Fuzzer 002

Average Error: 31.3 → 31.2

Time: 24.1s

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 r103900 = a;
        double r103901 = asin(r103900);
        double r103902 = fmod(r103900, r103901);
        double r103903 = atan(r103902);
        double r103904 = r103900 * r103900;
        double r103905 = pow(r103903, r103904);
        return r103905;
}

↓

double f(double a) {
        double r103906 = a;
        double r103907 = asin(r103906);
        double r103908 = fmod(r103906, r103907);
        double r103909 = atan(r103908);
        double r103910 = r103906 * r103906;
        double r103911 = 2.0;
        double r103912 = r103910 / r103911;
        double r103913 = pow(r103909, r103912);
        double r103914 = r103913 * r103913;
        return r103914;
}

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 31.2

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

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 2019303 
(FPCore (a)
  :name "Fuzzer 002"
  :precision binary64
  (pow (atan (fmod a (asin a))) (* a a)))