Henrywood and Agarwal, Equation (13)

Average Error: 59.4 → 32.3

Time: 8.8s

Precision: 64

• could not determine a ground truth for program body

  1. c0 = -1.0250875377805467e+160
  2. w = 8.062839620785231e-159
  3. h = 2.052090366739084e-95
  4. D = 2.4321753330764406e-70
  5. d = 4.626813409956245e+289
  6. M = 4.75641221467429e-290

Math

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

↓

\[\begin{array}{l} \mathbf{if}\;\frac{c0}{2 \cdot w} \cdot \left(\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \le 3.3002661492109247 \cdot 10^{188}:\\ \;\;\;\;\frac{c0}{2 \cdot w} \cdot \left(\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right)\\ \mathbf{else}:\\ \;\;\;\;\sqrt[3]{0}\\ \end{array}\]

C

double f(double c0, double w, double h, double D, double d, double M) {
        double r259184 = c0;
        double r259185 = 2.0;
        double r259186 = w;
        double r259187 = r259185 * r259186;
        double r259188 = r259184 / r259187;
        double r259189 = d;
        double r259190 = r259189 * r259189;
        double r259191 = r259184 * r259190;
        double r259192 = h;
        double r259193 = r259186 * r259192;
        double r259194 = D;
        double r259195 = r259194 * r259194;
        double r259196 = r259193 * r259195;
        double r259197 = r259191 / r259196;
        double r259198 = r259197 * r259197;
        double r259199 = M;
        double r259200 = r259199 * r259199;
        double r259201 = r259198 - r259200;
        double r259202 = sqrt(r259201);
        double r259203 = r259197 + r259202;
        double r259204 = r259188 * r259203;
        return r259204;
}

↓

double f(double c0, double w, double h, double D, double d, double M) {
        double r259205 = c0;
        double r259206 = 2.0;
        double r259207 = w;
        double r259208 = r259206 * r259207;
        double r259209 = r259205 / r259208;
        double r259210 = d;
        double r259211 = r259210 * r259210;
        double r259212 = r259205 * r259211;
        double r259213 = h;
        double r259214 = r259207 * r259213;
        double r259215 = D;
        double r259216 = r259215 * r259215;
        double r259217 = r259214 * r259216;
        double r259218 = r259212 / r259217;
        double r259219 = r259218 * r259218;
        double r259220 = M;
        double r259221 = r259220 * r259220;
        double r259222 = r259219 - r259221;
        double r259223 = sqrt(r259222);
        double r259224 = r259218 + r259223;
        double r259225 = r259209 * r259224;
        double r259226 = 3.3002661492109247e+188;
        bool r259227 = r259225 <= r259226;
        double r259228 = 0.0;
        double r259229 = cbrt(r259228);
        double r259230 = r259227 ? r259225 : r259229;
        return r259230;
}

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))))) < 3.3002661492109247e+188

   1. Initial program 35.2

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

   if 3.3002661492109247e+188 < (* (/ 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 63.8

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

   2. Taylor expanded around inf 33.9

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

   4. Applied add-cbrt-cube 33.9

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

   5. Applied add-cbrt-cube 41.6

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

   6. Applied add-cbrt-cube 41.6

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

   7. Applied cbrt-unprod 41.6

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

   8. Applied add-cbrt-cube 48.5

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

   9. Applied cbrt-undiv 48.9

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

   10. Applied cbrt-unprod 48.9

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

   11. Simplified 31.8

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

4. Final simplification 32.3

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{c0}{2 \cdot w} \cdot \left(\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \le 3.3002661492109247 \cdot 10^{188}:\\ \;\;\;\;\frac{c0}{2 \cdot w} \cdot \left(\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right)\\ \mathbf{else}:\\ \;\;\;\;\sqrt[3]{0}\\ \end{array}\]

Reproduce

herbie shell --seed 2020059 
(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))))))