Henrywood and Agarwal, Equation (13)

Average Error: 59.5 → 33.9

Time: 14.1s

Precision: 64

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

• could not determine a ground truth for program body

  1. c0 = 1.6945536356600665e+51
  2. w = -2.951126666883304e-198
  3. h = 4.632464796100937e-228
  4. D = -5.150456114061081e-84
  5. d = -7.926770742433422e+268
  6. M = 2.2914935331306628e-285

Math

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

↓

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

C

double f(double c0, double w, double h, double D, double d, double M) {
        double r189902 = c0;
        double r189903 = 2.0;
        double r189904 = w;
        double r189905 = r189903 * r189904;
        double r189906 = r189902 / r189905;
        double r189907 = d;
        double r189908 = r189907 * r189907;
        double r189909 = r189902 * r189908;
        double r189910 = h;
        double r189911 = r189904 * r189910;
        double r189912 = D;
        double r189913 = r189912 * r189912;
        double r189914 = r189911 * r189913;
        double r189915 = r189909 / r189914;
        double r189916 = r189915 * r189915;
        double r189917 = M;
        double r189918 = r189917 * r189917;
        double r189919 = r189916 - r189918;
        double r189920 = sqrt(r189919);
        double r189921 = r189915 + r189920;
        double r189922 = r189906 * r189921;
        return r189922;
}

↓

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 r189923 = 0.0;
        double r189924 = cbrt(r189923);
        double r189925 = r189923 * r189924;
        return r189925;
}

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 35.7

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

4. Applied add-cube-cbrt 35.7

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

5. Applied associate-*r* 35.7

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

6. Simplified 33.9

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

7. Final simplification 33.9

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

Reproduce

herbie shell --seed 2020042 +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))))))