465 = atan(r1297464);
        double r1297466 = r1297462 * r1297462;
        double r1297467 = pow(r1297465, r1297466);
        return r1297467;
}

↓

double f(double a) {
        double r1297468 = a;
        double r1297469 = asin(r1297468);
        double r1297470 = fmod(r1297468, r1297469);
        double r1297471 = atan(r1297470);
        double r1297472 = r1297468 * r1297468;
        double r1297473 = 2.0;
        double r1297474 = r1297472 / r1297473;
        double r1297475 = pow(r1297471, r1297474);
        double r1297476 = r1297475 * r1297475;
        return r1297476;
}

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 sqr-pow 31.3

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

4. Final simplification 31.3

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

Reproduce

herbie shell --seed 2019152 +o rules:numerics
(FPCore (a)
  :name "Fuzzer 002"
  (pow (atan (fmod a (asin a))) (* a a)))