Henrywood and Agarwal, Equation (13)

Average Error: 59.8 → 33.9

Time: 26.6s

Precision: 64

• could not determine a ground truth for program body

  1. c0 = 1.0354753041264744e+289
  2. w = 1.805639974384451e-278
  3. h = -1.666054489535506e-110
  4. D = -2.4785981274006074e+83
  5. d = 4.793015807732654e+257
  6. M = 1.6575375979987916e+218

Math

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

↓

\[\frac{1}{2} \cdot 0\]

C

double f(double c0, double w, double h, double D, double d, double M) {
        double r97973 = c0;
        double r97974 = 2.0;
        double r97975 = w;
        double r97976 = r97974 * r97975;
        double r97977 = r97973 / r97976;
        double r97978 = d;
        double r97979 = r97978 * r97978;
        double r97980 = r97973 * r97979;
        double r97981 = h;
        double r97982 = r97975 * r97981;
        double r97983 = D;
        double r97984 = r97983 * r97983;
        double r97985 = r97982 * r97984;
        double r97986 = r97980 / r97985;
        double r97987 = r97986 * r97986;
        double r97988 = M;
        double r97989 = r97988 * r97988;
        double r97990 = r97987 - r97989;
        double r97991 = sqrt(r97990);
        double r97992 = r97986 + r97991;
        double r97993 = r97977 * r97992;
        return r97993;
}

↓

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 r97994 = 1.0;
        double r97995 = 2.0;
        double r97996 = r97994 / r97995;
        double r97997 = 0.0;
        double r97998 = r97996 * r97997;
        return r97998;
}

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 36.0

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

4. Applied *-un-lft-identity 36.0

   \[\leadsto \frac{\color{blue}{1 \cdot c0}}{2 \cdot w} \cdot 0\]

5. Applied times-frac 36.0

   \[\leadsto \color{blue}{\left(\frac{1}{2} \cdot \frac{c0}{w}\right)} \cdot 0\]

6. Applied associate-*l* 36.0

   \[\leadsto \color{blue}{\frac{1}{2} \cdot \left(\frac{c0}{w} \cdot 0\right)}\]

7. Simplified 33.9

   \[\leadsto \frac{1}{2} \cdot \color{blue}{0}\]

8. Final simplification 33.9

   \[\leadsto \frac{1}{2} \cdot 0\]

Reproduce

herbie shell --seed 2019195 
(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))))))