Henrywood and Agarwal, Equation (13)

Average Error: 59.1 → 33.9

Time: 12.0s

Precision: 64

• could not determine a ground truth for program body

  1. c0 = -2.1132779545585976e+191
  2. w = -2.232697092575099e+129
  3. h = -4.606642287269655e-262
  4. D = 1.2237605914285715e-271
  5. d = -6.993977203582367e+172
  6. M = -7.956700050014334e+276

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 r183295 = c0;
        double r183296 = 2.0;
        double r183297 = w;
        double r183298 = r183296 * r183297;
        double r183299 = r183295 / r183298;
        double r183300 = d;
        double r183301 = r183300 * r183300;
        double r183302 = r183295 * r183301;
        double r183303 = h;
        double r183304 = r183297 * r183303;
        double r183305 = D;
        double r183306 = r183305 * r183305;
        double r183307 = r183304 * r183306;
        double r183308 = r183302 / r183307;
        double r183309 = r183308 * r183308;
        double r183310 = M;
        double r183311 = r183310 * r183310;
        double r183312 = r183309 - r183311;
        double r183313 = sqrt(r183312);
        double r183314 = r183308 + r183313;
        double r183315 = r183299 * r183314;
        return r183315;
}

↓

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 r183316 = 0.0;
        double r183317 = log(r183316);
        double r183318 = exp(r183317);
        return r183318;
}

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 35.9

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

4. Applied add-exp-log 35.9

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

5. Applied add-exp-log 49.9

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

6. Applied add-exp-log 49.9

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

7. Applied prod-exp 49.9

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

8. Applied add-exp-log 57.1

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

9. Applied div-exp 57.1

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

10. Applied prod-exp 56.6

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

11. Simplified 33.9

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

12. Final simplification 33.9

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

Reproduce

herbie shell --seed 2019353 +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))))))