Henrywood and Agarwal, Equation (13)

Average Error: 58.1 → 31.8

Time: 40.2s

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 r3409318 = c0;
        double r3409319 = 2.0;
        double r3409320 = w;
        double r3409321 = r3409319 * r3409320;
        double r3409322 = r3409318 / r3409321;
        double r3409323 = d;
        double r3409324 = r3409323 * r3409323;
        double r3409325 = r3409318 * r3409324;
        double r3409326 = h;
        double r3409327 = r3409320 * r3409326;
        double r3409328 = D;
        double r3409329 = r3409328 * r3409328;
        double r3409330 = r3409327 * r3409329;
        double r3409331 = r3409325 / r3409330;
        double r3409332 = r3409331 * r3409331;
        double r3409333 = M;
        double r3409334 = r3409333 * r3409333;
        double r3409335 = r3409332 - r3409334;
        double r3409336 = sqrt(r3409335);
        double r3409337 = r3409331 + r3409336;
        double r3409338 = r3409322 * r3409337;
        return r3409338;
}

↓

double f(double c0, double w, double h, double D, double d, double M) {
        double r3409339 = c0;
        double r3409340 = w;
        double r3409341 = 2.0;
        double r3409342 = r3409340 * r3409341;
        double r3409343 = r3409339 / r3409342;
        double r3409344 = d;
        double r3409345 = r3409344 * r3409344;
        double r3409346 = r3409339 * r3409345;
        double r3409347 = D;
        double r3409348 = r3409347 * r3409347;
        double r3409349 = h;
        double r3409350 = r3409340 * r3409349;
        double r3409351 = r3409348 * r3409350;
        double r3409352 = r3409346 / r3409351;
        double r3409353 = r3409352 * r3409352;
        double r3409354 = M;
        double r3409355 = r3409354 * r3409354;
        double r3409356 = r3409353 - r3409355;
        double r3409357 = sqrt(r3409356);
        double r3409358 = r3409357 + r3409352;
        double r3409359 = r3409343 * r3409358;
        double r3409360 = 2.608039255478076e+261;
        bool r3409361 = r3409359 <= r3409360;
        double r3409362 = 0.0;
        double r3409363 = r3409361 ? r3409359 : r3409362;
        return r3409363;
}

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. Taylor expanded around 0 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))))))