Random Jason Timeout Test 003

Average Error: 0.1 → 0.1

Time: 21.9s

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 r14189 = b;
        double r14190 = atan2(r14189, r14189);
        double r14191 = sqrt(r14190);
        double r14192 = a;
        double r14193 = r14189 - r14192;
        double r14194 = pow(r14191, r14193);
        double r14195 = sin(r14194);
        return r14195;
}

↓

double f(double a, double b) {
        double r14196 = b;
        double r14197 = atan2(r14196, r14196);
        double r14198 = 0.5;
        double r14199 = a;
        double r14200 = r14196 - r14199;
        double r14201 = r14198 * r14200;
        double r14202 = pow(r14197, r14201);
        double r14203 = sin(r14202);
        return r14203;
}

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 003"
  :precision binary64
  (sin (pow (sqrt (atan2 b b)) (- b a))))