Average Error: 0.1 → 0.2
Time: 23.1s
Precision: 64
\[\sin \left({\left(\sqrt{\tan^{-1}_* \frac{b}{b}}\right)}^{\left(b - a\right)}\right)\]
↓
\[\sin \left(\log \left(e^{\mathsf{expm1}\left(\mathsf{log1p}\left({\left(\sqrt{\tan^{-1}_* \frac{b}{b}}\right)}^{\left(b - a\right)}\right)\right)}\right)\right)\]
\sin \left({\left(\sqrt{\tan^{-1}_* \frac{b}{b}}\right)}^{\left(b - a\right)}\right)
↓
\sin \left(\log \left(e^{\mathsf{expm1}\left(\mathsf{log1p}\left({\left(\sqrt{\tan^{-1}_* \frac{b}{b}}\right)}^{\left(b - a\right)}\right)\right)}\right)\right)
double f(double a, double b) {
        double r20095 = b;
        double r20096 = atan2(r20095, r20095);
        double r20097 = sqrt(r20096);
        double r20098 = a;
        double r20099 = r20095 - r20098;
        double r20100 = pow(r20097, r20099);
        double r20101 = sin(r20100);
        return r20101;
}
↓
double f(double a, double b) {
        double r20102 = b;
        double r20103 = atan2(r20102, r20102);
        double r20104 = sqrt(r20103);
        double r20105 = a;
        double r20106 = r20102 - r20105;
        double r20107 = pow(r20104, r20106);
        double r20108 = log1p(r20107);
        double r20109 = expm1(r20108);
        double r20110 = exp(r20109);
        double r20111 = log(r20110);
        double r20112 = sin(r20111);
        return r20112;
}

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 expm1-log1p-u0.2

    \[\leadsto \sin \left(\log \left(e^{\color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left({\left(\sqrt{\tan^{-1}_* \frac{b}{b}}\right)}^{\left(b - a\right)}\right)\right)}}\right)\right)\]

  6. Final simplification0.2

    \[\leadsto \sin \left(\log \left(e^{\mathsf{expm1}\left(\mathsf{log1p}\left({\left(\sqrt{\tan^{-1}_* \frac{b}{b}}\right)}^{\left(b - a\right)}\right)\right)}\right)\right)\]

Reproduce

herbie shell --seed 2019235 +o rules:numerics
(FPCore (a b)
  :name "Random Jason Timeout Test 015"
  :precision binary64
  (sin (pow (sqrt (atan2 b b)) (- b a))))