Average Error: 0.1 → 0.1
Time: 4.3s
Precision: 64
\[\sin \left({\left(\sqrt{\tan^{-1}_* \frac{b}{b}}\right)}^{\left(b - a\right)}\right)\]
↓
\[\mathsf{log1p}\left(\mathsf{expm1}\left(\sin \left({\left(\sqrt{\tan^{-1}_* \frac{b}{b}}\right)}^{\left(b - a\right)}\right)\right)\right)\]
\sin \left({\left(\sqrt{\tan^{-1}_* \frac{b}{b}}\right)}^{\left(b - a\right)}\right)
↓
\mathsf{log1p}\left(\mathsf{expm1}\left(\sin \left({\left(\sqrt{\tan^{-1}_* \frac{b}{b}}\right)}^{\left(b - a\right)}\right)\right)\right)
double f(double a, double b) {
        double r15973 = b;
        double r15974 = atan2(r15973, r15973);
        double r15975 = sqrt(r15974);
        double r15976 = a;
        double r15977 = r15973 - r15976;
        double r15978 = pow(r15975, r15977);
        double r15979 = sin(r15978);
        return r15979;
}
↓
double f(double a, double b) {
        double r15980 = b;
        double r15981 = atan2(r15980, r15980);
        double r15982 = sqrt(r15981);
        double r15983 = a;
        double r15984 = r15980 - r15983;
        double r15985 = pow(r15982, r15984);
        double r15986 = sin(r15985);
        double r15987 = expm1(r15986);
        double r15988 = log1p(r15987);
        return r15988;
}

Error

Bits error versus a

Bits error versus b

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.1

    \[\sin \left({\left(\sqrt{\tan^{-1}_* \frac{b}{b}}\right)}^{\left(b - a\right)}\right)\]
  2. Using strategy rm

  3. Applied log1p-expm1-u0.1

    \[\leadsto \color{blue}{\mathsf{log1p}\left(\mathsf{expm1}\left(\sin \left({\left(\sqrt{\tan^{-1}_* \frac{b}{b}}\right)}^{\left(b - a\right)}\right)\right)\right)}\]

  4. Final simplification0.1

    \[\leadsto \mathsf{log1p}\left(\mathsf{expm1}\left(\sin \left({\left(\sqrt{\tan^{-1}_* \frac{b}{b}}\right)}^{\left(b - a\right)}\right)\right)\right)\]

Reproduce

herbie shell --seed 2020062 +o rules:numerics
(FPCore (a b)
  :name "Random Jason Timeout Test 003"
  :precision binary64
  (sin (pow (sqrt (atan2 b b)) (- b a))))