Henrywood and Agarwal, Equation (13)

Average Error: 58.1 → 51.8

Time: 52.9s

Precision: 64

• could not determine a ground truth for program body

  1. c0 = -6.231393320517686e-07
  2. w = 8.208834479867753e-259
  3. h = 3.8069239432935657e-271
  4. D = 1.0036506284230149e-209
  5. d = -3.8930863703004395e+295
  6. M = 8.045344466876928e+99

Math

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

↓

\[\frac{\sqrt[3]{\sqrt[3]{\sqrt{\left(\frac{\left(c0 \cdot \frac{d}{D}\right) \cdot \frac{d}{D}}{w \cdot h} - M\right) \cdot \left(M + \frac{\left(c0 \cdot \frac{d}{D}\right) \cdot \frac{d}{D}}{w \cdot h}\right)} + \frac{\left(c0 \cdot \frac{d}{D}\right) \cdot \frac{d}{D}}{w \cdot h}} \cdot \left(\sqrt[3]{\sqrt{\left(\frac{\left(c0 \cdot \frac{d}{D}\right) \cdot \frac{d}{D}}{w \cdot h} - M\right) \cdot \left(M + \frac{\left(c0 \cdot \frac{d}{D}\right) \cdot \frac{d}{D}}{w \cdot h}\right)} + \frac{\left(c0 \cdot \frac{d}{D}\right) \cdot \frac{d}{D}}{w \cdot h}} \cdot \sqrt[3]{\sqrt{\left(\frac{\left(c0 \cdot \frac{d}{D}\right) \cdot \frac{d}{D}}{w \cdot h} - M\right) \cdot \left(M + \frac{\left(c0 \cdot \frac{d}{D}\right) \cdot \frac{d}{D}}{w \cdot h}\right)} + \frac{\left(c0 \cdot \frac{d}{D}\right) \cdot \frac{d}{D}}{w \cdot h}}\right)} \cdot \left(\sqrt[3]{\sqrt{\left(\frac{\left(c0 \cdot \frac{d}{D}\right) \cdot \frac{d}{D}}{w \cdot h} - M\right) \cdot \left(M + \frac{\left(c0 \cdot \frac{d}{D}\right) \cdot \frac{d}{D}}{w \cdot h}\right)} + \frac{\left(c0 \cdot \frac{d}{D}\right) \cdot \frac{d}{D}}{w \cdot h}} \cdot \sqrt[3]{\sqrt{\left(\frac{\left(c0 \cdot \frac{d}{D}\right) \cdot \frac{d}{D}}{w \cdot h} - M\right) \cdot \left(M + \frac{\left(c0 \cdot \frac{d}{D}\right) \cdot \frac{d}{D}}{w \cdot h}\right)} + \frac{\left(c0 \cdot \frac{d}{D}\right) \cdot \frac{d}{D}}{w \cdot h}}\right)}{w} \cdot \frac{c0}{2}\]

C

double f(double c0, double w, double h, double D, double d, double M) {
        double r5797003 = c0;
        double r5797004 = 2.0;
        double r5797005 = w;
        double r5797006 = r5797004 * r5797005;
        double r5797007 = r5797003 / r5797006;
        double r5797008 = d;
        double r5797009 = r5797008 * r5797008;
        double r5797010 = r5797003 * r5797009;
        double r5797011 = h;
        double r5797012 = r5797005 * r5797011;
        double r5797013 = D;
        double r5797014 = r5797013 * r5797013;
        double r5797015 = r5797012 * r5797014;
        double r5797016 = r5797010 / r5797015;
        double r5797017 = r5797016 * r5797016;
        double r5797018 = M;
        double r5797019 = r5797018 * r5797018;
        double r5797020 = r5797017 - r5797019;
        double r5797021 = sqrt(r5797020);
        double r5797022 = r5797016 + r5797021;
        double r5797023 = r5797007 * r5797022;
        return r5797023;
}

↓

double f(double c0, double w, double h, double D, double d, double M) {
        double r5797024 = c0;
        double r5797025 = d;
        double r5797026 = D;
        double r5797027 = r5797025 / r5797026;
        double r5797028 = r5797024 * r5797027;
        double r5797029 = r5797028 * r5797027;
        double r5797030 = w;
        double r5797031 = h;
        double r5797032 = r5797030 * r5797031;
        double r5797033 = r5797029 / r5797032;
        double r5797034 = M;
        double r5797035 = r5797033 - r5797034;
        double r5797036 = r5797034 + r5797033;
        double r5797037 = r5797035 * r5797036;
        double r5797038 = sqrt(r5797037);
        double r5797039 = r5797038 + r5797033;
        double r5797040 = cbrt(r5797039);
        double r5797041 = r5797040 * r5797040;
        double r5797042 = r5797040 * r5797041;
        double r5797043 = cbrt(r5797042);
        double r5797044 = r5797043 * r5797041;
        double r5797045 = r5797044 / r5797030;
        double r5797046 = 2.0;
        double r5797047 = r5797024 / r5797046;
        double r5797048 = r5797045 * r5797047;
        return r5797048;
}

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 58.1

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

2. Simplified 51.7

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

4. Applied add-cube-cbrt 51.8

   \[\leadsto \frac{c0}{2} \cdot \frac{\color{blue}{\left(\sqrt[3]{\sqrt{\left(M + \frac{\left(c0 \cdot \frac{d}{D}\right) \cdot \frac{d}{D}}{w \cdot h}\right) \cdot \left(\frac{\left(c0 \cdot \frac{d}{D}\right) \cdot \frac{d}{D}}{w \cdot h} - M\right)} + \frac{\left(c0 \cdot \frac{d}{D}\right) \cdot \frac{d}{D}}{w \cdot h}} \cdot \sqrt[3]{\sqrt{\left(M + \frac{\left(c0 \cdot \frac{d}{D}\right) \cdot \frac{d}{D}}{w \cdot h}\right) \cdot \left(\frac{\left(c0 \cdot \frac{d}{D}\right) \cdot \frac{d}{D}}{w \cdot h} - M\right)} + \frac{\left(c0 \cdot \frac{d}{D}\right) \cdot \frac{d}{D}}{w \cdot h}}\right) \cdot \sqrt[3]{\sqrt{\left(M + \frac{\left(c0 \cdot \frac{d}{D}\right) \cdot \frac{d}{D}}{w \cdot h}\right) \cdot \left(\frac{\left(c0 \cdot \frac{d}{D}\right) \cdot \frac{d}{D}}{w \cdot h} - M\right)} + \frac{\left(c0 \cdot \frac{d}{D}\right) \cdot \frac{d}{D}}{w \cdot h}}}}{w}\]
5. Using strategy rm

6. Applied add-cube-cbrt 51.8

   \[\leadsto \frac{c0}{2} \cdot \frac{\left(\sqrt[3]{\sqrt{\left(M + \frac{\left(c0 \cdot \frac{d}{D}\right) \cdot \frac{d}{D}}{w \cdot h}\right) \cdot \left(\frac{\left(c0 \cdot \frac{d}{D}\right) \cdot \frac{d}{D}}{w \cdot h} - M\right)} + \frac{\left(c0 \cdot \frac{d}{D}\right) \cdot \frac{d}{D}}{w \cdot h}} \cdot \sqrt[3]{\sqrt{\left(M + \frac{\left(c0 \cdot \frac{d}{D}\right) \cdot \frac{d}{D}}{w \cdot h}\right) \cdot \left(\frac{\left(c0 \cdot \frac{d}{D}\right) \cdot \frac{d}{D}}{w \cdot h} - M\right)} + \frac{\left(c0 \cdot \frac{d}{D}\right) \cdot \frac{d}{D}}{w \cdot h}}\right) \cdot \sqrt[3]{\color{blue}{\left(\sqrt[3]{\sqrt{\left(M + \frac{\left(c0 \cdot \frac{d}{D}\right) \cdot \frac{d}{D}}{w \cdot h}\right) \cdot \left(\frac{\left(c0 \cdot \frac{d}{D}\right) \cdot \frac{d}{D}}{w \cdot h} - M\right)} + \frac{\left(c0 \cdot \frac{d}{D}\right) \cdot \frac{d}{D}}{w \cdot h}} \cdot \sqrt[3]{\sqrt{\left(M + \frac{\left(c0 \cdot \frac{d}{D}\right) \cdot \frac{d}{D}}{w \cdot h}\right) \cdot \left(\frac{\left(c0 \cdot \frac{d}{D}\right) \cdot \frac{d}{D}}{w \cdot h} - M\right)} + \frac{\left(c0 \cdot \frac{d}{D}\right) \cdot \frac{d}{D}}{w \cdot h}}\right) \cdot \sqrt[3]{\sqrt{\left(M + \frac{\left(c0 \cdot \frac{d}{D}\right) \cdot \frac{d}{D}}{w \cdot h}\right) \cdot \left(\frac{\left(c0 \cdot \frac{d}{D}\right) \cdot \frac{d}{D}}{w \cdot h} - M\right)} + \frac{\left(c0 \cdot \frac{d}{D}\right) \cdot \frac{d}{D}}{w \cdot h}}}}}{w}\]

7. Final simplification 51.8

   \[\leadsto \frac{\sqrt[3]{\sqrt[3]{\sqrt{\left(\frac{\left(c0 \cdot \frac{d}{D}\right) \cdot \frac{d}{D}}{w \cdot h} - M\right) \cdot \left(M + \frac{\left(c0 \cdot \frac{d}{D}\right) \cdot \frac{d}{D}}{w \cdot h}\right)} + \frac{\left(c0 \cdot \frac{d}{D}\right) \cdot \frac{d}{D}}{w \cdot h}} \cdot \left(\sqrt[3]{\sqrt{\left(\frac{\left(c0 \cdot \frac{d}{D}\right) \cdot \frac{d}{D}}{w \cdot h} - M\right) \cdot \left(M + \frac{\left(c0 \cdot \frac{d}{D}\right) \cdot \frac{d}{D}}{w \cdot h}\right)} + \frac{\left(c0 \cdot \frac{d}{D}\right) \cdot \frac{d}{D}}{w \cdot h}} \cdot \sqrt[3]{\sqrt{\left(\frac{\left(c0 \cdot \frac{d}{D}\right) \cdot \frac{d}{D}}{w \cdot h} - M\right) \cdot \left(M + \frac{\left(c0 \cdot \frac{d}{D}\right) \cdot \frac{d}{D}}{w \cdot h}\right)} + \frac{\left(c0 \cdot \frac{d}{D}\right) \cdot \frac{d}{D}}{w \cdot h}}\right)} \cdot \left(\sqrt[3]{\sqrt{\left(\frac{\left(c0 \cdot \frac{d}{D}\right) \cdot \frac{d}{D}}{w \cdot h} - M\right) \cdot \left(M + \frac{\left(c0 \cdot \frac{d}{D}\right) \cdot \frac{d}{D}}{w \cdot h}\right)} + \frac{\left(c0 \cdot \frac{d}{D}\right) \cdot \frac{d}{D}}{w \cdot h}} \cdot \sqrt[3]{\sqrt{\left(\frac{\left(c0 \cdot \frac{d}{D}\right) \cdot \frac{d}{D}}{w \cdot h} - M\right) \cdot \left(M + \frac{\left(c0 \cdot \frac{d}{D}\right) \cdot \frac{d}{D}}{w \cdot h}\right)} + \frac{\left(c0 \cdot \frac{d}{D}\right) \cdot \frac{d}{D}}{w \cdot h}}\right)}{w} \cdot \frac{c0}{2}\]

Reproduce

herbie shell --seed 2019164 
(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))))))