Henrywood and Agarwal, Equation (13)

Average Error: 59.5 → 33.4

Time: 14.5s

Precision: 64

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

• could not determine a ground truth for program body

  1. c0 = -5.249567668248059e+253
  2. w = 8.875439979397946e-145
  3. h = 1.5708184023001804e-38
  4. D = -1.834547769674711e-162
  5. d = -2.095161779972088e+180
  6. M = 1.2469301676143809e-108

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 r189493 = c0;
        double r189494 = 2.0;
        double r189495 = w;
        double r189496 = r189494 * r189495;
        double r189497 = r189493 / r189496;
        double r189498 = d;
        double r189499 = r189498 * r189498;
        double r189500 = r189493 * r189499;
        double r189501 = h;
        double r189502 = r189495 * r189501;
        double r189503 = D;
        double r189504 = r189503 * r189503;
        double r189505 = r189502 * r189504;
        double r189506 = r189500 / r189505;
        double r189507 = r189506 * r189506;
        double r189508 = M;
        double r189509 = r189508 * r189508;
        double r189510 = r189507 - r189509;
        double r189511 = sqrt(r189510);
        double r189512 = r189506 + r189511;
        double r189513 = r189497 * r189512;
        return r189513;
}

↓

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 r189514 = 0.0;
        double r189515 = r189514 * r189514;
        return r189515;
}

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 59.5

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

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 2020043 
(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))))))