Henrywood and Agarwal, Equation (13)

Average Error: 58.8 → 33.3

Time: 15.6s

Precision: 64

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

• could not determine a ground truth for program body

  1. c0 = 2.8655997710594172e+163
  2. w = 2.102907085087699e-100
  3. h = -2.3018055544130806e-238
  4. D = -2.0549592648782412e-253
  5. d = -3.6495880167778483e-14
  6. M = -3.2698908542786816e+72

Math

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

↓

\[0\]

C

double f(double c0, double w, double h, double D, double d, double M) {
        double r159001 = c0;
        double r159002 = 2.0;
        double r159003 = w;
        double r159004 = r159002 * r159003;
        double r159005 = r159001 / r159004;
        double r159006 = d;
        double r159007 = r159006 * r159006;
        double r159008 = r159001 * r159007;
        double r159009 = h;
        double r159010 = r159003 * r159009;
        double r159011 = D;
        double r159012 = r159011 * r159011;
        double r159013 = r159010 * r159012;
        double r159014 = r159008 / r159013;
        double r159015 = r159014 * r159014;
        double r159016 = M;
        double r159017 = r159016 * r159016;
        double r159018 = r159015 - r159017;
        double r159019 = sqrt(r159018);
        double r159020 = r159014 + r159019;
        double r159021 = r159005 * r159020;
        return r159021;
}

↓

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 r159022 = 0.0;
        return r159022;
}

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 58.8

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

2. Taylor expanded around inf 35.2

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

4. Applied pow1 35.2

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

5. Applied pow1 35.2

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

6. Applied pow-prod-down 35.2

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

7. Simplified 33.3

   \[\leadsto {\color{blue}{0}}^{1}\]

8. Final simplification 33.3

   \[\leadsto 0\]

Reproduce

herbie shell --seed 2019350 
(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))))))