Average Error: 0.1 → 0.1
Time: 3.9s
Precision: 64
\[\sin \left({\left(\sqrt{\tan^{-1}_* \frac{b}{b}}\right)}^{\left(b - a\right)}\right)\]
↓
\[\sin \left(\sqrt[3]{{\left({\left(\sqrt{\tan^{-1}_* \frac{b}{b}}\right)}^{\left(b - a\right)}\right)}^{3}}\right)\]
\sin \left({\left(\sqrt{\tan^{-1}_* \frac{b}{b}}\right)}^{\left(b - a\right)}\right)
↓
\sin \left(\sqrt[3]{{\left({\left(\sqrt{\tan^{-1}_* \frac{b}{b}}\right)}^{\left(b - a\right)}\right)}^{3}}\right)
double f(double a, double b) {
        double r12477 = b;
        double r12478 = atan2(r12477, r12477);
        double r12479 = sqrt(r12478);
        double r12480 = a;
        double r12481 = r12477 - r12480;
        double r12482 = pow(r12479, r12481);
        double r12483 = sin(r12482);
        return r12483;
}
↓
double f(double a, double b) {
        double r12484 = b;
        double r12485 = atan2(r12484, r12484);
        double r12486 = sqrt(r12485);
        double r12487 = a;
        double r12488 = r12484 - r12487;
        double r12489 = pow(r12486, r12488);
        double r12490 = 3.0;
        double r12491 = pow(r12489, r12490);
        double r12492 = cbrt(r12491);
        double r12493 = sin(r12492);
        return r12493;
}

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-cbrt-cube0.1

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

  4. Simplified0.1

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

  5. Final simplification0.1

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

Reproduce

herbie shell --seed 2020020 
(FPCore (a b)
  :name "Random Jason Timeout Test 003"
  :precision binary64
  (sin (pow (sqrt (atan2 b b)) (- b a))))