Henrywood and Agarwal, Equation (13)

Average Error: 59.2 → 33.6

Time: 15.2s

Precision: 64

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

• could not determine a ground truth for program body

  1. c0 = -5.89281512783517e+278
  2. w = 2.0811258398643613e-181
  3. h = 3.3361626967095587e-31
  4. D = 2.213512751948714e-257
  5. d = 1.380969855321755e+45
  6. M = 5.3925603759125965e+159

Math

\[\frac{c0}{2 \cdot w} \cdot \left(\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right)\]

↓

\[\frac{1}{2} \cdot 0\]

C

double f(double c0, double w, double h, double D, double d, double M) {
        double r284722 = c0;
        double r284723 = 2.0;
        double r284724 = w;
        double r284725 = r284723 * r284724;
        double r284726 = r284722 / r284725;
        double r284727 = d;
        double r284728 = r284727 * r284727;
        double r284729 = r284722 * r284728;
        double r284730 = h;
        double r284731 = r284724 * r284730;
        double r284732 = D;
        double r284733 = r284732 * r284732;
        double r284734 = r284731 * r284733;
        double r284735 = r284729 / r284734;
        double r284736 = r284735 * r284735;
        double r284737 = M;
        double r284738 = r284737 * r284737;
        double r284739 = r284736 - r284738;
        double r284740 = sqrt(r284739);
        double r284741 = r284735 + r284740;
        double r284742 = r284726 * r284741;
        return r284742;
}

↓

double f(double __attribute__((unused)) c0, double __attribute__((unused)) w, double __attribute__((unused)) h, double __attribute__((unused)) D, double __attribute__((unused)) d, double __attribute__((unused)) M) {
        double r284743 = 1.0;
        double r284744 = 2.0;
        double r284745 = r284743 / r284744;
        double r284746 = 0.0;
        double r284747 = r284745 * r284746;
        return r284747;
}

Error

Bits error versus c0

Bits error versus w

Bits error versus h

Bits error versus D

Bits error versus d

Bits error versus M

Derivation

1. Initial program 59.2

   \[\frac{c0}{2 \cdot w} \cdot \left(\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right)\]

2. Taylor expanded around inf 35.2

   \[\leadsto \frac{c0}{2 \cdot w} \cdot \color{blue}{0}\]
3. Using strategy rm

4. Applied *-un-lft-identity 35.2

   \[\leadsto \frac{\color{blue}{1 \cdot c0}}{2 \cdot w} \cdot 0\]

5. Applied times-frac 35.2

   \[\leadsto \color{blue}{\left(\frac{1}{2} \cdot \frac{c0}{w}\right)} \cdot 0\]

6. Applied associate-*l* 35.2

   \[\leadsto \color{blue}{\frac{1}{2} \cdot \left(\frac{c0}{w} \cdot 0\right)}\]

7. Simplified 33.6

   \[\leadsto \frac{1}{2} \cdot \color{blue}{0}\]

8. Final simplification 33.6

   \[\leadsto \frac{1}{2} \cdot 0\]

Reproduce

herbie shell --seed 2020047 +o rules:numerics
(FPCore (c0 w h D d M)
  :name "Henrywood and Agarwal, Equation (13)"
  :precision binary64
  (* (/ c0 (* 2 w)) (+ (/ (* c0 (* d d)) (* (* w h) (* D D))) (sqrt (- (* (/ (* c0 (* d d)) (* (* w h) (* D D))) (/ (* c0 (* d d)) (* (* w h) (* D D)))) (* M M))))))