Average Error: 0.1 → 0.1
Time: 17.8s
Precision: 64
\[\sin \left({\left(\sqrt{\tan^{-1}_* \frac{b}{b}}\right)}^{\left(b - a\right)}\right)\]
↓
\[\sin \left({\left({\left(\tan^{-1}_* \frac{b}{b}\right)}^{\left(\frac{1}{\sqrt[3]{2} \cdot \sqrt[3]{2}}\right)}\right)}^{\left(\frac{b - a}{\sqrt[3]{2}}\right)}\right)\]
\sin \left({\left(\sqrt{\tan^{-1}_* \frac{b}{b}}\right)}^{\left(b - a\right)}\right)
↓
\sin \left({\left({\left(\tan^{-1}_* \frac{b}{b}\right)}^{\left(\frac{1}{\sqrt[3]{2} \cdot \sqrt[3]{2}}\right)}\right)}^{\left(\frac{b - a}{\sqrt[3]{2}}\right)}\right)
double f(double a, double b) {
        double r1851540 = b;
        double r1851541 = atan2(r1851540, r1851540);
        double r1851542 = sqrt(r1851541);
        double r1851543 = a;
        double r1851544 = r1851540 - r1851543;
        double r1851545 = pow(r1851542, r1851544);
        double r1851546 = sin(r1851545);
        return r1851546;
}
↓
double f(double a, double b) {
        double r1851547 = b;
        double r1851548 = atan2(r1851547, r1851547);
        double r1851549 = 1.0;
        double r1851550 = 2.0;
        double r1851551 = cbrt(r1851550);
        double r1851552 = r1851551 * r1851551;
        double r1851553 = r1851549 / r1851552;
        double r1851554 = pow(r1851548, r1851553);
        double r1851555 = a;
        double r1851556 = r1851547 - r1851555;
        double r1851557 = r1851556 / r1851551;
        double r1851558 = pow(r1851554, r1851557);
        double r1851559 = sin(r1851558);
        return r1851559;
}

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 pow10.1

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

  4. Applied sqrt-pow10.1

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

  5. Applied pow-pow0.1

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

  6. Simplified0.1

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

  8. Applied add-cube-cbrt0.1

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

  9. Applied *-un-lft-identity0.1

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

  10. Applied times-frac0.1

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

  11. Applied pow-unpow0.1

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

  12. Final simplification0.1

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

Reproduce

herbie shell --seed 2019172 +o rules:numerics
(FPCore (a b)
  :name "Random Jason Timeout Test 003"
  (sin (pow (sqrt (atan2 b b)) (- b a))))