Henrywood and Agarwal, Equation (13)

Average Error: 57.7 → 32.1

Time: 59.1s

Precision: 64

• could not determine a ground truth for program body

  1. c0 = 5.3817823459246724e+156
  2. w = -9.134720524259611e-119
  3. h = 1.0899086701616802e-286
  4. D = 2.6126530325187734e-275
  5. d = 6.007843723589613e+153
  6. M = 3.5838997754907576e+51

Math

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

↓

\[\begin{array}{l} \mathbf{if}\;\frac{c0}{w \cdot 2} \cdot \left(\sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(D \cdot D\right) \cdot \left(w \cdot h\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(D \cdot D\right) \cdot \left(w \cdot h\right)} - M \cdot M} + \frac{c0 \cdot \left(d \cdot d\right)}{\left(D \cdot D\right) \cdot \left(w \cdot h\right)}\right) \le 6.851094008829388 \cdot 10^{+277}:\\ \;\;\;\;\frac{c0}{w \cdot 2} \cdot \left(\sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(D \cdot D\right) \cdot \left(w \cdot h\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(D \cdot D\right) \cdot \left(w \cdot h\right)} - M \cdot M} + \frac{c0 \cdot \left(d \cdot d\right)}{\left(D \cdot D\right) \cdot \left(w \cdot h\right)}\right)\\ \mathbf{else}:\\ \;\;\;\;0\\ \end{array}\]

C

double f(double c0, double w, double h, double D, double d, double M) {
        double r21901896 = c0;
        double r21901897 = 2.0;
        double r21901898 = w;
        double r21901899 = r21901897 * r21901898;
        double r21901900 = r21901896 / r21901899;
        double r21901901 = d;
        double r21901902 = r21901901 * r21901901;
        double r21901903 = r21901896 * r21901902;
        double r21901904 = h;
        double r21901905 = r21901898 * r21901904;
        double r21901906 = D;
        double r21901907 = r21901906 * r21901906;
        double r21901908 = r21901905 * r21901907;
        double r21901909 = r21901903 / r21901908;
        double r21901910 = r21901909 * r21901909;
        double r21901911 = M;
        double r21901912 = r21901911 * r21901911;
        double r21901913 = r21901910 - r21901912;
        double r21901914 = sqrt(r21901913);
        double r21901915 = r21901909 + r21901914;
        double r21901916 = r21901900 * r21901915;
        return r21901916;
}

↓

double f(double c0, double w, double h, double D, double d, double M) {
        double r21901917 = c0;
        double r21901918 = w;
        double r21901919 = 2.0;
        double r21901920 = r21901918 * r21901919;
        double r21901921 = r21901917 / r21901920;
        double r21901922 = d;
        double r21901923 = r21901922 * r21901922;
        double r21901924 = r21901917 * r21901923;
        double r21901925 = D;
        double r21901926 = r21901925 * r21901925;
        double r21901927 = h;
        double r21901928 = r21901918 * r21901927;
        double r21901929 = r21901926 * r21901928;
        double r21901930 = r21901924 / r21901929;
        double r21901931 = r21901930 * r21901930;
        double r21901932 = M;
        double r21901933 = r21901932 * r21901932;
        double r21901934 = r21901931 - r21901933;
        double r21901935 = sqrt(r21901934);
        double r21901936 = r21901935 + r21901930;
        double r21901937 = r21901921 * r21901936;
        double r21901938 = 6.851094008829388e+277;
        bool r21901939 = r21901937 <= r21901938;
        double r21901940 = 0.0;
        double r21901941 = r21901939 ? r21901937 : r21901940;
        return r21901941;
}

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 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))))) < 6.851094008829388e+277

   1. Initial program 32.6

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

   if 6.851094008829388e+277 < (* (/ 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)))))

   1. Initial program 62.7

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

   2. Simplified 56.1

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

   3. Taylor expanded around inf 34.0

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

   4. Taylor expanded around -inf 32.0

      \[\leadsto \color{blue}{0}\]
3. Recombined 2 regimes into one program.

4. Final simplification 32.1

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{c0}{w \cdot 2} \cdot \left(\sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(D \cdot D\right) \cdot \left(w \cdot h\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(D \cdot D\right) \cdot \left(w \cdot h\right)} - M \cdot M} + \frac{c0 \cdot \left(d \cdot d\right)}{\left(D \cdot D\right) \cdot \left(w \cdot h\right)}\right) \le 6.851094008829388 \cdot 10^{+277}:\\ \;\;\;\;\frac{c0}{w \cdot 2} \cdot \left(\sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(D \cdot D\right) \cdot \left(w \cdot h\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(D \cdot D\right) \cdot \left(w \cdot h\right)} - M \cdot M} + \frac{c0 \cdot \left(d \cdot d\right)}{\left(D \cdot D\right) \cdot \left(w \cdot h\right)}\right)\\ \mathbf{else}:\\ \;\;\;\;0\\ \end{array}\]

Reproduce

herbie shell --seed 2019119 +o rules:numerics
(FPCore (c0 w h D d M)
  :name "Henrywood and Agarwal, Equation (13)"
  (* (/ 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))))))