Fuzzer 002

Average Error: 31.1 → 31.1

Time: 20.7s

Precision: 64

Math

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

↓

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

C

double f(double a) {
        double r4874375 = a;
        double r4874376 = asin(r4874375);
        double r4874377 = fmod(r4874375, r4874376);
        double r4874378 = atan(r4874377);
        double r4874379 = r4874375 * r4874375;
        double r4874380 = pow(r4874378, r4874379);
        return r4874380;
}

↓

double f(double a) {
        double r4874381 = a;
        double r4874382 = asin(r4874381);
        double r4874383 = fmod(r4874381, r4874382);
        double r4874384 = sqrt(r4874383);
        double r4874385 = r4874384 * r4874384;
        double r4874386 = atan(r4874385);
        double r4874387 = r4874381 * r4874381;
        double r4874388 = pow(r4874386, r4874387);
        return r4874388;
}

Error

Bits error versus a

Derivation

1. Initial program 31.1

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

3. Applied add-sqr-sqrt 31.1

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

4. Final simplification 31.1

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

Reproduce

herbie shell --seed 2019163 
(FPCore (a)
  :name "Fuzzer 002"
  (pow (atan (fmod a (asin a))) (* a a)))