Random Jason Timeout Test 015

Average Error: 0.1 → 0.1

Time: 15.8s

Precision: 64

• could not determine a ground truth for program body

  1. a = 8.846670165818639e+179
  2. b = 1.4607888352624086e+40

Math

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

↓

\[\sin \left({\left(\sqrt[3]{\tan^{-1}_* \frac{b}{b}}\right)}^{\left(\left(b - a\right) \cdot \frac{1}{2}\right)} \cdot {\left(\sqrt[3]{\tan^{-1}_* \frac{b}{b}} \cdot \sqrt[3]{\tan^{-1}_* \frac{b}{b}}\right)}^{\left(\left(b - a\right) \cdot \frac{1}{2}\right)}\right)\]

C

double f(double a, double b) {
        double r18049 = b;
        double r18050 = atan2(r18049, r18049);
        double r18051 = sqrt(r18050);
        double r18052 = a;
        double r18053 = r18049 - r18052;
        double r18054 = pow(r18051, r18053);
        double r18055 = sin(r18054);
        return r18055;
}

↓

double f(double a, double b) {
        double r18056 = b;
        double r18057 = atan2(r18056, r18056);
        double r18058 = cbrt(r18057);
        double r18059 = a;
        double r18060 = r18056 - r18059;
        double r18061 = 0.5;
        double r18062 = r18060 * r18061;
        double r18063 = pow(r18058, r18062);
        double r18064 = r18058 * r18058;
        double r18065 = pow(r18064, r18062);
        double r18066 = r18063 * r18065;
        double r18067 = sin(r18066);
        return r18067;
}

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. Simplified 0.1

   \[\leadsto \sin \left({\left(\tan^{-1}_* \frac{b}{b}\right)}^{\color{blue}{\left(\left(b - a\right) \cdot \frac{1}{2}\right)}}\right)\]
6. Using strategy rm

7. Applied add-cube-cbrt 0.1

   \[\leadsto \sin \left({\color{blue}{\left(\left(\sqrt[3]{\tan^{-1}_* \frac{b}{b}} \cdot \sqrt[3]{\tan^{-1}_* \frac{b}{b}}\right) \cdot \sqrt[3]{\tan^{-1}_* \frac{b}{b}}\right)}}^{\left(\left(b - a\right) \cdot \frac{1}{2}\right)}\right)\]

8. Applied unpow-prod-down 0.1

   \[\leadsto \sin \color{blue}{\left({\left(\sqrt[3]{\tan^{-1}_* \frac{b}{b}} \cdot \sqrt[3]{\tan^{-1}_* \frac{b}{b}}\right)}^{\left(\left(b - a\right) \cdot \frac{1}{2}\right)} \cdot {\left(\sqrt[3]{\tan^{-1}_* \frac{b}{b}}\right)}^{\left(\left(b - a\right) \cdot \frac{1}{2}\right)}\right)}\]

9. Simplified 0.1

   \[\leadsto \sin \left(\color{blue}{{\left(\sqrt[3]{\tan^{-1}_* \frac{b}{b}} \cdot \sqrt[3]{\tan^{-1}_* \frac{b}{b}}\right)}^{\left(\frac{1}{2} \cdot \left(b - a\right)\right)}} \cdot {\left(\sqrt[3]{\tan^{-1}_* \frac{b}{b}}\right)}^{\left(\left(b - a\right) \cdot \frac{1}{2}\right)}\right)\]

10. Simplified 0.1

    \[\leadsto \sin \left({\left(\sqrt[3]{\tan^{-1}_* \frac{b}{b}} \cdot \sqrt[3]{\tan^{-1}_* \frac{b}{b}}\right)}^{\left(\frac{1}{2} \cdot \left(b - a\right)\right)} \cdot \color{blue}{{\left(\sqrt[3]{\tan^{-1}_* \frac{b}{b}}\right)}^{\left(\frac{1}{2} \cdot \left(b - a\right)\right)}}\right)\]

11. Final simplification 0.1

    \[\leadsto \sin \left({\left(\sqrt[3]{\tan^{-1}_* \frac{b}{b}}\right)}^{\left(\left(b - a\right) \cdot \frac{1}{2}\right)} \cdot {\left(\sqrt[3]{\tan^{-1}_* \frac{b}{b}} \cdot \sqrt[3]{\tan^{-1}_* \frac{b}{b}}\right)}^{\left(\left(b - a\right) \cdot \frac{1}{2}\right)}\right)\]

Reproduce

herbie shell --seed 2019194 
(FPCore (a b)
  :name "Random Jason Timeout Test 015"
  (sin (pow (sqrt (atan2 b b)) (- b a))))