Random Jason Timeout Test 015

Average Error: 0.1 → 0.8

Time: 7.0s

Precision: 64

• could not determine a ground truth for program body

  1. a = 6.77703429302794e+199
  2. b = 2.4141069970017172e-21

Math

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

↓

\[\sin \left({\left({\left(\sqrt{\sqrt{\tan^{-1}_* \frac{b}{b}}}\right)}^{\left(\sqrt[3]{b - a} \cdot \sqrt[3]{b - a}\right)}\right)}^{\left(e^{\log \left(\sqrt[3]{b - a}\right)}\right)} \cdot {\left(\sqrt{\sqrt{\tan^{-1}_* \frac{b}{b}}}\right)}^{\left(b - a\right)}\right)\]

C

double f(double a, double b) {
        double r16386 = b;
        double r16387 = atan2(r16386, r16386);
        double r16388 = sqrt(r16387);
        double r16389 = a;
        double r16390 = r16386 - r16389;
        double r16391 = pow(r16388, r16390);
        double r16392 = sin(r16391);
        return r16392;
}

↓

double f(double a, double b) {
        double r16393 = b;
        double r16394 = atan2(r16393, r16393);
        double r16395 = sqrt(r16394);
        double r16396 = sqrt(r16395);
        double r16397 = a;
        double r16398 = r16393 - r16397;
        double r16399 = cbrt(r16398);
        double r16400 = r16399 * r16399;
        double r16401 = pow(r16396, r16400);
        double r16402 = log(r16399);
        double r16403 = exp(r16402);
        double r16404 = pow(r16401, r16403);
        double r16405 = pow(r16396, r16398);
        double r16406 = r16404 * r16405;
        double r16407 = sin(r16406);
        return r16407;
}

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 add-sqr-sqrt 0.1

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

4. Applied sqrt-prod 0.1

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

5. Applied unpow-prod-down 0.1

   \[\leadsto \sin \color{blue}{\left({\left(\sqrt{\sqrt{\tan^{-1}_* \frac{b}{b}}}\right)}^{\left(b - a\right)} \cdot {\left(\sqrt{\sqrt{\tan^{-1}_* \frac{b}{b}}}\right)}^{\left(b - a\right)}\right)}\]
6. Using strategy rm

7. Applied add-cube-cbrt 0.1

   \[\leadsto \sin \left({\left(\sqrt{\sqrt{\tan^{-1}_* \frac{b}{b}}}\right)}^{\color{blue}{\left(\left(\sqrt[3]{b - a} \cdot \sqrt[3]{b - a}\right) \cdot \sqrt[3]{b - a}\right)}} \cdot {\left(\sqrt{\sqrt{\tan^{-1}_* \frac{b}{b}}}\right)}^{\left(b - a\right)}\right)\]

8. Applied pow-unpow 0.1

   \[\leadsto \sin \left(\color{blue}{{\left({\left(\sqrt{\sqrt{\tan^{-1}_* \frac{b}{b}}}\right)}^{\left(\sqrt[3]{b - a} \cdot \sqrt[3]{b - a}\right)}\right)}^{\left(\sqrt[3]{b - a}\right)}} \cdot {\left(\sqrt{\sqrt{\tan^{-1}_* \frac{b}{b}}}\right)}^{\left(b - a\right)}\right)\]
9. Using strategy rm

10. Applied add-exp-log 0.8

    \[\leadsto \sin \left({\left({\left(\sqrt{\sqrt{\tan^{-1}_* \frac{b}{b}}}\right)}^{\left(\sqrt[3]{b - a} \cdot \sqrt[3]{b - a}\right)}\right)}^{\color{blue}{\left(e^{\log \left(\sqrt[3]{b - a}\right)}\right)}} \cdot {\left(\sqrt{\sqrt{\tan^{-1}_* \frac{b}{b}}}\right)}^{\left(b - a\right)}\right)\]

11. Final simplification 0.8

    \[\leadsto \sin \left({\left({\left(\sqrt{\sqrt{\tan^{-1}_* \frac{b}{b}}}\right)}^{\left(\sqrt[3]{b - a} \cdot \sqrt[3]{b - a}\right)}\right)}^{\left(e^{\log \left(\sqrt[3]{b - a}\right)}\right)} \cdot {\left(\sqrt{\sqrt{\tan^{-1}_* \frac{b}{b}}}\right)}^{\left(b - a\right)}\right)\]

Reproduce

herbie shell --seed 2019322 
(FPCore (a b)
  :name "Random Jason Timeout Test 015"
  :precision binary64
  (sin (pow (sqrt (atan2 b b)) (- b a))))