Random Jason Timeout Test 003

Average Error: 0.1 → 0.1

Time: 19.2s

Precision: 64

• could not determine a ground truth for program body

  1. a = 8.335205808559965e+218
  2. b = 1.1248754533781247e-11

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 r3569182 = b;
        double r3569183 = atan2(r3569182, r3569182);
        double r3569184 = sqrt(r3569183);
        double r3569185 = a;
        double r3569186 = r3569182 - r3569185;
        double r3569187 = pow(r3569184, r3569186);
        double r3569188 = sin(r3569187);
        return r3569188;
}

↓

double f(double a, double b) {
        double r3569189 = b;
        double r3569190 = atan2(r3569189, r3569189);
        double r3569191 = 0.5;
        double r3569192 = a;
        double r3569193 = r3569189 - r3569192;
        double r3569194 = r3569191 * r3569193;
        double r3569195 = pow(r3569190, r3569194);
        double r3569196 = sin(r3569195);
        return r3569196;
}

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 2019173 +o rules:numerics
(FPCore (a b)
  :name "Random Jason Timeout Test 003"
  (sin (pow (sqrt (atan2 b b)) (- b a))))