Henrywood and Agarwal, Equation (13)

Average Error: 59.4 → 34.4

Time: 39.2s

Precision: 64

• could not determine a ground truth for program body

  1. c0 = 5.018742092799993e+190
  2. w = 1.1454916979639543e-163
  3. h = -8.146810325846195e-101
  4. D = 1.0991076224086447e+80
  5. d = 7.954112350416888e+286
  6. M = 1.0233711920082547e+44

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 r218705 = c0;
        double r218706 = 2.0;
        double r218707 = w;
        double r218708 = r218706 * r218707;
        double r218709 = r218705 / r218708;
        double r218710 = d;
        double r218711 = r218710 * r218710;
        double r218712 = r218705 * r218711;
        double r218713 = h;
        double r218714 = r218707 * r218713;
        double r218715 = D;
        double r218716 = r218715 * r218715;
        double r218717 = r218714 * r218716;
        double r218718 = r218712 / r218717;
        double r218719 = r218718 * r218718;
        double r218720 = M;
        double r218721 = r218720 * r218720;
        double r218722 = r218719 - r218721;
        double r218723 = sqrt(r218722);
        double r218724 = r218718 + r218723;
        double r218725 = r218709 * r218724;
        return r218725;
}

↓

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 r218726 = 0.0;
        return r218726;
}

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 59.4

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

2. Taylor expanded around inf 36.2

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

4. Applied add-cube-cbrt 36.2

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

5. Simplified 36.2

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

6. Simplified 34.4

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

7. Final simplification 34.4

   \[\leadsto 0\]

Reproduce

herbie shell --seed 2019199 
(FPCore (c0 w h D d M)
  :name "Henrywood and Agarwal, Equation (13)"
  (* (/ c0 (* 2.0 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))))))