Average Error: 0.1 → 0.1
Time: 4.4s
Precision: 64
\[\sin \left({\left(\sqrt{\tan^{-1}_* \frac{b}{b}}\right)}^{\left(b - a\right)}\right)\]
↓
\[\sin \left({\left(\left|\sqrt[3]{\tan^{-1}_* \frac{b}{b}}\right| \cdot \sqrt{\sqrt[3]{\tan^{-1}_* \frac{b}{b}}}\right)}^{\left(\frac{b - a}{2}\right)} \cdot {\left(\sqrt{\tan^{-1}_* \frac{b}{b}}\right)}^{\left(\frac{b - a}{2}\right)}\right)\]
\sin \left({\left(\sqrt{\tan^{-1}_* \frac{b}{b}}\right)}^{\left(b - a\right)}\right)
↓
\sin \left({\left(\left|\sqrt[3]{\tan^{-1}_* \frac{b}{b}}\right| \cdot \sqrt{\sqrt[3]{\tan^{-1}_* \frac{b}{b}}}\right)}^{\left(\frac{b - a}{2}\right)} \cdot {\left(\sqrt{\tan^{-1}_* \frac{b}{b}}\right)}^{\left(\frac{b - a}{2}\right)}\right)
double f(double a, double b) {
        double r7050 = b;
        double r7051 = atan2(r7050, r7050);
        double r7052 = sqrt(r7051);
        double r7053 = a;
        double r7054 = r7050 - r7053;
        double r7055 = pow(r7052, r7054);
        double r7056 = sin(r7055);
        return r7056;
}
↓
double f(double a, double b) {
        double r7057 = b;
        double r7058 = atan2(r7057, r7057);
        double r7059 = cbrt(r7058);
        double r7060 = fabs(r7059);
        double r7061 = sqrt(r7059);
        double r7062 = r7060 * r7061;
        double r7063 = a;
        double r7064 = r7057 - r7063;
        double r7065 = 2.0;
        double r7066 = r7064 / r7065;
        double r7067 = pow(r7062, r7066);
        double r7068 = sqrt(r7058);
        double r7069 = pow(r7068, r7066);
        double r7070 = r7067 * r7069;
        double r7071 = sin(r7070);
        return r7071;
}

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 sqr-pow0.1

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

  5. Applied add-cube-cbrt0.1

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

  6. Applied sqrt-prod0.1

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

  7. Simplified0.1

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

  8. Final simplification0.1

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

Reproduce

herbie shell --seed 2019354 
(FPCore (a b)
  :name "Random Jason Timeout Test 015"
  :precision binary64
  (sin (pow (sqrt (atan2 b b)) (- b a))))