Random Jason Timeout Test 015

Average Error: 0.1 → 0.1

Time: 16.5s

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 r18043 = b;
        double r18044 = atan2(r18043, r18043);
        double r18045 = sqrt(r18044);
        double r18046 = a;
        double r18047 = r18043 - r18046;
        double r18048 = pow(r18045, r18047);
        double r18049 = sin(r18048);
        return r18049;
}

↓

double f(double a, double b) {
        double r18050 = b;
        double r18051 = atan2(r18050, r18050);
        double r18052 = cbrt(r18051);
        double r18053 = a;
        double r18054 = r18050 - r18053;
        double r18055 = 0.5;
        double r18056 = r18054 * r18055;
        double r18057 = pow(r18052, r18056);
        double r18058 = r18052 * r18052;
        double r18059 = pow(r18058, r18056);
        double r18060 = r18057 * r18059;
        double r18061 = sin(r18060);
        return r18061;
}

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))))