Fuzzer 002

Average Error: 31.2 → 31.2

Time: 24.2s

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 r65313 = a;
        double r65314 = asin(r65313);
        double r65315 = fmod(r65313, r65314);
        double r65316 = atan(r65315);
        double r65317 = r65313 * r65313;
        double r65318 = pow(r65316, r65317);
        return r65318;
}

↓

double f(double a) {
        double r65319 = a;
        double r65320 = asin(r65319);
        double r65321 = fmod(r65319, r65320);
        double r65322 = atan(r65321);
        double r65323 = r65319 * r65319;
        double r65324 = 2.0;
        double r65325 = r65323 / r65324;
        double r65326 = pow(r65322, r65325);
        double r65327 = r65326 * r65326;
        return r65327;
}

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 31.2

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

4. Final simplification 31.2

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

Reproduce

herbie shell --seed 2019323 
(FPCore (a)
  :name "Fuzzer 002"
  :precision binary64
  (pow (atan (fmod a (asin a))) (* a a)))