Random Jason Timeout Test 003

Average Error: 0.1 → 0.1

Time: 24.2s

Precision: 64

• could not determine a ground truth for program body

  1. a = 7.953652505345186e+78
  2. b = 2.911049425072326e-200

Math

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

↓

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

C

double f(double a, double b) {
        double r21213 = b;
        double r21214 = atan2(r21213, r21213);
        double r21215 = sqrt(r21214);
        double r21216 = a;
        double r21217 = r21213 - r21216;
        double r21218 = pow(r21215, r21217);
        double r21219 = sin(r21218);
        return r21219;
}

↓

double f(double a, double b) {
        double r21220 = b;
        double r21221 = atan2(r21220, r21220);
        double r21222 = 0.5;
        double r21223 = a;
        double r21224 = r21220 - r21223;
        double r21225 = r21222 * r21224;
        double r21226 = pow(r21221, r21225);
        double r21227 = sin(r21226);
        return r21227;
}

Error

Bits error versus a

Bits error versus b

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 pow1/2 0.1

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

4. Applied pow-pow 0.1

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

5. Final simplification 0.1

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

Reproduce

herbie shell --seed 2019326 +o rules:numerics
(FPCore (a b)
  :name "Random Jason Timeout Test 003"
  :precision binary64
  (sin (pow (sqrt (atan2 b b)) (- b a))))