Average Error: 0.1 → 0.1
Time: 4.9s
Precision: 64
\[\sin \left({\left(\sqrt{\tan^{-1}_* \frac{b}{b}}\right)}^{\left(b - a\right)}\right)\]
↓
\[\sin \left({\left({\left(\sqrt{\tan^{-1}_* \frac{b}{b}}\right)}^{\left(\sqrt[3]{b - a} \cdot \sqrt[3]{b - a}\right)}\right)}^{\left(\sqrt[3]{b - a}\right)}\right)\]
\sin \left({\left(\sqrt{\tan^{-1}_* \frac{b}{b}}\right)}^{\left(b - a\right)}\right)
↓
\sin \left({\left({\left(\sqrt{\tan^{-1}_* \frac{b}{b}}\right)}^{\left(\sqrt[3]{b - a} \cdot \sqrt[3]{b - a}\right)}\right)}^{\left(\sqrt[3]{b - a}\right)}\right)
double f(double a, double b) {
        double r21600 = b;
        double r21601 = atan2(r21600, r21600);
        double r21602 = sqrt(r21601);
        double r21603 = a;
        double r21604 = r21600 - r21603;
        double r21605 = pow(r21602, r21604);
        double r21606 = sin(r21605);
        return r21606;
}
↓
double f(double a, double b) {
        double r21607 = b;
        double r21608 = atan2(r21607, r21607);
        double r21609 = sqrt(r21608);
        double r21610 = a;
        double r21611 = r21607 - r21610;
        double r21612 = cbrt(r21611);
        double r21613 = r21612 * r21612;
        double r21614 = pow(r21609, r21613);
        double r21615 = pow(r21614, r21612);
        double r21616 = sin(r21615);
        return r21616;
}

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

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

  4. Applied pow-unpow0.1

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

  5. Final simplification0.1

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

Reproduce

herbie shell --seed 2020001 
(FPCore (a b)
  :name "Random Jason Timeout Test 003"
  :precision binary64
  (sin (pow (sqrt (atan2 b b)) (- b a))))