Henrywood and Agarwal, Equation (13)

Average Error: 59.4 → 31.9

Time: 36.5s

Precision: 64

• could not determine a ground truth for program body

  1. c0 = -7.445886573290126e+150
  2. w = 1.4951439070500593e-167
  3. h = 1.1234319124140777e-63
  4. D = 1.4687448223423728e-136
  5. d = -2.9292428393042427e+268
  6. M = -1.737537130071185e+306

Math

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

↓

\[\begin{array}{l} \mathbf{if}\;\frac{c0}{2 \cdot w} \cdot \left(\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) = -\infty \lor \neg \left(\frac{c0}{2 \cdot w} \cdot \left(\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \le 1.227496136123471417705745916826608723776 \cdot 10^{222}\right):\\ \;\;\;\;0\\ \mathbf{else}:\\ \;\;\;\;\frac{c0}{2 \cdot w} \cdot \left(\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right)\\ \end{array}\]

C

double f(double c0, double w, double h, double D, double d, double M) {
        double r121876 = c0;
        double r121877 = 2.0;
        double r121878 = w;
        double r121879 = r121877 * r121878;
        double r121880 = r121876 / r121879;
        double r121881 = d;
        double r121882 = r121881 * r121881;
        double r121883 = r121876 * r121882;
        double r121884 = h;
        double r121885 = r121878 * r121884;
        double r121886 = D;
        double r121887 = r121886 * r121886;
        double r121888 = r121885 * r121887;
        double r121889 = r121883 / r121888;
        double r121890 = r121889 * r121889;
        double r121891 = M;
        double r121892 = r121891 * r121891;
        double r121893 = r121890 - r121892;
        double r121894 = sqrt(r121893);
        double r121895 = r121889 + r121894;
        double r121896 = r121880 * r121895;
        return r121896;
}

↓

double f(double c0, double w, double h, double D, double d, double M) {
        double r121897 = c0;
        double r121898 = 2.0;
        double r121899 = w;
        double r121900 = r121898 * r121899;
        double r121901 = r121897 / r121900;
        double r121902 = d;
        double r121903 = r121902 * r121902;
        double r121904 = r121897 * r121903;
        double r121905 = h;
        double r121906 = r121899 * r121905;
        double r121907 = D;
        double r121908 = r121907 * r121907;
        double r121909 = r121906 * r121908;
        double r121910 = r121904 / r121909;
        double r121911 = r121910 * r121910;
        double r121912 = M;
        double r121913 = r121912 * r121912;
        double r121914 = r121911 - r121913;
        double r121915 = sqrt(r121914);
        double r121916 = r121910 + r121915;
        double r121917 = r121901 * r121916;
        double r121918 = -inf.0;
        bool r121919 = r121917 <= r121918;
        double r121920 = 1.2274961361234714e+222;
        bool r121921 = r121917 <= r121920;
        double r121922 = !r121921;
        bool r121923 = r121919 || r121922;
        double r121924 = 0.0;
        double r121925 = r121923 ? r121924 : r121917;
        return r121925;
}

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. Split input into 2 regimes

2. if (* (/ c0 (* 2.0 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))))) < -inf.0 or 1.2274961361234714e+222 < (* (/ c0 (* 2.0 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)))))

   1. Initial program 63.9

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

   2. Taylor expanded around inf 35.3

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

   4. Applied add-cube-cbrt 35.3

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

   5. Applied associate-*r* 35.3

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

   6. Simplified 33.1

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

   if -inf.0 < (* (/ c0 (* 2.0 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))))) < 1.2274961361234714e+222

   1. Initial program 21.9

      \[\frac{c0}{2 \cdot w} \cdot \left(\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right)\]
3. Recombined 2 regimes into one program.

4. Final simplification 31.9

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{c0}{2 \cdot w} \cdot \left(\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) = -\infty \lor \neg \left(\frac{c0}{2 \cdot w} \cdot \left(\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \le 1.227496136123471417705745916826608723776 \cdot 10^{222}\right):\\ \;\;\;\;0\\ \mathbf{else}:\\ \;\;\;\;\frac{c0}{2 \cdot w} \cdot \left(\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right)\\ \end{array}\]

Reproduce

herbie shell --seed 2019208 +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))))))