Henrywood and Agarwal, Equation (13)

Average Error: 59.1 → 33.4

Time: 11.6s

Precision: 64

• could not determine a ground truth for program body

  1. c0 = -1.6556564630747375e+280
  2. w = -5.683204155343632e-190
  3. h = -2.660191539110354e-86
  4. D = 9.690684346264828e-121
  5. d = 1.907708711662111e+194
  6. M = -5.18356964059049e+291

Math

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

↓

\[0 \cdot 0\]

C

double f(double c0, double w, double h, double D, double d, double M) {
        double r122687 = c0;
        double r122688 = 2.0;
        double r122689 = w;
        double r122690 = r122688 * r122689;
        double r122691 = r122687 / r122690;
        double r122692 = d;
        double r122693 = r122692 * r122692;
        double r122694 = r122687 * r122693;
        double r122695 = h;
        double r122696 = r122689 * r122695;
        double r122697 = D;
        double r122698 = r122697 * r122697;
        double r122699 = r122696 * r122698;
        double r122700 = r122694 / r122699;
        double r122701 = r122700 * r122700;
        double r122702 = M;
        double r122703 = r122702 * r122702;
        double r122704 = r122701 - r122703;
        double r122705 = sqrt(r122704);
        double r122706 = r122700 + r122705;
        double r122707 = r122691 * r122706;
        return r122707;
}

↓

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 r122708 = 0.0;
        double r122709 = r122708 * r122708;
        return r122709;
}

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 35.3

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

4. Applied add-cube-cbrt 35.3

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

5. Simplified 35.3

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

6. Simplified 33.4

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

7. Final simplification 33.4

   \[\leadsto 0 \cdot 0\]

Reproduce

herbie shell --seed 2020083 
(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))))))