Average Error: 0.2 → 0.2
Time: 13.1s
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 r22092 = b;
        double r22093 = atan2(r22092, r22092);
        double r22094 = sqrt(r22093);
        double r22095 = a;
        double r22096 = r22092 - r22095;
        double r22097 = pow(r22094, r22096);
        double r22098 = sin(r22097);
        return r22098;
}
↓
double f(double a, double b) {
        double r22099 = b;
        double r22100 = atan2(r22099, r22099);
        double r22101 = sqrt(r22100);
        double r22102 = a;
        double r22103 = r22099 - r22102;
        double r22104 = pow(r22101, r22103);
        double r22105 = sin(r22104);
        double r22106 = log1p(r22105);
        double r22107 = expm1(r22106);
        return r22107;
}

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 003"
  :precision binary64
  (sin (pow (sqrt (atan2 b b)) (- b a))))