Henrywood and Agarwal, Equation (13)

Average Error: 59.2 → 33.5

Time: 14.6s

Precision: 64

• Falling back on racket egraph because egg-herbie package not installed

• 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

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

↓

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

C

double f(double c0, double w, double h, double D, double d, double M) {
        double r172466 = c0;
        double r172467 = 2.0;
        double r172468 = w;
        double r172469 = r172467 * r172468;
        double r172470 = r172466 / r172469;
        double r172471 = d;
        double r172472 = r172471 * r172471;
        double r172473 = r172466 * r172472;
        double r172474 = h;
        double r172475 = r172468 * r172474;
        double r172476 = D;
        double r172477 = r172476 * r172476;
        double r172478 = r172475 * r172477;
        double r172479 = r172473 / r172478;
        double r172480 = r172479 * r172479;
        double r172481 = M;
        double r172482 = r172481 * r172481;
        double r172483 = r172480 - r172482;
        double r172484 = sqrt(r172483);
        double r172485 = r172479 + r172484;
        double r172486 = r172470 * r172485;
        return r172486;
}

↓

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 r172487 = 0.0;
        double r172488 = cbrt(r172487);
        return r172488;
}

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-cbrt-cube 35.2

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

5. Applied add-cbrt-cube 41.8

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

6. Applied add-cbrt-cube 41.8

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

7. Applied cbrt-unprod 41.8

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

8. Applied add-cbrt-cube 48.6

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

9. Applied cbrt-undiv 49.1

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

10. Applied cbrt-unprod 49.1

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

11. Simplified 33.5

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

12. Final simplification 33.5

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

Reproduce

herbie shell --seed 2020046 +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))))))