Henrywood and Agarwal, Equation (13)

Average Error: 59.1 → 33.3

Time: 13.3s

Precision: 64

• could not determine a ground truth for program body

  1. c0 = -0.0019174381104543623
  2. w = 1.8157614023659142e-141
  3. h = 4.070116352762377e-85
  4. D = -2.138254835842433e-217
  5. d = 1.4438415993186157e+259
  6. M = -1.3495990944802807e-217

Math

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

↓

\[e^{\log 0}\]

C

double f(double c0, double w, double h, double D, double d, double M) {
        double r130343 = c0;
        double r130344 = 2.0;
        double r130345 = w;
        double r130346 = r130344 * r130345;
        double r130347 = r130343 / r130346;
        double r130348 = d;
        double r130349 = r130348 * r130348;
        double r130350 = r130343 * r130349;
        double r130351 = h;
        double r130352 = r130345 * r130351;
        double r130353 = D;
        double r130354 = r130353 * r130353;
        double r130355 = r130352 * r130354;
        double r130356 = r130350 / r130355;
        double r130357 = r130356 * r130356;
        double r130358 = M;
        double r130359 = r130358 * r130358;
        double r130360 = r130357 - r130359;
        double r130361 = sqrt(r130360);
        double r130362 = r130356 + r130361;
        double r130363 = r130347 * r130362;
        return r130363;
}

↓

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 r130364 = 0.0;
        double r130365 = log(r130364);
        double r130366 = exp(r130365);
        return r130366;
}

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 35.2

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

4. Applied add-exp-log 35.2

   \[\leadsto \frac{c0}{2 \cdot w} \cdot \color{blue}{e^{\log 0}}\]

5. Applied add-exp-log 49.6

   \[\leadsto \frac{c0}{2 \cdot \color{blue}{e^{\log w}}} \cdot e^{\log 0}\]

6. Applied add-exp-log 49.6

   \[\leadsto \frac{c0}{\color{blue}{e^{\log 2}} \cdot e^{\log w}} \cdot e^{\log 0}\]

7. Applied prod-exp 49.6

   \[\leadsto \frac{c0}{\color{blue}{e^{\log 2 + \log w}}} \cdot e^{\log 0}\]

8. Applied add-exp-log 56.5

   \[\leadsto \frac{\color{blue}{e^{\log c0}}}{e^{\log 2 + \log w}} \cdot e^{\log 0}\]

9. Applied div-exp 56.5

   \[\leadsto \color{blue}{e^{\log c0 - \left(\log 2 + \log w\right)}} \cdot e^{\log 0}\]

10. Applied prod-exp 56.0

    \[\leadsto \color{blue}{e^{\left(\log c0 - \left(\log 2 + \log w\right)\right) + \log 0}}\]

11. Simplified 33.3

    \[\leadsto e^{\color{blue}{\log 0}}\]

12. Final simplification 33.3

    \[\leadsto e^{\log 0}\]

Reproduce

herbie shell --seed 2020034 +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))))))