Fuzzer 002

Average Error: 31.3 → 31.3

Time: 22.9s

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 r3766542 = a;
        double r3766543 = asin(r3766542);
        double r3766544 = fmod(r3766542, r3766543);
        double r3766545 = atan(r3766544);
        double r3766546 = r3766542 * r3766542;
        double r3766547 = pow(r3766545, r3766546);
        return r3766547;
}

↓

double f(double a) {
        double r3766548 = a;
        double r3766549 = asin(r3766548);
        double r3766550 = fmod(r3766548, r3766549);
        double r3766551 = atan(r3766550);
        double r3766552 = r3766548 * r3766548;
        double r3766553 = 2.0;
        double r3766554 = r3766552 / r3766553;
        double r3766555 = pow(r3766551, r3766554);
        double r3766556 = r3766555 * r3766555;
        return r3766556;
}

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 
(FPCore (a)
  :name "Fuzzer 002"
  (pow (atan (fmod a (asin a))) (* a a)))