Random Jason Timeout Test 015

Average Error: 0.1 → 0.1

Time: 21.4s

Precision: 64

• could not determine a ground truth for program body

  1. a = 1.5073988265699047e+58
  2. b = 1.2879098321665655e-149

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 r12513 = b;
        double r12514 = atan2(r12513, r12513);
        double r12515 = sqrt(r12514);
        double r12516 = a;
        double r12517 = r12513 - r12516;
        double r12518 = pow(r12515, r12517);
        double r12519 = sin(r12518);
        return r12519;
}

↓

double f(double a, double b) {
        double r12520 = b;
        double r12521 = atan2(r12520, r12520);
        double r12522 = 0.5;
        double r12523 = a;
        double r12524 = r12520 - r12523;
        double r12525 = r12522 * r12524;
        double r12526 = pow(r12521, r12525);
        double r12527 = sin(r12526);
        return r12527;
}

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 2019209 +o rules:numerics
(FPCore (a b)
  :name "Random Jason Timeout Test 015"
  :precision binary64
  (sin (pow (sqrt (atan2 b b)) (- b a))))