Average Error: 0.1 → 0.1
Time: 20.7s
Precision: 64
\[\sin \left({\left(\sqrt{\tan^{-1}_* \frac{b}{b}}\right)}^{\left(b - a\right)}\right)\]
↓
\[\sin \left({\left(\tan^{-1}_* \frac{b}{b}\right)}^{\left(\left(b - a\right) \cdot \frac{1}{2}\right)}\right)\]
\sin \left({\left(\sqrt{\tan^{-1}_* \frac{b}{b}}\right)}^{\left(b - a\right)}\right)
↓
\sin \left({\left(\tan^{-1}_* \frac{b}{b}\right)}^{\left(\left(b - a\right) \cdot \frac{1}{2}\right)}\right)
double f(double a, double b) {
        double r2417070 = b;
        double r2417071 = atan2(r2417070, r2417070);
        double r2417072 = sqrt(r2417071);
        double r2417073 = a;
        double r2417074 = r2417070 - r2417073;
        double r2417075 = pow(r2417072, r2417074);
        double r2417076 = sin(r2417075);
        return r2417076;
}
↓
double f(double a, double b) {
        double r2417077 = b;
        double r2417078 = atan2(r2417077, r2417077);
        double r2417079 = a;
        double r2417080 = r2417077 - r2417079;
        double r2417081 = 0.5;
        double r2417082 = r2417080 * r2417081;
        double r2417083 = pow(r2417078, r2417082);
        double r2417084 = sin(r2417083);
        return r2417084;
}

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 pow10.1

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

  4. Applied sqrt-pow10.1

    \[\leadsto \sin \left({\color{blue}{\left({\left(\tan^{-1}_* \frac{b}{b}\right)}^{\left(\frac{1}{2}\right)}\right)}}^{\left(b - a\right)}\right)\]

  5. Applied pow-pow0.1

    \[\leadsto \sin \color{blue}{\left({\left(\tan^{-1}_* \frac{b}{b}\right)}^{\left(\frac{1}{2} \cdot \left(b - a\right)\right)}\right)}\]

  6. Simplified0.1

    \[\leadsto \sin \left({\left(\tan^{-1}_* \frac{b}{b}\right)}^{\color{blue}{\left(\left(b - a\right) \cdot \frac{1}{2}\right)}}\right)\]

  7. Final simplification0.1

    \[\leadsto \sin \left({\left(\tan^{-1}_* \frac{b}{b}\right)}^{\left(\left(b - a\right) \cdot \frac{1}{2}\right)}\right)\]

Reproduce

herbie shell --seed 2019173 +o rules:numerics
(FPCore (a b)
  :name "Random Jason Timeout Test 015"
  (sin (pow (sqrt (atan2 b b)) (- b a))))