Average Error: 0.1 → 0.1
Time: 5.3s
Precision: 64
\[\sin \left({\left(\sqrt{\tan^{-1}_* \frac{b}{b}}\right)}^{\left(b - a\right)}\right)\]
↓
\[\sin \left({\left(\sqrt{\sqrt{\tan^{-1}_* \frac{b}{b}}}\right)}^{\left(b - a\right)} \cdot \left({\left(\sqrt{\sqrt{\sqrt[3]{\tan^{-1}_* \frac{b}{b}} \cdot \sqrt[3]{\tan^{-1}_* \frac{b}{b}}}}\right)}^{\left(b - a\right)} \cdot {\left(\sqrt{\sqrt{\sqrt[3]{\tan^{-1}_* \frac{b}{b}}}}\right)}^{\left(b - a\right)}\right)\right)\]
\sin \left({\left(\sqrt{\tan^{-1}_* \frac{b}{b}}\right)}^{\left(b - a\right)}\right)
↓
\sin \left({\left(\sqrt{\sqrt{\tan^{-1}_* \frac{b}{b}}}\right)}^{\left(b - a\right)} \cdot \left({\left(\sqrt{\sqrt{\sqrt[3]{\tan^{-1}_* \frac{b}{b}} \cdot \sqrt[3]{\tan^{-1}_* \frac{b}{b}}}}\right)}^{\left(b - a\right)} \cdot {\left(\sqrt{\sqrt{\sqrt[3]{\tan^{-1}_* \frac{b}{b}}}}\right)}^{\left(b - a\right)}\right)\right)
double f(double a, double b) {
        double r24026 = b;
        double r24027 = atan2(r24026, r24026);
        double r24028 = sqrt(r24027);
        double r24029 = a;
        double r24030 = r24026 - r24029;
        double r24031 = pow(r24028, r24030);
        double r24032 = sin(r24031);
        return r24032;
}
↓
double f(double a, double b) {
        double r24033 = b;
        double r24034 = atan2(r24033, r24033);
        double r24035 = sqrt(r24034);
        double r24036 = sqrt(r24035);
        double r24037 = a;
        double r24038 = r24033 - r24037;
        double r24039 = pow(r24036, r24038);
        double r24040 = cbrt(r24034);
        double r24041 = r24040 * r24040;
        double r24042 = sqrt(r24041);
        double r24043 = sqrt(r24042);
        double r24044 = pow(r24043, r24038);
        double r24045 = sqrt(r24040);
        double r24046 = sqrt(r24045);
        double r24047 = pow(r24046, r24038);
        double r24048 = r24044 * r24047;
        double r24049 = r24039 * r24048;
        double r24050 = sin(r24049);
        return r24050;
}

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 add-cube-cbrt0.1

    \[\leadsto \sin \left({\left(\sqrt{\sqrt{\tan^{-1}_* \frac{b}{b}}}\right)}^{\left(b - a\right)} \cdot {\left(\sqrt{\sqrt{\color{blue}{\left(\sqrt[3]{\tan^{-1}_* \frac{b}{b}} \cdot \sqrt[3]{\tan^{-1}_* \frac{b}{b}}\right) \cdot \sqrt[3]{\tan^{-1}_* \frac{b}{b}}}}}\right)}^{\left(b - a\right)}\right)\]

  8. Applied sqrt-prod0.1

    \[\leadsto \sin \left({\left(\sqrt{\sqrt{\tan^{-1}_* \frac{b}{b}}}\right)}^{\left(b - a\right)} \cdot {\left(\sqrt{\color{blue}{\sqrt{\sqrt[3]{\tan^{-1}_* \frac{b}{b}} \cdot \sqrt[3]{\tan^{-1}_* \frac{b}{b}}} \cdot \sqrt{\sqrt[3]{\tan^{-1}_* \frac{b}{b}}}}}\right)}^{\left(b - a\right)}\right)\]

  9. Applied sqrt-prod0.1

    \[\leadsto \sin \left({\left(\sqrt{\sqrt{\tan^{-1}_* \frac{b}{b}}}\right)}^{\left(b - a\right)} \cdot {\color{blue}{\left(\sqrt{\sqrt{\sqrt[3]{\tan^{-1}_* \frac{b}{b}} \cdot \sqrt[3]{\tan^{-1}_* \frac{b}{b}}}} \cdot \sqrt{\sqrt{\sqrt[3]{\tan^{-1}_* \frac{b}{b}}}}\right)}}^{\left(b - a\right)}\right)\]

  10. Applied unpow-prod-down0.1

    \[\leadsto \sin \left({\left(\sqrt{\sqrt{\tan^{-1}_* \frac{b}{b}}}\right)}^{\left(b - a\right)} \cdot \color{blue}{\left({\left(\sqrt{\sqrt{\sqrt[3]{\tan^{-1}_* \frac{b}{b}} \cdot \sqrt[3]{\tan^{-1}_* \frac{b}{b}}}}\right)}^{\left(b - a\right)} \cdot {\left(\sqrt{\sqrt{\sqrt[3]{\tan^{-1}_* \frac{b}{b}}}}\right)}^{\left(b - a\right)}\right)}\right)\]

  11. Final simplification0.1

    \[\leadsto \sin \left({\left(\sqrt{\sqrt{\tan^{-1}_* \frac{b}{b}}}\right)}^{\left(b - a\right)} \cdot \left({\left(\sqrt{\sqrt{\sqrt[3]{\tan^{-1}_* \frac{b}{b}} \cdot \sqrt[3]{\tan^{-1}_* \frac{b}{b}}}}\right)}^{\left(b - a\right)} \cdot {\left(\sqrt{\sqrt{\sqrt[3]{\tan^{-1}_* \frac{b}{b}}}}\right)}^{\left(b - a\right)}\right)\right)\]

Reproduce

herbie shell --seed 2019347 +o rules:numerics
(FPCore (a b)
  :name "Random Jason Timeout Test 003"
  :precision binary64
  (sin (pow (sqrt (atan2 b b)) (- b a))))