Henrywood and Agarwal, Equation (13)

Average Error: 58.9 → 33.3

Time: 29.6s

Precision: 64

• could not determine a ground truth for program body

  1. c0 = -7.577232354044003e+225
  2. w = -2.9359266437475263e-127
  3. h = -1.4748069476452327e+19
  4. D = -5.302367957985033e-272
  5. d = 8.107108173459963e+64
  6. M = 9.971901005542815e-257

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 r114572 = c0;
        double r114573 = 2.0;
        double r114574 = w;
        double r114575 = r114573 * r114574;
        double r114576 = r114572 / r114575;
        double r114577 = d;
        double r114578 = r114577 * r114577;
        double r114579 = r114572 * r114578;
        double r114580 = h;
        double r114581 = r114574 * r114580;
        double r114582 = D;
        double r114583 = r114582 * r114582;
        double r114584 = r114581 * r114583;
        double r114585 = r114579 / r114584;
        double r114586 = r114585 * r114585;
        double r114587 = M;
        double r114588 = r114587 * r114587;
        double r114589 = r114586 - r114588;
        double r114590 = sqrt(r114589);
        double r114591 = r114585 + r114590;
        double r114592 = r114576 * r114591;
        return r114592;
}

↓

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 r114593 = 1.0;
        double r114594 = 2.0;
        double r114595 = r114593 / r114594;
        double r114596 = 0.0;
        double r114597 = r114595 * r114596;
        return r114597;
}

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 58.9

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

2. Taylor expanded around inf 35.2

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

4. Applied *-un-lft-identity 35.2

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

5. Applied times-frac 35.2

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

6. Applied associate-*l* 35.2

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

7. Simplified 33.3

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

8. Final simplification 33.3

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

Reproduce

herbie shell --seed 2019322 +o rules:numerics
(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))))))