Henrywood and Agarwal, Equation (13)

Average Error: 59.2 → 34.0

Time: 14.6s

Precision: 64

• could not determine a ground truth for program body

  1. c0 = 2.5667675461719508e+120
  2. w = 2.1728968967176598e-303
  3. h = -3.499023702118064e-166
  4. D = 1.6570728508123302e-279
  5. d = -1.035569136802742e-90
  6. M = 1.7408175636706706e+142

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 r133863 = c0;
        double r133864 = 2.0;
        double r133865 = w;
        double r133866 = r133864 * r133865;
        double r133867 = r133863 / r133866;
        double r133868 = d;
        double r133869 = r133868 * r133868;
        double r133870 = r133863 * r133869;
        double r133871 = h;
        double r133872 = r133865 * r133871;
        double r133873 = D;
        double r133874 = r133873 * r133873;
        double r133875 = r133872 * r133874;
        double r133876 = r133870 / r133875;
        double r133877 = r133876 * r133876;
        double r133878 = M;
        double r133879 = r133878 * r133878;
        double r133880 = r133877 - r133879;
        double r133881 = sqrt(r133880);
        double r133882 = r133876 + r133881;
        double r133883 = r133867 * r133882;
        return r133883;
}

↓

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 r133884 = 0.0;
        double r133885 = cbrt(r133884);
        return r133885;
}

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 35.8

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

4. Applied add-cbrt-cube 35.8

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

5. Applied add-cbrt-cube 42.8

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

6. Applied add-cbrt-cube 42.8

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

7. Applied cbrt-unprod 42.8

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

8. Applied add-cbrt-cube 49.4

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

9. Applied cbrt-undiv 49.8

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

10. Applied cbrt-unprod 49.8

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

11. Simplified 34.0

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

12. Final simplification 34.0

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

Reproduce

herbie shell --seed 2020035 +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))))))