Average Error: 0.1 → 0.1
Time: 5.0s
Precision: 64
\[\sin \left({\left(\sqrt{\tan^{-1}_* \frac{b}{b}}\right)}^{\left(b - a\right)}\right)\]
↓
\[\mathsf{log1p}\left(\mathsf{expm1}\left(\sin \left({\left(\tan^{-1}_* \frac{b}{b}\right)}^{\left(\frac{1}{2} \cdot \left(b - a\right)\right)}\right)\right)\right)\]
\sin \left({\left(\sqrt{\tan^{-1}_* \frac{b}{b}}\right)}^{\left(b - a\right)}\right)
↓
\mathsf{log1p}\left(\mathsf{expm1}\left(\sin \left({\left(\tan^{-1}_* \frac{b}{b}\right)}^{\left(\frac{1}{2} \cdot \left(b - a\right)\right)}\right)\right)\right)
double f(double a, double b) {
        double r7612 = b;
        double r7613 = atan2(r7612, r7612);
        double r7614 = sqrt(r7613);
        double r7615 = a;
        double r7616 = r7612 - r7615;
        double r7617 = pow(r7614, r7616);
        double r7618 = sin(r7617);
        return r7618;
}
↓
double f(double a, double b) {
        double r7619 = b;
        double r7620 = atan2(r7619, r7619);
        double r7621 = 0.5;
        double r7622 = a;
        double r7623 = r7619 - r7622;
        double r7624 = r7621 * r7623;
        double r7625 = pow(r7620, r7624);
        double r7626 = sin(r7625);
        double r7627 = expm1(r7626);
        double r7628 = log1p(r7627);
        return r7628;
}

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 pow1/20.1

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

  4. Applied pow-pow0.1

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

  6. Applied log1p-expm1-u0.1

    \[\leadsto \color{blue}{\mathsf{log1p}\left(\mathsf{expm1}\left(\sin \left({\left(\tan^{-1}_* \frac{b}{b}\right)}^{\left(\frac{1}{2} \cdot \left(b - a\right)\right)}\right)\right)\right)}\]

  7. Final simplification0.1

    \[\leadsto \mathsf{log1p}\left(\mathsf{expm1}\left(\sin \left({\left(\tan^{-1}_* \frac{b}{b}\right)}^{\left(\frac{1}{2} \cdot \left(b - a\right)\right)}\right)\right)\right)\]

Reproduce

herbie shell --seed 2019352 +o rules:numerics
(FPCore (a b)
  :name "Random Jason Timeout Test 015"
  :precision binary64
  (sin (pow (sqrt (atan2 b b)) (- b a))))