Average Error: 0.1 → 0.1
Time: 3.1s
Precision: 64
\[\sin \left({\left(\sqrt{\tan^{-1}_* \frac{b}{b}}\right)}^{\left(b - a\right)}\right)\]
↓
\[\sin \left(\mathsf{expm1}\left(\mathsf{log1p}\left({\left({\left(\sqrt{\tan^{-1}_* \frac{b}{b}}\right)}^{\frac{1}{2}} \cdot {\left(\sqrt{\tan^{-1}_* \frac{b}{b}}\right)}^{\frac{1}{2}}\right)}^{\left(b - a\right)}\right)\right)\right)\]
\sin \left({\left(\sqrt{\tan^{-1}_* \frac{b}{b}}\right)}^{\left(b - a\right)}\right)
↓
\sin \left(\mathsf{expm1}\left(\mathsf{log1p}\left({\left({\left(\sqrt{\tan^{-1}_* \frac{b}{b}}\right)}^{\frac{1}{2}} \cdot {\left(\sqrt{\tan^{-1}_* \frac{b}{b}}\right)}^{\frac{1}{2}}\right)}^{\left(b - a\right)}\right)\right)\right)
double f(double a, double b) {
        double r17770 = b;
        double r17771 = atan2(r17770, r17770);
        double r17772 = sqrt(r17771);
        double r17773 = a;
        double r17774 = r17770 - r17773;
        double r17775 = pow(r17772, r17774);
        double r17776 = sin(r17775);
        return r17776;
}
↓
double f(double a, double b) {
        double r17777 = b;
        double r17778 = atan2(r17777, r17777);
        double r17779 = sqrt(r17778);
        double r17780 = 0.5;
        double r17781 = pow(r17779, r17780);
        double r17782 = r17781 * r17781;
        double r17783 = a;
        double r17784 = r17777 - r17783;
        double r17785 = pow(r17782, r17784);
        double r17786 = log1p(r17785);
        double r17787 = expm1(r17786);
        double r17788 = sin(r17787);
        return r17788;
}

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-sqr-sqrt0.1

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

  4. Applied sqrt-prod0.1

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

  5. Simplified0.1

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

  6. Simplified0.1

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

  8. Applied expm1-log1p-u0.1

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

  9. Final simplification0.1

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

Reproduce

herbie shell --seed 2020024 +o rules:numerics
(FPCore (a b)
  :name "Random Jason Timeout Test 003"
  :precision binary64
  (sin (pow (sqrt (atan2 b b)) (- b a))))