Average Error: 28.9 → 28.9
Time: 27.2s
Precision: 64
\[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644704999984242022037506103515625\right) \cdot y + 230661.5106160000141244381666183471679688\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\]
↓
\[\frac{\left(\left(\sqrt[3]{\left(\left(x \cdot y + z\right) \cdot y + 27464.7644704999984242022037506103515625\right) \cdot y} \cdot \sqrt[3]{\left(\left(x \cdot y + z\right) \cdot y + 27464.7644704999984242022037506103515625\right) \cdot y}\right) \cdot \sqrt[3]{\left(\left(x \cdot y + z\right) \cdot y + 27464.7644704999984242022037506103515625\right) \cdot y} + 230661.5106160000141244381666183471679688\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\]
\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644704999984242022037506103515625\right) \cdot y + 230661.5106160000141244381666183471679688\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}
↓
\frac{\left(\left(\sqrt[3]{\left(\left(x \cdot y + z\right) \cdot y + 27464.7644704999984242022037506103515625\right) \cdot y} \cdot \sqrt[3]{\left(\left(x \cdot y + z\right) \cdot y + 27464.7644704999984242022037506103515625\right) \cdot y}\right) \cdot \sqrt[3]{\left(\left(x \cdot y + z\right) \cdot y + 27464.7644704999984242022037506103515625\right) \cdot y} + 230661.5106160000141244381666183471679688\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r68328 = x;
        double r68329 = y;
        double r68330 = r68328 * r68329;
        double r68331 = z;
        double r68332 = r68330 + r68331;
        double r68333 = r68332 * r68329;
        double r68334 = 27464.7644705;
        double r68335 = r68333 + r68334;
        double r68336 = r68335 * r68329;
        double r68337 = 230661.510616;
        double r68338 = r68336 + r68337;
        double r68339 = r68338 * r68329;
        double r68340 = t;
        double r68341 = r68339 + r68340;
        double r68342 = a;
        double r68343 = r68329 + r68342;
        double r68344 = r68343 * r68329;
        double r68345 = b;
        double r68346 = r68344 + r68345;
        double r68347 = r68346 * r68329;
        double r68348 = c;
        double r68349 = r68347 + r68348;
        double r68350 = r68349 * r68329;
        double r68351 = i;
        double r68352 = r68350 + r68351;
        double r68353 = r68341 / r68352;
        return r68353;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r68354 = x;
        double r68355 = y;
        double r68356 = r68354 * r68355;
        double r68357 = z;
        double r68358 = r68356 + r68357;
        double r68359 = r68358 * r68355;
        double r68360 = 27464.7644705;
        double r68361 = r68359 + r68360;
        double r68362 = r68361 * r68355;
        double r68363 = cbrt(r68362);
        double r68364 = r68363 * r68363;
        double r68365 = r68364 * r68363;
        double r68366 = 230661.510616;
        double r68367 = r68365 + r68366;
        double r68368 = r68367 * r68355;
        double r68369 = t;
        double r68370 = r68368 + r68369;
        double r68371 = a;
        double r68372 = r68355 + r68371;
        double r68373 = r68372 * r68355;
        double r68374 = b;
        double r68375 = r68373 + r68374;
        double r68376 = r68375 * r68355;
        double r68377 = c;
        double r68378 = r68376 + r68377;
        double r68379 = r68378 * r68355;
        double r68380 = i;
        double r68381 = r68379 + r68380;
        double r68382 = r68370 / r68381;
        return r68382;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Bits error versus a

Bits error versus b

Bits error versus c

Bits error versus i

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 28.9

    \[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644704999984242022037506103515625\right) \cdot y + 230661.5106160000141244381666183471679688\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\]
  2. Using strategy rm

  3. Applied add-cube-cbrt28.9

    \[\leadsto \frac{\left(\color{blue}{\left(\sqrt[3]{\left(\left(x \cdot y + z\right) \cdot y + 27464.7644704999984242022037506103515625\right) \cdot y} \cdot \sqrt[3]{\left(\left(x \cdot y + z\right) \cdot y + 27464.7644704999984242022037506103515625\right) \cdot y}\right) \cdot \sqrt[3]{\left(\left(x \cdot y + z\right) \cdot y + 27464.7644704999984242022037506103515625\right) \cdot y}} + 230661.5106160000141244381666183471679688\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\]

  4. Final simplification28.9

    \[\leadsto \frac{\left(\left(\sqrt[3]{\left(\left(x \cdot y + z\right) \cdot y + 27464.7644704999984242022037506103515625\right) \cdot y} \cdot \sqrt[3]{\left(\left(x \cdot y + z\right) \cdot y + 27464.7644704999984242022037506103515625\right) \cdot y}\right) \cdot \sqrt[3]{\left(\left(x \cdot y + z\right) \cdot y + 27464.7644704999984242022037506103515625\right) \cdot y} + 230661.5106160000141244381666183471679688\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\]

Reproduce

herbie shell --seed 2019322 
(FPCore (x y z t a b c i)
  :name "Numeric.SpecFunctions:logGamma from math-functions-0.1.5.2"
  :precision binary64
  (/ (+ (* (+ (* (+ (* (+ (* x y) z) y) 27464.7644705) y) 230661.510616) y) t) (+ (* (+ (* (+ (* (+ y a) y) b) y) c) y) i)))