Random Jason Timeout Test 015

Average Error: 0.1 → 0.1

Time: 23.4s

Precision: 64

• could not determine a ground truth for program body

  1. a = 3.11214772715739e+301
  2. b = 1.3033505323871184e+57

Math

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

↓

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

C

double f(double a, double b) {
        double r1303034 = b;
        double r1303035 = atan2(r1303034, r1303034);
        double r1303036 = sqrt(r1303035);
        double r1303037 = a;
        double r1303038 = r1303034 - r1303037;
        double r1303039 = pow(r1303036, r1303038);
        double r1303040 = sin(r1303039);
        return r1303040;
}

↓

double f(double a, double b) {
        double r1303041 = b;
        double r1303042 = atan2(r1303041, r1303041);
        double r1303043 = sqrt(r1303042);
        double r1303044 = sqrt(r1303043);
        double r1303045 = a;
        double r1303046 = r1303041 - r1303045;
        double r1303047 = cbrt(r1303046);
        double r1303048 = r1303047 * r1303047;
        double r1303049 = pow(r1303044, r1303048);
        double r1303050 = r1303041 + r1303045;
        double r1303051 = r1303046 * r1303050;
        double r1303052 = cbrt(r1303051);
        double r1303053 = cbrt(r1303050);
        double r1303054 = r1303052 / r1303053;
        double r1303055 = pow(r1303049, r1303054);
        double r1303056 = pow(r1303044, r1303046);
        double r1303057 = r1303055 * r1303056;
        double r1303058 = sin(r1303057);
        return r1303058;
}

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

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

8. Applied pow-unpow 0.1

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

10. Applied flip-- 3.9

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

11. Applied cbrt-div 3.9

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

12. Simplified 0.1

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

13. Final simplification 0.1

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

Reproduce

herbie shell --seed 2019171 
(FPCore (a b)
  :name "Random Jason Timeout Test 015"
  (sin (pow (sqrt (atan2 b b)) (- b a))))