Henrywood and Agarwal, Equation (13)

Average Error: 59.1 → 33.2

Time: 11.9s

Precision: 64

• could not determine a ground truth for program body

  1. c0 = -2.2736486955259513e-10
  2. w = 4.3811697035537754e-170
  3. h = 1.2862806256912123e-229
  4. D = 2.5855309822038082e-138
  5. d = -2.3068824554677546e+222
  6. M = 5.352451769654128e+34

Math

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

↓

\[\frac{\sqrt[3]{c0} \cdot \sqrt[3]{c0}}{2} \cdot 0\]

C

double f(double c0, double w, double h, double D, double d, double M) {
        double r138243 = c0;
        double r138244 = 2.0;
        double r138245 = w;
        double r138246 = r138244 * r138245;
        double r138247 = r138243 / r138246;
        double r138248 = d;
        double r138249 = r138248 * r138248;
        double r138250 = r138243 * r138249;
        double r138251 = h;
        double r138252 = r138245 * r138251;
        double r138253 = D;
        double r138254 = r138253 * r138253;
        double r138255 = r138252 * r138254;
        double r138256 = r138250 / r138255;
        double r138257 = r138256 * r138256;
        double r138258 = M;
        double r138259 = r138258 * r138258;
        double r138260 = r138257 - r138259;
        double r138261 = sqrt(r138260);
        double r138262 = r138256 + r138261;
        double r138263 = r138247 * r138262;
        return r138263;
}

↓

double f(double c0, double __attribute__((unused)) w, double __attribute__((unused)) h, double __attribute__((unused)) D, double __attribute__((unused)) d, double __attribute__((unused)) M) {
        double r138264 = c0;
        double r138265 = cbrt(r138264);
        double r138266 = r138265 * r138265;
        double r138267 = 2.0;
        double r138268 = r138266 / r138267;
        double r138269 = 0.0;
        double r138270 = r138268 * r138269;
        return r138270;
}

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 59.1

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

2. Taylor expanded around inf 35.1

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

4. Applied add-cube-cbrt 35.1

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

5. Applied times-frac 35.1

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

6. Applied associate-*l* 33.7

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

7. Simplified 33.2

   \[\leadsto \frac{\sqrt[3]{c0} \cdot \sqrt[3]{c0}}{2} \cdot \color{blue}{0}\]

8. Final simplification 33.2

   \[\leadsto \frac{\sqrt[3]{c0} \cdot \sqrt[3]{c0}}{2} \cdot 0\]

Reproduce

herbie shell --seed 2020001 
(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))))))