Henrywood and Agarwal, Equation (13)

Average Error: 59.4 → 33.2

Time: 13.7s

Precision: 64

• could not determine a ground truth for program body

  1. c0 = 6.433640136672922e+235
  2. w = 8.452956519243837e+92
  3. h = -6.731738964690938e+154
  4. D = 3.1207514136900935e-304
  5. d = -1.1145600677088552e+306
  6. M = -1.903026018846269e+29

Math

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

↓

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

C

double f(double c0, double w, double h, double D, double d, double M) {
        double r174096 = c0;
        double r174097 = 2.0;
        double r174098 = w;
        double r174099 = r174097 * r174098;
        double r174100 = r174096 / r174099;
        double r174101 = d;
        double r174102 = r174101 * r174101;
        double r174103 = r174096 * r174102;
        double r174104 = h;
        double r174105 = r174098 * r174104;
        double r174106 = D;
        double r174107 = r174106 * r174106;
        double r174108 = r174105 * r174107;
        double r174109 = r174103 / r174108;
        double r174110 = r174109 * r174109;
        double r174111 = M;
        double r174112 = r174111 * r174111;
        double r174113 = r174110 - r174112;
        double r174114 = sqrt(r174113);
        double r174115 = r174109 + r174114;
        double r174116 = r174100 * r174115;
        return r174116;
}

↓

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 r174117 = 0.0;
        double r174118 = cbrt(r174117);
        double r174119 = r174117 * r174118;
        return r174119;
}

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 59.4

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

2. Taylor expanded around inf 35.0

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

4. Applied add-cube-cbrt 35.0

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

5. Applied associate-*r* 35.0

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

6. Simplified 33.2

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

7. Final simplification 33.2

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

Reproduce

herbie shell --seed 2020036 
(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))))))