Fuzzer 002

Average Error: 30.7 → 30.7

Time: 27.8s

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 r3522575 = a;
        double r3522576 = asin(r3522575);
        double r3522577 = fmod(r3522575, r3522576);
        double r3522578 = atan(r3522577);
        double r3522579 = r3522575 * r3522575;
        double r3522580 = pow(r3522578, r3522579);
        return r3522580;
}

↓

double f(double a) {
        double r3522581 = a;
        double r3522582 = asin(r3522581);
        double r3522583 = fmod(r3522581, r3522582);
        double r3522584 = atan(r3522583);
        double r3522585 = r3522581 * r3522581;
        double r3522586 = 2.0;
        double r3522587 = r3522585 / r3522586;
        double r3522588 = pow(r3522584, r3522587);
        double r3522589 = r3522588 * r3522588;
        return r3522589;
}

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 +o rules:numerics
(FPCore (a)
  :name "Fuzzer 002"
  (pow (atan (fmod a (asin a))) (* a a)))