Henrywood and Agarwal, Equation (13)

Average Error: 59.8 → 33.3

Time: 12.4s

Precision: 64

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

• could not determine a ground truth for program body

  1. c0 = -1.0350484507269592e+185
  2. w = -1.7353128656778376e+18
  3. h = -5.478379097427606e-296
  4. D = 4.1008237962433196e-257
  5. d = 9.429902918018724e+96
  6. M = 1.690105319616841e-183

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 r80535 = c0;
        double r80536 = 2.0;
        double r80537 = w;
        double r80538 = r80536 * r80537;
        double r80539 = r80535 / r80538;
        double r80540 = d;
        double r80541 = r80540 * r80540;
        double r80542 = r80535 * r80541;
        double r80543 = h;
        double r80544 = r80537 * r80543;
        double r80545 = D;
        double r80546 = r80545 * r80545;
        double r80547 = r80544 * r80546;
        double r80548 = r80542 / r80547;
        double r80549 = r80548 * r80548;
        double r80550 = M;
        double r80551 = r80550 * r80550;
        double r80552 = r80549 - r80551;
        double r80553 = sqrt(r80552);
        double r80554 = r80548 + r80553;
        double r80555 = r80539 * r80554;
        return r80555;
}

↓

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 r80556 = 0.0;
        double r80557 = r80556 * r80556;
        return r80557;
}

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 59.8

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

2. Taylor expanded around inf 35.2

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

4. Applied add-cube-cbrt 35.2

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

5. Simplified 35.2

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

6. Simplified 33.3

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

7. Final simplification 33.3

   \[\leadsto 0 \cdot 0\]

Reproduce

herbie shell --seed 2020045 +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))))))