Henrywood and Agarwal, Equation (13)

Average Error: 59.3 → 33.9

Time: 27.7s

Precision: 64

• could not determine a ground truth for program body

  1. c0 = -1.9223366757178428e+272
  2. w = -4.229672497930909e-233
  3. h = -4.821880340259577e+242
  4. D = -3.0781381641647126e-166
  5. d = -9.035983238058826e+172
  6. M = 3.778636398349861e+119

Math

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

↓

\[\frac{1}{2} \cdot 0\]

C

double f(double c0, double w, double h, double D, double d, double M) {
        double r111783 = c0;
        double r111784 = 2.0;
        double r111785 = w;
        double r111786 = r111784 * r111785;
        double r111787 = r111783 / r111786;
        double r111788 = d;
        double r111789 = r111788 * r111788;
        double r111790 = r111783 * r111789;
        double r111791 = h;
        double r111792 = r111785 * r111791;
        double r111793 = D;
        double r111794 = r111793 * r111793;
        double r111795 = r111792 * r111794;
        double r111796 = r111790 / r111795;
        double r111797 = r111796 * r111796;
        double r111798 = M;
        double r111799 = r111798 * r111798;
        double r111800 = r111797 - r111799;
        double r111801 = sqrt(r111800);
        double r111802 = r111796 + r111801;
        double r111803 = r111787 * r111802;
        return r111803;
}

↓

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 r111804 = 1.0;
        double r111805 = 2.0;
        double r111806 = r111804 / r111805;
        double r111807 = 0.0;
        double r111808 = r111806 * r111807;
        return r111808;
}

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 59.3

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

2. Taylor expanded around inf 35.8

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

4. Applied *-un-lft-identity 35.8

   \[\leadsto \frac{\color{blue}{1 \cdot c0}}{2 \cdot w} \cdot 0\]

5. Applied times-frac 35.8

   \[\leadsto \color{blue}{\left(\frac{1}{2} \cdot \frac{c0}{w}\right)} \cdot 0\]

6. Applied associate-*l* 35.8

   \[\leadsto \color{blue}{\frac{1}{2} \cdot \left(\frac{c0}{w} \cdot 0\right)}\]

7. Simplified 33.9

   \[\leadsto \frac{1}{2} \cdot \color{blue}{0}\]

8. Final simplification 33.9

   \[\leadsto \frac{1}{2} \cdot 0\]

Reproduce

herbie shell --seed 2019305 +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))))))