Henrywood and Agarwal, Equation (13)

Average Error: 57.7 → 49.8

Time: 2.5m

Precision: 64

• could not determine a ground truth for program body

  1. c0 = 5.3817823459246724e+156
  2. w = -9.134720524259611e-119
  3. h = 1.0899086701616802e-286
  4. D = 2.6126530325187734e-275
  5. d = 6.007843723589613e+153
  6. M = 3.5838997754907576e+51

Math

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

↓

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

C

double f(double c0, double w, double h, double D, double d, double M) {
        double r40559898 = c0;
        double r40559899 = 2.0;
        double r40559900 = w;
        double r40559901 = r40559899 * r40559900;
        double r40559902 = r40559898 / r40559901;
        double r40559903 = d;
        double r40559904 = r40559903 * r40559903;
        double r40559905 = r40559898 * r40559904;
        double r40559906 = h;
        double r40559907 = r40559900 * r40559906;
        double r40559908 = D;
        double r40559909 = r40559908 * r40559908;
        double r40559910 = r40559907 * r40559909;
        double r40559911 = r40559905 / r40559910;
        double r40559912 = r40559911 * r40559911;
        double r40559913 = M;
        double r40559914 = r40559913 * r40559913;
        double r40559915 = r40559912 - r40559914;
        double r40559916 = sqrt(r40559915);
        double r40559917 = r40559911 + r40559916;
        double r40559918 = r40559902 * r40559917;
        return r40559918;
}

↓

double f(double c0, double w, double h, double D, double d, double M) {
        double r40559919 = c0;
        double r40559920 = w;
        double r40559921 = r40559919 / r40559920;
        double r40559922 = d;
        double r40559923 = D;
        double r40559924 = r40559922 / r40559923;
        double r40559925 = r40559921 * r40559924;
        double r40559926 = r40559925 * r40559924;
        double r40559927 = h;
        double r40559928 = r40559926 / r40559927;
        double r40559929 = M;
        double r40559930 = r40559929 + r40559928;
        double r40559931 = r40559928 - r40559929;
        double r40559932 = r40559930 * r40559931;
        double r40559933 = sqrt(r40559932);
        double r40559934 = r40559928 + r40559933;
        double r40559935 = r40559934 * r40559921;
        double r40559936 = 2.0;
        double r40559937 = r40559935 / r40559936;
        return r40559937;
}

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 57.7

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

2. Simplified 51.9

   \[\leadsto \color{blue}{\frac{\left(\sqrt{\left(M + \frac{\frac{c0}{w} \cdot \left(\frac{d}{D} \cdot \frac{d}{D}\right)}{h}\right) \cdot \left(\frac{\frac{c0}{w} \cdot \left(\frac{d}{D} \cdot \frac{d}{D}\right)}{h} - M\right)} + \frac{\frac{c0}{w} \cdot \left(\frac{d}{D} \cdot \frac{d}{D}\right)}{h}\right) \cdot \frac{c0}{w}}{2}}\]
3. Using strategy rm

4. Applied associate-*r* 52.5

   \[\leadsto \frac{\left(\sqrt{\left(M + \frac{\frac{c0}{w} \cdot \left(\frac{d}{D} \cdot \frac{d}{D}\right)}{h}\right) \cdot \left(\frac{\color{blue}{\left(\frac{c0}{w} \cdot \frac{d}{D}\right) \cdot \frac{d}{D}}}{h} - M\right)} + \frac{\frac{c0}{w} \cdot \left(\frac{d}{D} \cdot \frac{d}{D}\right)}{h}\right) \cdot \frac{c0}{w}}{2}\]
5. Using strategy rm

6. Applied associate-*r* 52.4

   \[\leadsto \frac{\left(\sqrt{\left(M + \frac{\frac{c0}{w} \cdot \left(\frac{d}{D} \cdot \frac{d}{D}\right)}{h}\right) \cdot \left(\frac{\left(\frac{c0}{w} \cdot \frac{d}{D}\right) \cdot \frac{d}{D}}{h} - M\right)} + \frac{\color{blue}{\left(\frac{c0}{w} \cdot \frac{d}{D}\right) \cdot \frac{d}{D}}}{h}\right) \cdot \frac{c0}{w}}{2}\]
7. Using strategy rm

8. Applied associate-*r* 49.8

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

9. Final simplification 49.8

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

Reproduce

herbie shell --seed 2019119 
(FPCore (c0 w h D d M)
  :name "Henrywood and Agarwal, Equation (13)"
  (* (/ 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))))))