Average Error: 30.7 → 30.7
Time: 14.5s
Precision: 64
\[{\left(\tan^{-1} \left(a \bmod \left(\sin^{-1} a\right)\right)\right)}^{\left(a \cdot a\right)}\]
↓
\[{\left(\tan^{-1} \left(a \bmod \left(\sin^{-1} a\right)\right)\right)}^{\left(\frac{a \cdot a}{2}\right)} \cdot {\left(\tan^{-1} \left(a \bmod \left(\sin^{-1} a\right)\right)\right)}^{\left(\frac{a \cdot a}{2}\right)}\]
{\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)}
double f(double a) {
        double r115122 = a;
        double r115123 = asin(r115122);
        double r115124 = fmod(r115122, r115123);
        double r115125 = atan(r115124);
        double r115126 = r115122 * r115122;
        double r115127 = pow(r115125, r115126);
        return r115127;
}
↓
double f(double a) {
        double r115128 = a;
        double r115129 = asin(r115128);
        double r115130 = fmod(r115128, r115129);
        double r115131 = atan(r115130);
        double r115132 = r115128 * r115128;
        double r115133 = 2.0;
        double r115134 = r115132 / r115133;
        double r115135 = pow(r115131, r115134);
        double r115136 = r115135 * r115135;
        return r115136;
}

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-pow30.7

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

  4. Final simplification30.7

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

Reproduce

herbie shell --seed 2020042 +o rules:numerics
(FPCore (a)
  :name "Fuzzer 002"
  :precision binary64
  (pow (atan (fmod a (asin a))) (* a a)))