Average Error: 0.1 → 0.1
Time: 22.0s
Precision: 64
\[\sin \left({\left(\sqrt{\tan^{-1}_* \frac{b}{b}}\right)}^{\left(b - a\right)}\right)\]
↓
\[\sin \left({\left(\tan^{-1}_* \frac{b}{b}\right)}^{\left(\frac{\frac{b - a}{2}}{2}\right)} \cdot {\left(\tan^{-1}_* \frac{b}{b}\right)}^{\left(\frac{\frac{b - a}{2}}{2}\right)}\right)\]
\sin \left({\left(\sqrt{\tan^{-1}_* \frac{b}{b}}\right)}^{\left(b - a\right)}\right)
↓
\sin \left({\left(\tan^{-1}_* \frac{b}{b}\right)}^{\left(\frac{\frac{b - a}{2}}{2}\right)} \cdot {\left(\tan^{-1}_* \frac{b}{b}\right)}^{\left(\frac{\frac{b - a}{2}}{2}\right)}\right)
double f(double a, double b) {
        double r1374524 = b;
        double r1374525 = atan2(r1374524, r1374524);
        double r1374526 = sqrt(r1374525);
        double r1374527 = a;
        double r1374528 = r1374524 - r1374527;
        double r1374529 = pow(r1374526, r1374528);
        double r1374530 = sin(r1374529);
        return r1374530;
}
↓
double f(double a, double b) {
        double r1374531 = b;
        double r1374532 = atan2(r1374531, r1374531);
        double r1374533 = a;
        double r1374534 = r1374531 - r1374533;
        double r1374535 = 2.0;
        double r1374536 = r1374534 / r1374535;
        double r1374537 = r1374536 / r1374535;
        double r1374538 = pow(r1374532, r1374537);
        double r1374539 = r1374538 * r1374538;
        double r1374540 = sin(r1374539);
        return r1374540;
}

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 sqrt-pow20.1

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

  5. Applied sqr-pow0.1

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

  6. Final simplification0.1

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

Reproduce

herbie shell --seed 2019158 
(FPCore (a b)
  :name "Random Jason Timeout Test 015"
  (sin (pow (sqrt (atan2 b b)) (- b a))))