Random Jason Timeout Test 003

Average Error: 0.1 → 0.8

Time: 26.7s

Precision: 64

• could not determine a ground truth for program body

  1. a = 6.77703429302794e+199
  2. b = 2.4141069970017172e-21

Math

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

↓

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

C

double f(double a, double b) {
        double r30152 = b;
        double r30153 = atan2(r30152, r30152);
        double r30154 = sqrt(r30153);
        double r30155 = a;
        double r30156 = r30152 - r30155;
        double r30157 = pow(r30154, r30156);
        double r30158 = sin(r30157);
        return r30158;
}

↓

double f(double a, double b) {
        double r30159 = b;
        double r30160 = atan2(r30159, r30159);
        double r30161 = sqrt(r30160);
        double r30162 = sqrt(r30161);
        double r30163 = a;
        double r30164 = r30159 - r30163;
        double r30165 = cbrt(r30164);
        double r30166 = r30165 * r30165;
        double r30167 = pow(r30162, r30166);
        double r30168 = log(r30165);
        double r30169 = exp(r30168);
        double r30170 = pow(r30167, r30169);
        double r30171 = pow(r30162, r30164);
        double r30172 = r30170 * r30171;
        double r30173 = sin(r30172);
        return r30173;
}

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

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

8. Applied pow-unpow 0.1

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

10. Applied add-exp-log 0.8

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

11. Final simplification 0.8

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

Reproduce

herbie shell --seed 2019322 +o rules:numerics
(FPCore (a b)
  :name "Random Jason Timeout Test 003"
  :precision binary64
  (sin (pow (sqrt (atan2 b b)) (- b a))))