Henrywood and Agarwal, Equation (13)

Average Error: 59.3 → 33.4

Time: 33.8s

Precision: 64

• could not determine a ground truth for program body

  1. c0 = -2.295024957636829e+132
  2. w = -1.0459561824906476e-187
  3. h = -6.187928141723591e-216
  4. D = -2.661563675686751e-249
  5. d = 5.049148371172753e+293
  6. M = 2.2438624246711994e+121

Math

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

↓

\[0\]

C

double f(double c0, double w, double h, double D, double d, double M) {
        double r91509 = c0;
        double r91510 = 2.0;
        double r91511 = w;
        double r91512 = r91510 * r91511;
        double r91513 = r91509 / r91512;
        double r91514 = d;
        double r91515 = r91514 * r91514;
        double r91516 = r91509 * r91515;
        double r91517 = h;
        double r91518 = r91511 * r91517;
        double r91519 = D;
        double r91520 = r91519 * r91519;
        double r91521 = r91518 * r91520;
        double r91522 = r91516 / r91521;
        double r91523 = r91522 * r91522;
        double r91524 = M;
        double r91525 = r91524 * r91524;
        double r91526 = r91523 - r91525;
        double r91527 = sqrt(r91526);
        double r91528 = r91522 + r91527;
        double r91529 = r91513 * r91528;
        return r91529;
}

↓

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 r91530 = 0.0;
        return r91530;
}

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 35.4

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

4. Applied add-cube-cbrt 35.4

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

5. Simplified 35.4

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

6. Simplified 33.4

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

7. Final simplification 33.4

   \[\leadsto 0\]

Reproduce

herbie shell --seed 2019303 
(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))))))