Average Error: 0.1 → 0.1
Time: 5.0s
Precision: 64
\[\sin \left({\left(\sqrt{\tan^{-1}_* \frac{b}{b}}\right)}^{\left(b - a\right)}\right)\]
↓
\[\mathsf{log1p}\left(\mathsf{expm1}\left(\sin \left({\left(\sqrt{\sqrt{\tan^{-1}_* \frac{b}{b}}}\right)}^{\left(b - a\right)} \cdot \mathsf{expm1}\left(\mathsf{log1p}\left({\left(\sqrt{\sqrt{\tan^{-1}_* \frac{b}{b}}}\right)}^{\left(b - a\right)}\right)\right)\right)\right)\right)\]
\sin \left({\left(\sqrt{\tan^{-1}_* \frac{b}{b}}\right)}^{\left(b - a\right)}\right)
↓
\mathsf{log1p}\left(\mathsf{expm1}\left(\sin \left({\left(\sqrt{\sqrt{\tan^{-1}_* \frac{b}{b}}}\right)}^{\left(b - a\right)} \cdot \mathsf{expm1}\left(\mathsf{log1p}\left({\left(\sqrt{\sqrt{\tan^{-1}_* \frac{b}{b}}}\right)}^{\left(b - a\right)}\right)\right)\right)\right)\right)
double f(double a, double b) {
        double r6782 = b;
        double r6783 = atan2(r6782, r6782);
        double r6784 = sqrt(r6783);
        double r6785 = a;
        double r6786 = r6782 - r6785;
        double r6787 = pow(r6784, r6786);
        double r6788 = sin(r6787);
        return r6788;
}
↓
double f(double a, double b) {
        double r6789 = b;
        double r6790 = atan2(r6789, r6789);
        double r6791 = sqrt(r6790);
        double r6792 = sqrt(r6791);
        double r6793 = a;
        double r6794 = r6789 - r6793;
        double r6795 = pow(r6792, r6794);
        double r6796 = log1p(r6795);
        double r6797 = expm1(r6796);
        double r6798 = r6795 * r6797;
        double r6799 = sin(r6798);
        double r6800 = expm1(r6799);
        double r6801 = log1p(r6800);
        return r6801;
}

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. Applied unpow-prod-down0.1

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

  7. Applied expm1-log1p-u0.1

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

  9. Applied log1p-expm1-u0.1

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

  10. Final simplification0.1

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

Reproduce

herbie shell --seed 2019362 +o rules:numerics
(FPCore (a b)
  :name "Random Jason Timeout Test 015"
  :precision binary64
  (sin (pow (sqrt (atan2 b b)) (- b a))))