Random Jason Timeout Test 003

Average Error: 0.2 → 0.2

Time: 11.5s

Precision: 64

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

• could not determine a ground truth for program body

  1. a = 10920358539895.18
  2. b = 9.278264258908537e-20

Math

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

↓

\[\mathsf{expm1}\left(\mathsf{log1p}\left(\sin \left({\left(\sqrt{\tan^{-1}_* \frac{b}{b}}\right)}^{\left(b - a\right)}\right)\right)\right)\]

C

double f(double a, double b) {
        double r20560 = b;
        double r20561 = atan2(r20560, r20560);
        double r20562 = sqrt(r20561);
        double r20563 = a;
        double r20564 = r20560 - r20563;
        double r20565 = pow(r20562, r20564);
        double r20566 = sin(r20565);
        return r20566;
}

↓

double f(double a, double b) {
        double r20567 = b;
        double r20568 = atan2(r20567, r20567);
        double r20569 = sqrt(r20568);
        double r20570 = a;
        double r20571 = r20567 - r20570;
        double r20572 = pow(r20569, r20571);
        double r20573 = sin(r20572);
        double r20574 = log1p(r20573);
        double r20575 = expm1(r20574);
        return r20575;
}

Error

Bits error versus a

Bits error versus b

Derivation

1. Initial program 0.2

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

3. Applied expm1-log1p-u 0.2

   \[\leadsto \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\sin \left({\left(\sqrt{\tan^{-1}_* \frac{b}{b}}\right)}^{\left(b - a\right)}\right)\right)\right)}\]

4. Final simplification 0.2

   \[\leadsto \mathsf{expm1}\left(\mathsf{log1p}\left(\sin \left({\left(\sqrt{\tan^{-1}_* \frac{b}{b}}\right)}^{\left(b - a\right)}\right)\right)\right)\]

Reproduce

herbie shell --seed 2020046 +o rules:numerics
(FPCore (a b)
  :name "Random Jason Timeout Test 003"
  :precision binary64
  (sin (pow (sqrt (atan2 b b)) (- b a))))