Henrywood and Agarwal, Equation (13)

Average Error: 59.2 → 33.5

Time: 8.9s

Precision: 64

• could not determine a ground truth for program body

  1. c0 = 1.082084726917846e+287
  2. w = 1.56037796305268e-83
  3. h = -9.379441670507973e-171
  4. D = -9.069080929345551e-285
  5. d = -2.7089457078913576e+37
  6. M = -1.4763414349710623e+154

Math

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

↓

\[\log 1\]

C

double f(double c0, double w, double h, double D, double d, double M) {
        double r286419 = c0;
        double r286420 = 2.0;
        double r286421 = w;
        double r286422 = r286420 * r286421;
        double r286423 = r286419 / r286422;
        double r286424 = d;
        double r286425 = r286424 * r286424;
        double r286426 = r286419 * r286425;
        double r286427 = h;
        double r286428 = r286421 * r286427;
        double r286429 = D;
        double r286430 = r286429 * r286429;
        double r286431 = r286428 * r286430;
        double r286432 = r286426 / r286431;
        double r286433 = r286432 * r286432;
        double r286434 = M;
        double r286435 = r286434 * r286434;
        double r286436 = r286433 - r286435;
        double r286437 = sqrt(r286436);
        double r286438 = r286432 + r286437;
        double r286439 = r286423 * r286438;
        return r286439;
}

↓

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 r286440 = 1.0;
        double r286441 = log(r286440);
        return r286441;
}

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 59.2

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

2. Taylor expanded around inf 35.2

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

4. Applied add-log-exp 35.2

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

5. Simplified 33.5

   \[\leadsto \log \color{blue}{1}\]

6. Final simplification 33.5

   \[\leadsto \log 1\]

Reproduce

herbie shell --seed 2020046 
(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))))))