Henrywood and Agarwal, Equation (13)

Average Error: 58.9 → 33.7

Time: 9.1s

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

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

↓

\[\sqrt[3]{0}\]

C

double f(double c0, double w, double h, double D, double d, double M) {
        double r173737 = c0;
        double r173738 = 2.0;
        double r173739 = w;
        double r173740 = r173738 * r173739;
        double r173741 = r173737 / r173740;
        double r173742 = d;
        double r173743 = r173742 * r173742;
        double r173744 = r173737 * r173743;
        double r173745 = h;
        double r173746 = r173739 * r173745;
        double r173747 = D;
        double r173748 = r173747 * r173747;
        double r173749 = r173746 * r173748;
        double r173750 = r173744 / r173749;
        double r173751 = r173750 * r173750;
        double r173752 = M;
        double r173753 = r173752 * r173752;
        double r173754 = r173751 - r173753;
        double r173755 = sqrt(r173754);
        double r173756 = r173750 + r173755;
        double r173757 = r173741 * r173756;
        return r173757;
}

↓

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 r173758 = 0.0;
        double r173759 = cbrt(r173758);
        return r173759;
}

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-cbrt-cube 35.5

   \[\leadsto \frac{c0}{2 \cdot w} \cdot \color{blue}{\sqrt[3]{\left(0 \cdot 0\right) \cdot 0}}\]

5. Applied add-cbrt-cube 42.0

   \[\leadsto \frac{c0}{2 \cdot \color{blue}{\sqrt[3]{\left(w \cdot w\right) \cdot w}}} \cdot \sqrt[3]{\left(0 \cdot 0\right) \cdot 0}\]

6. Applied add-cbrt-cube 42.0

   \[\leadsto \frac{c0}{\color{blue}{\sqrt[3]{\left(2 \cdot 2\right) \cdot 2}} \cdot \sqrt[3]{\left(w \cdot w\right) \cdot w}} \cdot \sqrt[3]{\left(0 \cdot 0\right) \cdot 0}\]

7. Applied cbrt-unprod 42.0

   \[\leadsto \frac{c0}{\color{blue}{\sqrt[3]{\left(\left(2 \cdot 2\right) \cdot 2\right) \cdot \left(\left(w \cdot w\right) \cdot w\right)}}} \cdot \sqrt[3]{\left(0 \cdot 0\right) \cdot 0}\]

8. Applied add-cbrt-cube 48.4

   \[\leadsto \frac{\color{blue}{\sqrt[3]{\left(c0 \cdot c0\right) \cdot c0}}}{\sqrt[3]{\left(\left(2 \cdot 2\right) \cdot 2\right) \cdot \left(\left(w \cdot w\right) \cdot w\right)}} \cdot \sqrt[3]{\left(0 \cdot 0\right) \cdot 0}\]

9. Applied cbrt-undiv 49.0

   \[\leadsto \color{blue}{\sqrt[3]{\frac{\left(c0 \cdot c0\right) \cdot c0}{\left(\left(2 \cdot 2\right) \cdot 2\right) \cdot \left(\left(w \cdot w\right) \cdot w\right)}}} \cdot \sqrt[3]{\left(0 \cdot 0\right) \cdot 0}\]

10. Applied cbrt-unprod 49.0

    \[\leadsto \color{blue}{\sqrt[3]{\frac{\left(c0 \cdot c0\right) \cdot c0}{\left(\left(2 \cdot 2\right) \cdot 2\right) \cdot \left(\left(w \cdot w\right) \cdot w\right)} \cdot \left(\left(0 \cdot 0\right) \cdot 0\right)}}\]

11. Simplified 33.7

    \[\leadsto \sqrt[3]{\color{blue}{0}}\]

12. Final simplification 33.7

    \[\leadsto \sqrt[3]{0}\]

Reproduce

herbie shell --seed 2020018 
(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))))))