Average Error: 0.1 → 0.1
Time: 21.5s
Precision: 64
\[\sin \left({\left(\sqrt{\tan^{-1}_* \frac{b}{b}}\right)}^{\left(b - a\right)}\right)\]
↓
\[\sin \left({\left(\left|\sqrt[3]{\tan^{-1}_* \frac{b}{b}}\right|\right)}^{\left(b - a\right)} \cdot {\left(\sqrt{\sqrt[3]{\tan^{-1}_* \frac{b}{b}}}\right)}^{\left(b - a\right)}\right)\]
\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|\right)}^{\left(b - a\right)} \cdot {\left(\sqrt{\sqrt[3]{\tan^{-1}_* \frac{b}{b}}}\right)}^{\left(b - a\right)}\right)
double f(double a, double b) {
        double r24587 = b;
        double r24588 = atan2(r24587, r24587);
        double r24589 = sqrt(r24588);
        double r24590 = a;
        double r24591 = r24587 - r24590;
        double r24592 = pow(r24589, r24591);
        double r24593 = sin(r24592);
        return r24593;
}
↓
double f(double a, double b) {
        double r24594 = b;
        double r24595 = atan2(r24594, r24594);
        double r24596 = cbrt(r24595);
        double r24597 = fabs(r24596);
        double r24598 = a;
        double r24599 = r24594 - r24598;
        double r24600 = pow(r24597, r24599);
        double r24601 = sqrt(r24596);
        double r24602 = pow(r24601, r24599);
        double r24603 = r24600 * r24602;
        double r24604 = sin(r24603);
        return r24604;
}

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. Final simplification0.1

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

Reproduce

herbie shell --seed 2019325 +o rules:numerics
(FPCore (a b)
  :name "Random Jason Timeout Test 003"
  :precision binary64
  (sin (pow (sqrt (atan2 b b)) (- b a))))