Average Error: 0.1 → 0.1
Time: 4.8s
Precision: 64
\[\sin \left({\left(\sqrt{\tan^{-1}_* \frac{b}{b}}\right)}^{\left(b - a\right)}\right)\]
↓
\[\sin \left(e^{\log \left({\left(\sqrt{\tan^{-1}_* \frac{b}{b}}\right)}^{\left(b - a\right)}\right)}\right)\]
\sin \left({\left(\sqrt{\tan^{-1}_* \frac{b}{b}}\right)}^{\left(b - a\right)}\right)
↓
\sin \left(e^{\log \left({\left(\sqrt{\tan^{-1}_* \frac{b}{b}}\right)}^{\left(b - a\right)}\right)}\right)
double f(double a, double b) {
        double r7672 = b;
        double r7673 = atan2(r7672, r7672);
        double r7674 = sqrt(r7673);
        double r7675 = a;
        double r7676 = r7672 - r7675;
        double r7677 = pow(r7674, r7676);
        double r7678 = sin(r7677);
        return r7678;
}
↓
double f(double a, double b) {
        double r7679 = b;
        double r7680 = atan2(r7679, r7679);
        double r7681 = sqrt(r7680);
        double r7682 = a;
        double r7683 = r7679 - r7682;
        double r7684 = pow(r7681, r7683);
        double r7685 = log(r7684);
        double r7686 = exp(r7685);
        double r7687 = sin(r7686);
        return r7687;
}

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-exp-log0.1

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

  4. Applied pow-exp0.1

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

  5. Simplified0.1

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

  6. Final simplification0.1

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

Reproduce

herbie shell --seed 2020039 
(FPCore (a b)
  :name "Random Jason Timeout Test 015"
  :precision binary64
  (sin (pow (sqrt (atan2 b b)) (- b a))))