Henrywood and Agarwal, Equation (13)

Average Error: 59.2 → 32.3

Time: 45.3s

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

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

↓

\[\begin{array}{l} \mathbf{if}\;\frac{c0}{2 \cdot w} \cdot \left(\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \le 3.59339556793099782905505395424773047473 \cdot 10^{241}:\\ \;\;\;\;\frac{c0}{2 \cdot w} \cdot \left(\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right)\\ \mathbf{else}:\\ \;\;\;\;0\\ \end{array}\]

C

double f(double c0, double w, double h, double D, double d, double M) {
        double r6179961 = c0;
        double r6179962 = 2.0;
        double r6179963 = w;
        double r6179964 = r6179962 * r6179963;
        double r6179965 = r6179961 / r6179964;
        double r6179966 = d;
        double r6179967 = r6179966 * r6179966;
        double r6179968 = r6179961 * r6179967;
        double r6179969 = h;
        double r6179970 = r6179963 * r6179969;
        double r6179971 = D;
        double r6179972 = r6179971 * r6179971;
        double r6179973 = r6179970 * r6179972;
        double r6179974 = r6179968 / r6179973;
        double r6179975 = r6179974 * r6179974;
        double r6179976 = M;
        double r6179977 = r6179976 * r6179976;
        double r6179978 = r6179975 - r6179977;
        double r6179979 = sqrt(r6179978);
        double r6179980 = r6179974 + r6179979;
        double r6179981 = r6179965 * r6179980;
        return r6179981;
}

↓

double f(double c0, double w, double h, double D, double d, double M) {
        double r6179982 = c0;
        double r6179983 = 2.0;
        double r6179984 = w;
        double r6179985 = r6179983 * r6179984;
        double r6179986 = r6179982 / r6179985;
        double r6179987 = d;
        double r6179988 = r6179987 * r6179987;
        double r6179989 = r6179982 * r6179988;
        double r6179990 = h;
        double r6179991 = r6179984 * r6179990;
        double r6179992 = D;
        double r6179993 = r6179992 * r6179992;
        double r6179994 = r6179991 * r6179993;
        double r6179995 = r6179989 / r6179994;
        double r6179996 = r6179995 * r6179995;
        double r6179997 = M;
        double r6179998 = r6179997 * r6179997;
        double r6179999 = r6179996 - r6179998;
        double r6180000 = sqrt(r6179999);
        double r6180001 = r6179995 + r6180000;
        double r6180002 = r6179986 * r6180001;
        double r6180003 = 3.593395567930998e+241;
        bool r6180004 = r6180002 <= r6180003;
        double r6180005 = 0.0;
        double r6180006 = r6180004 ? r6180002 : r6180005;
        return r6180006;
}

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. Split input into 2 regimes

2. if (* (/ 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))))) < 3.593395567930998e+241

   1. Initial program 34.1

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

   if 3.593395567930998e+241 < (* (/ 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)))))

   1. Initial program 63.9

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

   2. Simplified 57.6

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

   3. Taylor expanded around inf 34.3

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

   5. Applied mul0 31.9

      \[\leadsto \color{blue}{0}\]
3. Recombined 2 regimes into one program.

4. Final simplification 32.3

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{c0}{2 \cdot w} \cdot \left(\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right) \le 3.59339556793099782905505395424773047473 \cdot 10^{241}:\\ \;\;\;\;\frac{c0}{2 \cdot w} \cdot \left(\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} + \sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(w \cdot h\right) \cdot \left(D \cdot D\right)} - M \cdot M}\right)\\ \mathbf{else}:\\ \;\;\;\;0\\ \end{array}\]

Reproduce

herbie shell --seed 2019174 +o rules:numerics
(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))))))