Average Error: 0.1 → 0.2
Time: 22.2s
Precision: 64
\[\sin \left({\left(\sqrt{\tan^{-1}_* \frac{b}{b}}\right)}^{\left(b - a\right)}\right)\]
↓
\[\sin \left(\log \left(e^{\mathsf{expm1}\left(\mathsf{log1p}\left({\left(\sqrt{\tan^{-1}_* \frac{b}{b}}\right)}^{\left(b - a\right)}\right)\right)}\right)\right)\]
\sin \left({\left(\sqrt{\tan^{-1}_* \frac{b}{b}}\right)}^{\left(b - a\right)}\right)
↓
\sin \left(\log \left(e^{\mathsf{expm1}\left(\mathsf{log1p}\left({\left(\sqrt{\tan^{-1}_* \frac{b}{b}}\right)}^{\left(b - a\right)}\right)\right)}\right)\right)
double f(double a, double b) {
        double r20359 = b;
        double r20360 = atan2(r20359, r20359);
        double r20361 = sqrt(r20360);
        double r20362 = a;
        double r20363 = r20359 - r20362;
        double r20364 = pow(r20361, r20363);
        double r20365 = sin(r20364);
        return r20365;
}
↓
double f(double a, double b) {
        double r20366 = b;
        double r20367 = atan2(r20366, r20366);
        double r20368 = sqrt(r20367);
        double r20369 = a;
        double r20370 = r20366 - r20369;
        double r20371 = pow(r20368, r20370);
        double r20372 = log1p(r20371);
        double r20373 = expm1(r20372);
        double r20374 = exp(r20373);
        double r20375 = log(r20374);
        double r20376 = sin(r20375);
        return r20376;
}

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 add-log-exp0.2

    \[\leadsto \sin \color{blue}{\left(\log \left(e^{{\left(\sqrt{\tan^{-1}_* \frac{b}{b}}\right)}^{\left(b - a\right)}}\right)\right)}\]
  4. Using strategy rm

  5. Applied expm1-log1p-u0.2

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

  6. Final simplification0.2

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

Reproduce

herbie shell --seed 2019235 +o rules:numerics
(FPCore (a b)
  :name "Random Jason Timeout Test 003"
  :precision binary64
  (sin (pow (sqrt (atan2 b b)) (- b a))))