Henrywood and Agarwal, Equation (13)

Average Error: 59.1 → 33.2

Time: 11.4s

Precision: 64

• could not determine a ground truth for program body

  1. c0 = -2.2736486955259513e-10
  2. w = 4.3811697035537754e-170
  3. h = 1.2862806256912123e-229
  4. D = 2.5855309822038082e-138
  5. d = -2.3068824554677546e+222
  6. M = 5.352451769654128e+34

Math

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

↓

\[e^{\log 0}\]

C

double f(double c0, double w, double h, double D, double d, double M) {
        double r131895 = c0;
        double r131896 = 2.0;
        double r131897 = w;
        double r131898 = r131896 * r131897;
        double r131899 = r131895 / r131898;
        double r131900 = d;
        double r131901 = r131900 * r131900;
        double r131902 = r131895 * r131901;
        double r131903 = h;
        double r131904 = r131897 * r131903;
        double r131905 = D;
        double r131906 = r131905 * r131905;
        double r131907 = r131904 * r131906;
        double r131908 = r131902 / r131907;
        double r131909 = r131908 * r131908;
        double r131910 = M;
        double r131911 = r131910 * r131910;
        double r131912 = r131909 - r131911;
        double r131913 = sqrt(r131912);
        double r131914 = r131908 + r131913;
        double r131915 = r131899 * r131914;
        return r131915;
}

↓

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 r131916 = 0.0;
        double r131917 = log(r131916);
        double r131918 = exp(r131917);
        return r131918;
}

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 59.1

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

2. Taylor expanded around inf 35.1

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

4. Applied add-exp-log 35.1

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

5. Applied add-exp-log 49.5

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

6. Applied add-exp-log 49.5

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

7. Applied prod-exp 49.5

   \[\leadsto \frac{c0}{\color{blue}{e^{\log 2 + \log w}}} \cdot e^{\log 0}\]

8. Applied add-exp-log 56.7

   \[\leadsto \frac{\color{blue}{e^{\log c0}}}{e^{\log 2 + \log w}} \cdot e^{\log 0}\]

9. Applied div-exp 56.7

   \[\leadsto \color{blue}{e^{\log c0 - \left(\log 2 + \log w\right)}} \cdot e^{\log 0}\]

10. Applied prod-exp 56.2

    \[\leadsto \color{blue}{e^{\left(\log c0 - \left(\log 2 + \log w\right)\right) + \log 0}}\]

11. Simplified 33.2

    \[\leadsto e^{\color{blue}{\log 0}}\]

12. Final simplification 33.2

    \[\leadsto e^{\log 0}\]

Reproduce

herbie shell --seed 2020001 
(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))))))