Average Error: 0.1 → 0.1
Time: 21.6s
Precision: 64
\[\sin \left({\left(\sqrt{\tan^{-1}_* \frac{b}{b}}\right)}^{\left(b - a\right)}\right)\]
↓
\[\sin \left({\left(\sqrt[3]{\tan^{-1}_* \frac{b}{b}}\right)}^{\left(\frac{1}{2} \cdot \left(b - a\right)\right)} \cdot {\left(\left|\sqrt[3]{\tan^{-1}_* \frac{b}{b}}\right|\right)}^{\left(b - a\right)}\right)\]
\sin \left({\left(\sqrt{\tan^{-1}_* \frac{b}{b}}\right)}^{\left(b - a\right)}\right)
↓
\sin \left({\left(\sqrt[3]{\tan^{-1}_* \frac{b}{b}}\right)}^{\left(\frac{1}{2} \cdot \left(b - a\right)\right)} \cdot {\left(\left|\sqrt[3]{\tan^{-1}_* \frac{b}{b}}\right|\right)}^{\left(b - a\right)}\right)
double f(double a, double b) {
        double r2721992 = b;
        double r2721993 = atan2(r2721992, r2721992);
        double r2721994 = sqrt(r2721993);
        double r2721995 = a;
        double r2721996 = r2721992 - r2721995;
        double r2721997 = pow(r2721994, r2721996);
        double r2721998 = sin(r2721997);
        return r2721998;
}
↓
double f(double a, double b) {
        double r2721999 = b;
        double r2722000 = atan2(r2721999, r2721999);
        double r2722001 = cbrt(r2722000);
        double r2722002 = 0.5;
        double r2722003 = a;
        double r2722004 = r2721999 - r2722003;
        double r2722005 = r2722002 * r2722004;
        double r2722006 = pow(r2722001, r2722005);
        double r2722007 = fabs(r2722001);
        double r2722008 = pow(r2722007, r2722004);
        double r2722009 = r2722006 * r2722008;
        double r2722010 = sin(r2722009);
        return r2722010;
}

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-cube-cbrt0.1

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

  4. Applied sqrt-prod0.1

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

  5. Applied unpow-prod-down0.1

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

  6. Simplified0.1

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

  8. Applied pow1/20.1

    \[\leadsto \sin \left({\left(\left|\sqrt[3]{\tan^{-1}_* \frac{b}{b}}\right|\right)}^{\left(b - a\right)} \cdot {\color{blue}{\left({\left(\sqrt[3]{\tan^{-1}_* \frac{b}{b}}\right)}^{\frac{1}{2}}\right)}}^{\left(b - a\right)}\right)\]

  9. Applied pow-pow0.1

    \[\leadsto \sin \left({\left(\left|\sqrt[3]{\tan^{-1}_* \frac{b}{b}}\right|\right)}^{\left(b - a\right)} \cdot \color{blue}{{\left(\sqrt[3]{\tan^{-1}_* \frac{b}{b}}\right)}^{\left(\frac{1}{2} \cdot \left(b - a\right)\right)}}\right)\]

  10. Final simplification0.1

    \[\leadsto \sin \left({\left(\sqrt[3]{\tan^{-1}_* \frac{b}{b}}\right)}^{\left(\frac{1}{2} \cdot \left(b - a\right)\right)} \cdot {\left(\left|\sqrt[3]{\tan^{-1}_* \frac{b}{b}}\right|\right)}^{\left(b - a\right)}\right)\]

Reproduce

herbie shell --seed 2019164 +o rules:numerics
(FPCore (a b)
  :name "Random Jason Timeout Test 003"
  (sin (pow (sqrt (atan2 b b)) (- b a))))