Henrywood and Agarwal, Equation (13)

Average Error: 58.9 → 33.7

Time: 9.5s

Precision: 64

• could not determine a ground truth for program body

  1. c0 = -8.553249826973297e+197
  2. w = 5.508102111168851e-131
  3. h = 5.434287859603879e-211
  4. D = 2.5284670701262942e-176
  5. d = -5.263120436589766e+72
  6. M = 1.8776756967526624e+149

Math

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

↓

\[0 \cdot \sqrt{0}\]

C

double f(double c0, double w, double h, double D, double d, double M) {
        double r220837 = c0;
        double r220838 = 2.0;
        double r220839 = w;
        double r220840 = r220838 * r220839;
        double r220841 = r220837 / r220840;
        double r220842 = d;
        double r220843 = r220842 * r220842;
        double r220844 = r220837 * r220843;
        double r220845 = h;
        double r220846 = r220839 * r220845;
        double r220847 = D;
        double r220848 = r220847 * r220847;
        double r220849 = r220846 * r220848;
        double r220850 = r220844 / r220849;
        double r220851 = r220850 * r220850;
        double r220852 = M;
        double r220853 = r220852 * r220852;
        double r220854 = r220851 - r220853;
        double r220855 = sqrt(r220854);
        double r220856 = r220850 + r220855;
        double r220857 = r220841 * r220856;
        return r220857;
}

↓

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 r220858 = 0.0;
        double r220859 = sqrt(r220858);
        double r220860 = r220858 * r220859;
        return r220860;
}

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 58.9

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

2. Taylor expanded around inf 35.5

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

4. Applied add-sqr-sqrt 35.5

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

5. Applied associate-*r* 35.5

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

6. Simplified 33.7

   \[\leadsto \color{blue}{0} \cdot \sqrt{0}\]

7. Final simplification 33.7

   \[\leadsto 0 \cdot \sqrt{0}\]

Reproduce

herbie shell --seed 2020018 +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))))))