Average Error: 29.5 → 29.6
Time: 8.1s
Precision: 64
\[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644704999984242022037506103515625\right) \cdot y + 230661.5106160000141244381666183471679688\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\]
↓
\[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644704999984242022037506103515625\right) \cdot y + 230661.5106160000141244381666183471679688\right) \cdot y + t}{\left(\left(\sqrt[3]{\left(y + a\right) \cdot y + b} \cdot \sqrt[3]{\left(y + a\right) \cdot y + b}\right) \cdot \left(\sqrt[3]{\left(y + a\right) \cdot y + b} \cdot y\right) + c\right) \cdot y + i}\]
\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(\left(x \cdot y + z\right) \cdot y + 27464.7644704999984242022037506103515625\right) \cdot y + 230661.5106160000141244381666183471679688\right) \cdot y + t}{\left(\left(\sqrt[3]{\left(y + a\right) \cdot y + b} \cdot \sqrt[3]{\left(y + a\right) \cdot y + b}\right) \cdot \left(\sqrt[3]{\left(y + a\right) \cdot y + b} \cdot y\right) + c\right) \cdot y + i}
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r68337 = x;
        double r68338 = y;
        double r68339 = r68337 * r68338;
        double r68340 = z;
        double r68341 = r68339 + r68340;
        double r68342 = r68341 * r68338;
        double r68343 = 27464.7644705;
        double r68344 = r68342 + r68343;
        double r68345 = r68344 * r68338;
        double r68346 = 230661.510616;
        double r68347 = r68345 + r68346;
        double r68348 = r68347 * r68338;
        double r68349 = t;
        double r68350 = r68348 + r68349;
        double r68351 = a;
        double r68352 = r68338 + r68351;
        double r68353 = r68352 * r68338;
        double r68354 = b;
        double r68355 = r68353 + r68354;
        double r68356 = r68355 * r68338;
        double r68357 = c;
        double r68358 = r68356 + r68357;
        double r68359 = r68358 * r68338;
        double r68360 = i;
        double r68361 = r68359 + r68360;
        double r68362 = r68350 / r68361;
        return r68362;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r68363 = x;
        double r68364 = y;
        double r68365 = r68363 * r68364;
        double r68366 = z;
        double r68367 = r68365 + r68366;
        double r68368 = r68367 * r68364;
        double r68369 = 27464.7644705;
        double r68370 = r68368 + r68369;
        double r68371 = r68370 * r68364;
        double r68372 = 230661.510616;
        double r68373 = r68371 + r68372;
        double r68374 = r68373 * r68364;
        double r68375 = t;
        double r68376 = r68374 + r68375;
        double r68377 = a;
        double r68378 = r68364 + r68377;
        double r68379 = r68378 * r68364;
        double r68380 = b;
        double r68381 = r68379 + r68380;
        double r68382 = cbrt(r68381);
        double r68383 = r68382 * r68382;
        double r68384 = r68382 * r68364;
        double r68385 = r68383 * r68384;
        double r68386 = c;
        double r68387 = r68385 + r68386;
        double r68388 = r68387 * r68364;
        double r68389 = i;
        double r68390 = r68388 + r68389;
        double r68391 = r68376 / r68390;
        return r68391;
}

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 29.5

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

  3. Applied add-cube-cbrt29.6

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

  4. Applied associate-*l*29.6

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

  5. Final simplification29.6

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

Reproduce

herbie shell --seed 2019356 
(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)))