Random Jason Timeout Test 003

Average Error: 0.1 → 0.1

Time: 15.3s

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 r29012 = b;
        double r29013 = atan2(r29012, r29012);
        double r29014 = sqrt(r29013);
        double r29015 = a;
        double r29016 = r29012 - r29015;
        double r29017 = pow(r29014, r29016);
        double r29018 = sin(r29017);
        return r29018;
}

↓

double f(double a, double b) {
        double r29019 = b;
        double r29020 = atan2(r29019, r29019);
        double r29021 = cbrt(r29020);
        double r29022 = a;
        double r29023 = r29019 - r29022;
        double r29024 = 0.5;
        double r29025 = r29023 * r29024;
        double r29026 = pow(r29021, r29025);
        double r29027 = r29021 * r29021;
        double r29028 = pow(r29027, r29025);
        double r29029 = r29026 * r29028;
        double r29030 = sin(r29029);
        return r29030;
}

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 003"
  (sin (pow (sqrt (atan2 b b)) (- b a))))