Average Error: 0.1 → 0.2
Time: 21.3s
Precision: 64
\[\sin \left({\left(\sqrt{\tan^{-1}_* \frac{b}{b}}\right)}^{\left(b - a\right)}\right)\]
↓
\[\sin \left(\log \left(\sqrt{e^{{\left(\sqrt{\tan^{-1}_* \frac{b}{b}}\right)}^{\left(b - a\right)}}}\right) + \log \left(\sqrt{e^{{\left(\sqrt{\tan^{-1}_* \frac{b}{b}}\right)}^{\left(b - a\right)}}}\right)\right)\]
\sin \left({\left(\sqrt{\tan^{-1}_* \frac{b}{b}}\right)}^{\left(b - a\right)}\right)
↓
\sin \left(\log \left(\sqrt{e^{{\left(\sqrt{\tan^{-1}_* \frac{b}{b}}\right)}^{\left(b - a\right)}}}\right) + \log \left(\sqrt{e^{{\left(\sqrt{\tan^{-1}_* \frac{b}{b}}\right)}^{\left(b - a\right)}}}\right)\right)
double f(double a, double b) {
        double r1546480 = b;
        double r1546481 = atan2(r1546480, r1546480);
        double r1546482 = sqrt(r1546481);
        double r1546483 = a;
        double r1546484 = r1546480 - r1546483;
        double r1546485 = pow(r1546482, r1546484);
        double r1546486 = sin(r1546485);
        return r1546486;
}
↓
double f(double a, double b) {
        double r1546487 = b;
        double r1546488 = atan2(r1546487, r1546487);
        double r1546489 = sqrt(r1546488);
        double r1546490 = a;
        double r1546491 = r1546487 - r1546490;
        double r1546492 = pow(r1546489, r1546491);
        double r1546493 = exp(r1546492);
        double r1546494 = sqrt(r1546493);
        double r1546495 = log(r1546494);
        double r1546496 = r1546495 + r1546495;
        double r1546497 = sin(r1546496);
        return r1546497;
}

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-log-exp0.2

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

  5. Applied add-sqr-sqrt0.2

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

  6. Applied log-prod0.2

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

  7. Final simplification0.2

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

Reproduce

herbie shell --seed 2019192 +o rules:numerics
(FPCore (a b)
  :name "Random Jason Timeout Test 015"
  (sin (pow (sqrt (atan2 b b)) (- b a))))