Random Jason Timeout Test 015

Average Error: 0.1 → 0.1

Time: 27.5s

Precision: 64

• could not determine a ground truth for program body

  1. a = 1.0362876411490344e+263
  2. b = 9.656044930860567e+126

Math

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

↓

\[\sin \left(\left(\sqrt{{\left(\sqrt{\sqrt{\tan^{-1}_* \frac{b}{b}}}\right)}^{\left(b - a\right)}} \cdot \sqrt{e^{\left(b - a\right) \cdot \left(\frac{1}{4} \cdot \log \left(\tan^{-1}_* \frac{b}{b}\right)\right)}}\right) \cdot {\left(\sqrt{\sqrt{\tan^{-1}_* \frac{b}{b}}}\right)}^{\left(b - a\right)}\right)\]

C

double f(double a, double b) {
        double r975961 = b;
        double r975962 = atan2(r975961, r975961);
        double r975963 = sqrt(r975962);
        double r975964 = a;
        double r975965 = r975961 - r975964;
        double r975966 = pow(r975963, r975965);
        double r975967 = sin(r975966);
        return r975967;
}

↓

double f(double a, double b) {
        double r975968 = b;
        double r975969 = atan2(r975968, r975968);
        double r975970 = sqrt(r975969);
        double r975971 = sqrt(r975970);
        double r975972 = a;
        double r975973 = r975968 - r975972;
        double r975974 = pow(r975971, r975973);
        double r975975 = sqrt(r975974);
        double r975976 = 0.25;
        double r975977 = log(r975969);
        double r975978 = r975976 * r975977;
        double r975979 = r975973 * r975978;
        double r975980 = exp(r975979);
        double r975981 = sqrt(r975980);
        double r975982 = r975975 * r975981;
        double r975983 = r975982 * r975974;
        double r975984 = sin(r975983);
        return r975984;
}

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-sqr-sqrt 0.1

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

8. Taylor expanded around inf 0.1

   \[\leadsto \sin \left(\left(\sqrt{{\left(\sqrt{\sqrt{\tan^{-1}_* \frac{b}{b}}}\right)}^{\left(b - a\right)}} \cdot \color{blue}{\sqrt{{\left({\left(\tan^{-1}_* \frac{b}{b}\right)}^{\frac{1}{4}}\right)}^{\left(b - a\right)}}}\right) \cdot {\left(\sqrt{\sqrt{\tan^{-1}_* \frac{b}{b}}}\right)}^{\left(b - a\right)}\right)\]

9. Simplified 0.1

   \[\leadsto \sin \left(\left(\sqrt{{\left(\sqrt{\sqrt{\tan^{-1}_* \frac{b}{b}}}\right)}^{\left(b - a\right)}} \cdot \color{blue}{\sqrt{e^{\left(b - a\right) \cdot \left(\log \left(\tan^{-1}_* \frac{b}{b}\right) \cdot \frac{1}{4}\right)}}}\right) \cdot {\left(\sqrt{\sqrt{\tan^{-1}_* \frac{b}{b}}}\right)}^{\left(b - a\right)}\right)\]

10. Final simplification 0.1

    \[\leadsto \sin \left(\left(\sqrt{{\left(\sqrt{\sqrt{\tan^{-1}_* \frac{b}{b}}}\right)}^{\left(b - a\right)}} \cdot \sqrt{e^{\left(b - a\right) \cdot \left(\frac{1}{4} \cdot \log \left(\tan^{-1}_* \frac{b}{b}\right)\right)}}\right) \cdot {\left(\sqrt{\sqrt{\tan^{-1}_* \frac{b}{b}}}\right)}^{\left(b - a\right)}\right)\]

Reproduce

herbie shell --seed 2019146 
(FPCore (a b)
  :name "Random Jason Timeout Test 015"
  (sin (pow (sqrt (atan2 b b)) (- b a))))