Random Jason Timeout Test 003

Average Error: 0.1 → 0.1

Time: 16.3s

Precision: 64

• Falling back on racket egraph because egg-herbie package not installed

• could not determine a ground truth for program body

  1. a = 1.61157953583811e+280
  2. b = 1.4915374553808526e-197

Math

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

↓

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

C

double f(double a, double b) {
        double r18856 = b;
        double r18857 = atan2(r18856, r18856);
        double r18858 = sqrt(r18857);
        double r18859 = a;
        double r18860 = r18856 - r18859;
        double r18861 = pow(r18858, r18860);
        double r18862 = sin(r18861);
        return r18862;
}

↓

double f(double a, double b) {
        double r18863 = b;
        double r18864 = atan2(r18863, r18863);
        double r18865 = sqrt(r18864);
        double r18866 = a;
        double r18867 = r18863 - r18866;
        double r18868 = pow(r18865, r18867);
        double r18869 = sin(r18868);
        return r18869;
}

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 *-un-lft-identity 0.1

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

4. Final simplification 0.1

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

Reproduce

herbie shell --seed 2020043 
(FPCore (a b)
  :name "Random Jason Timeout Test 003"
  :precision binary64
  (sin (pow (sqrt (atan2 b b)) (- b a))))