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

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

↓

\[0 \cdot \sqrt[3]{0}\]

C

double f(double c0, double w, double h, double D, double d, double M) {
        double r183608 = c0;
        double r183609 = 2.0;
        double r183610 = w;
        double r183611 = r183609 * r183610;
        double r183612 = r183608 / r183611;
        double r183613 = d;
        double r183614 = r183613 * r183613;
        double r183615 = r183608 * r183614;
        double r183616 = h;
        double r183617 = r183610 * r183616;
        double r183618 = D;
        double r183619 = r183618 * r183618;
        double r183620 = r183617 * r183619;
        double r183621 = r183615 / r183620;
        double r183622 = r183621 * r183621;
        double r183623 = M;
        double r183624 = r183623 * r183623;
        double r183625 = r183622 - r183624;
        double r183626 = sqrt(r183625);
        double r183627 = r183621 + r183626;
        double r183628 = r183612 * r183627;
        return r183628;
}

↓

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 r183629 = 0.0;
        double r183630 = cbrt(r183629);
        double r183631 = r183629 * r183630;
        return r183631;
}

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-cube-cbrt 35.9

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

5. Applied associate-*r* 35.9

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

6. Simplified 33.9

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

7. Final simplification 33.9

   \[\leadsto 0 \cdot \sqrt[3]{0}\]

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))))))