Henrywood and Agarwal, Equation (13)

Average Error: 59.2 → 32.3

Time: 36.4s

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

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

↓

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

C

double f(double c0, double w, double h, double D, double d, double M) {
        double r7972276 = c0;
        double r7972277 = 2.0;
        double r7972278 = w;
        double r7972279 = r7972277 * r7972278;
        double r7972280 = r7972276 / r7972279;
        double r7972281 = d;
        double r7972282 = r7972281 * r7972281;
        double r7972283 = r7972276 * r7972282;
        double r7972284 = h;
        double r7972285 = r7972278 * r7972284;
        double r7972286 = D;
        double r7972287 = r7972286 * r7972286;
        double r7972288 = r7972285 * r7972287;
        double r7972289 = r7972283 / r7972288;
        double r7972290 = r7972289 * r7972289;
        double r7972291 = M;
        double r7972292 = r7972291 * r7972291;
        double r7972293 = r7972290 - r7972292;
        double r7972294 = sqrt(r7972293);
        double r7972295 = r7972289 + r7972294;
        double r7972296 = r7972280 * r7972295;
        return r7972296;
}

↓

double f(double c0, double w, double h, double D, double d, double M) {
        double r7972297 = c0;
        double r7972298 = 2.0;
        double r7972299 = w;
        double r7972300 = r7972298 * r7972299;
        double r7972301 = r7972297 / r7972300;
        double r7972302 = d;
        double r7972303 = r7972302 * r7972302;
        double r7972304 = r7972297 * r7972303;
        double r7972305 = h;
        double r7972306 = r7972299 * r7972305;
        double r7972307 = D;
        double r7972308 = r7972307 * r7972307;
        double r7972309 = r7972306 * r7972308;
        double r7972310 = r7972304 / r7972309;
        double r7972311 = r7972310 * r7972310;
        double r7972312 = M;
        double r7972313 = r7972312 * r7972312;
        double r7972314 = r7972311 - r7972313;
        double r7972315 = sqrt(r7972314);
        double r7972316 = r7972310 + r7972315;
        double r7972317 = r7972301 * r7972316;
        double r7972318 = 3.593395567930998e+241;
        bool r7972319 = r7972317 <= r7972318;
        double r7972320 = 0.0;
        double r7972321 = r7972319 ? r7972317 : r7972320;
        return r7972321;
}

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

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

   3. Taylor expanded around inf 34.3

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

   4. Taylor expanded around 0 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 
(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))))))