Henrywood and Agarwal, Equation (13)

Average Error: 59.2 → 33.7

Time: 27.4s

Precision: 64

• could not determine a ground truth for program body

  1. c0 = 4.046401737432886e+231
  2. w = -1.3554673749956964e-176
  3. h = 9.954080561998736e-55
  4. D = 4.360008815267399e-238
  5. d = 2.536808514302376e+298
  6. M = -1.9185588755758526e-34

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 r153994 = c0;
        double r153995 = 2.0;
        double r153996 = w;
        double r153997 = r153995 * r153996;
        double r153998 = r153994 / r153997;
        double r153999 = d;
        double r154000 = r153999 * r153999;
        double r154001 = r153994 * r154000;
        double r154002 = h;
        double r154003 = r153996 * r154002;
        double r154004 = D;
        double r154005 = r154004 * r154004;
        double r154006 = r154003 * r154005;
        double r154007 = r154001 / r154006;
        double r154008 = r154007 * r154007;
        double r154009 = M;
        double r154010 = r154009 * r154009;
        double r154011 = r154008 - r154010;
        double r154012 = sqrt(r154011);
        double r154013 = r154007 + r154012;
        double r154014 = r153998 * r154013;
        return r154014;
}

↓

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 r154015 = 0.0;
        return r154015;
}

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 59.2

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

2. Taylor expanded around inf 35.8

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

4. Applied add-cube-cbrt 35.8

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

5. Simplified 35.8

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

6. Simplified 33.7

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

7. Final simplification 33.7

   \[\leadsto 0\]

Reproduce

herbie shell --seed 2019174 
(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))))))