Average Error: 0.1 → 0.1
Time: 4.3s
Precision: 64
\[\sin \left({\left(\sqrt{\tan^{-1}_* \frac{b}{b}}\right)}^{\left(b - a\right)}\right)\]
↓
\[\sin \left({\left(\tan^{-1}_* \frac{b}{b}\right)}^{\left(\frac{1}{2} \cdot \left(b - a\right)\right)}\right)\]
\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(\frac{1}{2} \cdot \left(b - a\right)\right)}\right)
double f(double a, double b) {
        double r16144 = b;
        double r16145 = atan2(r16144, r16144);
        double r16146 = sqrt(r16145);
        double r16147 = a;
        double r16148 = r16144 - r16147;
        double r16149 = pow(r16146, r16148);
        double r16150 = sin(r16149);
        return r16150;
}
↓
double f(double a, double b) {
        double r16151 = b;
        double r16152 = atan2(r16151, r16151);
        double r16153 = 0.5;
        double r16154 = a;
        double r16155 = r16151 - r16154;
        double r16156 = r16153 * r16155;
        double r16157 = pow(r16152, r16156);
        double r16158 = sin(r16157);
        return r16158;
}

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 pow1/20.1

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

  4. Applied pow-pow0.1

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

  5. Final simplification0.1

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

Reproduce

herbie shell --seed 2019344 
(FPCore (a b)
  :name "Random Jason Timeout Test 003"
  :precision binary64
  (sin (pow (sqrt (atan2 b b)) (- b a))))