Average Error: 0.2 → 0.2
Time: 11.5s
Precision: 64
\[\sin \left({\left(\sqrt{\tan^{-1}_* \frac{b}{b}}\right)}^{\left(b - a\right)}\right)\]
↓
\[\mathsf{expm1}\left(\mathsf{log1p}\left(\sin \left({\left(\sqrt{\tan^{-1}_* \frac{b}{b}}\right)}^{\left(b - a\right)}\right)\right)\right)\]
\sin \left({\left(\sqrt{\tan^{-1}_* \frac{b}{b}}\right)}^{\left(b - a\right)}\right)
↓
\mathsf{expm1}\left(\mathsf{log1p}\left(\sin \left({\left(\sqrt{\tan^{-1}_* \frac{b}{b}}\right)}^{\left(b - a\right)}\right)\right)\right)
double f(double a, double b) {
        double r3573 = b;
        double r3574 = atan2(r3573, r3573);
        double r3575 = sqrt(r3574);
        double r3576 = a;
        double r3577 = r3573 - r3576;
        double r3578 = pow(r3575, r3577);
        double r3579 = sin(r3578);
        return r3579;
}
↓
double f(double a, double b) {
        double r3580 = b;
        double r3581 = atan2(r3580, r3580);
        double r3582 = sqrt(r3581);
        double r3583 = a;
        double r3584 = r3580 - r3583;
        double r3585 = pow(r3582, r3584);
        double r3586 = sin(r3585);
        double r3587 = log1p(r3586);
        double r3588 = expm1(r3587);
        return r3588;
}

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 0.2

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

  3. Applied expm1-log1p-u0.2

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

  4. Final simplification0.2

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

Reproduce

herbie shell --seed 2020046 +o rules:numerics
(FPCore (a b)
  :name "Random Jason Timeout Test 015"
  :precision binary64
  (sin (pow (sqrt (atan2 b b)) (- b a))))