Henrywood and Agarwal, Equation (13)

Average Error: 58.1 → 31.8

Time: 1.5m

Precision: 64

• could not determine a ground truth for program body

  1. c0 = 2.365951752076539e+256
  2. w = -1.597050900171122e-98
  3. h = 2.7421650851285317e-178
  4. D = 1.951146446221059e-304
  5. d = -4.1946076574544436e-132
  6. M = -3.7762789558399307e+40

Math

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

↓

\[\begin{array}{l} \mathbf{if}\;\frac{c0}{w \cdot 2} \cdot \left(\sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(D \cdot D\right) \cdot \left(w \cdot h\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(D \cdot D\right) \cdot \left(w \cdot h\right)} - M \cdot M} + \frac{c0 \cdot \left(d \cdot d\right)}{\left(D \cdot D\right) \cdot \left(w \cdot h\right)}\right) \le 2.608039255478076 \cdot 10^{+261}:\\ \;\;\;\;\frac{c0}{w \cdot 2} \cdot \left(\sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(D \cdot D\right) \cdot \left(w \cdot h\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(D \cdot D\right) \cdot \left(w \cdot h\right)} - M \cdot M} + \frac{c0 \cdot \left(d \cdot d\right)}{\left(D \cdot D\right) \cdot \left(w \cdot h\right)}\right)\\ \mathbf{else}:\\ \;\;\;\;0\\ \end{array}\]

C

double f(double c0, double w, double h, double D, double d, double M) {
        double r54450313 = c0;
        double r54450314 = 2.0;
        double r54450315 = w;
        double r54450316 = r54450314 * r54450315;
        double r54450317 = r54450313 / r54450316;
        double r54450318 = d;
        double r54450319 = r54450318 * r54450318;
        double r54450320 = r54450313 * r54450319;
        double r54450321 = h;
        double r54450322 = r54450315 * r54450321;
        double r54450323 = D;
        double r54450324 = r54450323 * r54450323;
        double r54450325 = r54450322 * r54450324;
        double r54450326 = r54450320 / r54450325;
        double r54450327 = r54450326 * r54450326;
        double r54450328 = M;
        double r54450329 = r54450328 * r54450328;
        double r54450330 = r54450327 - r54450329;
        double r54450331 = sqrt(r54450330);
        double r54450332 = r54450326 + r54450331;
        double r54450333 = r54450317 * r54450332;
        return r54450333;
}

↓

double f(double c0, double w, double h, double D, double d, double M) {
        double r54450334 = c0;
        double r54450335 = w;
        double r54450336 = 2.0;
        double r54450337 = r54450335 * r54450336;
        double r54450338 = r54450334 / r54450337;
        double r54450339 = d;
        double r54450340 = r54450339 * r54450339;
        double r54450341 = r54450334 * r54450340;
        double r54450342 = D;
        double r54450343 = r54450342 * r54450342;
        double r54450344 = h;
        double r54450345 = r54450335 * r54450344;
        double r54450346 = r54450343 * r54450345;
        double r54450347 = r54450341 / r54450346;
        double r54450348 = r54450347 * r54450347;
        double r54450349 = M;
        double r54450350 = r54450349 * r54450349;
        double r54450351 = r54450348 - r54450350;
        double r54450352 = sqrt(r54450351);
        double r54450353 = r54450352 + r54450347;
        double r54450354 = r54450338 * r54450353;
        double r54450355 = 2.608039255478076e+261;
        bool r54450356 = r54450354 <= r54450355;
        double r54450357 = 0.0;
        double r54450358 = r54450356 ? r54450354 : r54450357;
        return r54450358;
}

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 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))))) < 2.608039255478076e+261

   1. Initial program 33.7

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

   if 2.608039255478076e+261 < (* (/ 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)))))

   1. Initial program 62.7

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

   2. Simplified 55.1

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

   3. Taylor expanded around -inf 33.5

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

   5. Applied mul0 31.4

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

4. Final simplification 31.8

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{c0}{w \cdot 2} \cdot \left(\sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(D \cdot D\right) \cdot \left(w \cdot h\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(D \cdot D\right) \cdot \left(w \cdot h\right)} - M \cdot M} + \frac{c0 \cdot \left(d \cdot d\right)}{\left(D \cdot D\right) \cdot \left(w \cdot h\right)}\right) \le 2.608039255478076 \cdot 10^{+261}:\\ \;\;\;\;\frac{c0}{w \cdot 2} \cdot \left(\sqrt{\frac{c0 \cdot \left(d \cdot d\right)}{\left(D \cdot D\right) \cdot \left(w \cdot h\right)} \cdot \frac{c0 \cdot \left(d \cdot d\right)}{\left(D \cdot D\right) \cdot \left(w \cdot h\right)} - M \cdot M} + \frac{c0 \cdot \left(d \cdot d\right)}{\left(D \cdot D\right) \cdot \left(w \cdot h\right)}\right)\\ \mathbf{else}:\\ \;\;\;\;0\\ \end{array}\]

Reproduce

herbie shell --seed 2019128 +o rules:numerics
(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))))))