Random Jason Timeout Test 003

Average Error: 0.1 → 0.1

Time: 22.8s

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 r14660 = b;
        double r14661 = atan2(r14660, r14660);
        double r14662 = sqrt(r14661);
        double r14663 = a;
        double r14664 = r14660 - r14663;
        double r14665 = pow(r14662, r14664);
        double r14666 = sin(r14665);
        return r14666;
}

↓

double f(double a, double b) {
        double r14667 = b;
        double r14668 = atan2(r14667, r14667);
        double r14669 = 0.5;
        double r14670 = a;
        double r14671 = r14667 - r14670;
        double r14672 = r14669 * r14671;
        double r14673 = pow(r14668, r14672);
        double r14674 = sin(r14673);
        return r14674;
}

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