Henrywood and Agarwal, Equation (13)

Average Error: 59.2 → 33.2

Time: 9.2s

Precision: 64

• could not determine a ground truth for program body

  1. c0 = -5.03854716504617e+246
  2. w = 2.3557496717304043e-256
  3. h = 4.099329634204151e+82
  4. D = -1.9238414610311788e-75
  5. d = -1.297553324752022e+214
  6. M = 1.4347206616743273e-175

Math

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

↓

\[\frac{1}{2} \cdot 0\]

C

double f(double c0, double w, double h, double D, double d, double M) {
        double r251714 = c0;
        double r251715 = 2.0;
        double r251716 = w;
        double r251717 = r251715 * r251716;
        double r251718 = r251714 / r251717;
        double r251719 = d;
        double r251720 = r251719 * r251719;
        double r251721 = r251714 * r251720;
        double r251722 = h;
        double r251723 = r251716 * r251722;
        double r251724 = D;
        double r251725 = r251724 * r251724;
        double r251726 = r251723 * r251725;
        double r251727 = r251721 / r251726;
        double r251728 = r251727 * r251727;
        double r251729 = M;
        double r251730 = r251729 * r251729;
        double r251731 = r251728 - r251730;
        double r251732 = sqrt(r251731);
        double r251733 = r251727 + r251732;
        double r251734 = r251718 * r251733;
        return r251734;
}

↓

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 r251735 = 1.0;
        double r251736 = 2.0;
        double r251737 = r251735 / r251736;
        double r251738 = 0.0;
        double r251739 = r251737 * r251738;
        return r251739;
}

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 59.2

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

2. Taylor expanded around inf 35.1

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

4. Applied *-un-lft-identity 35.1

   \[\leadsto \frac{\color{blue}{1 \cdot c0}}{2 \cdot w} \cdot 0\]

5. Applied times-frac 35.1

   \[\leadsto \color{blue}{\left(\frac{1}{2} \cdot \frac{c0}{w}\right)} \cdot 0\]

6. Applied associate-*l* 35.1

   \[\leadsto \color{blue}{\frac{1}{2} \cdot \left(\frac{c0}{w} \cdot 0\right)}\]

7. Simplified 33.2

   \[\leadsto \frac{1}{2} \cdot \color{blue}{0}\]

8. Final simplification 33.2

   \[\leadsto \frac{1}{2} \cdot 0\]

Reproduce

herbie shell --seed 2020039 
(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))))))