Henrywood and Agarwal, Equation (13)

Average Error: 59.3 → 33.4

Time: 32.4s

Precision: 64

• could not determine a ground truth for program body

  1. c0 = -2.295024957636829e+132
  2. w = -1.0459561824906476e-187
  3. h = -6.187928141723591e-216
  4. D = -2.661563675686751e-249
  5. d = 5.049148371172753e+293
  6. M = 2.2438624246711994e+121

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 r141995 = c0;
        double r141996 = 2.0;
        double r141997 = w;
        double r141998 = r141996 * r141997;
        double r141999 = r141995 / r141998;
        double r142000 = d;
        double r142001 = r142000 * r142000;
        double r142002 = r141995 * r142001;
        double r142003 = h;
        double r142004 = r141997 * r142003;
        double r142005 = D;
        double r142006 = r142005 * r142005;
        double r142007 = r142004 * r142006;
        double r142008 = r142002 / r142007;
        double r142009 = r142008 * r142008;
        double r142010 = M;
        double r142011 = r142010 * r142010;
        double r142012 = r142009 - r142011;
        double r142013 = sqrt(r142012);
        double r142014 = r142008 + r142013;
        double r142015 = r141999 * r142014;
        return r142015;
}

↓

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 r142016 = 1.0;
        double r142017 = 2.0;
        double r142018 = r142016 / r142017;
        double r142019 = 0.0;
        double r142020 = r142018 * r142019;
        return r142020;
}

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 59.3

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

2. Taylor expanded around inf 35.4

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

4. Applied *-un-lft-identity 35.4

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

5. Applied times-frac 35.4

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

6. Applied associate-*l* 35.4

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

7. Simplified 33.4

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

8. Final simplification 33.4

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

Reproduce

herbie shell --seed 2019303 +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))))))