Average Error: 0.1 → 0.2
Time: 19.8s
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 r2509932 = b;
        double r2509933 = atan2(r2509932, r2509932);
        double r2509934 = sqrt(r2509933);
        double r2509935 = a;
        double r2509936 = r2509932 - r2509935;
        double r2509937 = pow(r2509934, r2509936);
        double r2509938 = sin(r2509937);
        return r2509938;
}
↓
double f(double a, double b) {
        double r2509939 = b;
        double r2509940 = atan2(r2509939, r2509939);
        double r2509941 = sqrt(r2509940);
        double r2509942 = a;
        double r2509943 = r2509939 - r2509942;
        double r2509944 = pow(r2509941, r2509943);
        double r2509945 = exp(r2509944);
        double r2509946 = sqrt(r2509945);
        double r2509947 = log(r2509946);
        double r2509948 = r2509947 + r2509947;
        double r2509949 = sin(r2509948);
        return r2509949;
}

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 003"
  (sin (pow (sqrt (atan2 b b)) (- b a))))