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 r310847 = c0;
        double r310848 = 2.0;
        double r310849 = w;
        double r310850 = r310848 * r310849;
        double r310851 = r310847 / r310850;
        double r310852 = d;
        double r310853 = r310852 * r310852;
        double r310854 = r310847 * r310853;
        double r310855 = h;
        double r310856 = r310849 * r310855;
        double r310857 = D;
        double r310858 = r310857 * r310857;
        double r310859 = r310856 * r310858;
        double r310860 = r310854 / r310859;
        double r310861 = r310860 * r310860;
        double r310862 = M;
        double r310863 = r310862 * r310862;
        double r310864 = r310861 - r310863;
        double r310865 = sqrt(r310864);
        double r310866 = r310860 + r310865;
        double r310867 = r310851 * r310866;
        return r310867;
}

↓

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 r310868 = 0.0;
        double r310869 = r310868 * r310868;
        return r310869;
}

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 
(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))))))