Average Error: 28.7 → 28.8
Time: 31.8s
Precision: 64
\[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644704999984242022037506103515625\right) \cdot y + 230661.5106160000141244381666183471679688\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\]
↓
\[\left(\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644704999984242022037506103515625\right) \cdot y + 230661.5106160000141244381666183471679688\right) \cdot y + t\right) \cdot \frac{1}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\]
\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}
↓
\left(\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644704999984242022037506103515625\right) \cdot y + 230661.5106160000141244381666183471679688\right) \cdot y + t\right) \cdot \frac{1}{\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 r67335 = x;
        double r67336 = y;
        double r67337 = r67335 * r67336;
        double r67338 = z;
        double r67339 = r67337 + r67338;
        double r67340 = r67339 * r67336;
        double r67341 = 27464.7644705;
        double r67342 = r67340 + r67341;
        double r67343 = r67342 * r67336;
        double r67344 = 230661.510616;
        double r67345 = r67343 + r67344;
        double r67346 = r67345 * r67336;
        double r67347 = t;
        double r67348 = r67346 + r67347;
        double r67349 = a;
        double r67350 = r67336 + r67349;
        double r67351 = r67350 * r67336;
        double r67352 = b;
        double r67353 = r67351 + r67352;
        double r67354 = r67353 * r67336;
        double r67355 = c;
        double r67356 = r67354 + r67355;
        double r67357 = r67356 * r67336;
        double r67358 = i;
        double r67359 = r67357 + r67358;
        double r67360 = r67348 / r67359;
        return r67360;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r67361 = x;
        double r67362 = y;
        double r67363 = r67361 * r67362;
        double r67364 = z;
        double r67365 = r67363 + r67364;
        double r67366 = r67365 * r67362;
        double r67367 = 27464.7644705;
        double r67368 = r67366 + r67367;
        double r67369 = r67368 * r67362;
        double r67370 = 230661.510616;
        double r67371 = r67369 + r67370;
        double r67372 = r67371 * r67362;
        double r67373 = t;
        double r67374 = r67372 + r67373;
        double r67375 = 1.0;
        double r67376 = a;
        double r67377 = r67362 + r67376;
        double r67378 = r67377 * r67362;
        double r67379 = b;
        double r67380 = r67378 + r67379;
        double r67381 = r67380 * r67362;
        double r67382 = c;
        double r67383 = r67381 + r67382;
        double r67384 = r67383 * r67362;
        double r67385 = i;
        double r67386 = r67384 + r67385;
        double r67387 = r67375 / r67386;
        double r67388 = r67374 * r67387;
        return r67388;
}

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 28.7

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

  3. Applied div-inv28.8

    \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644704999984242022037506103515625\right) \cdot y + 230661.5106160000141244381666183471679688\right) \cdot y + t\right) \cdot \frac{1}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}}\]

  4. Final simplification28.8

    \[\leadsto \left(\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644704999984242022037506103515625\right) \cdot y + 230661.5106160000141244381666183471679688\right) \cdot y + t\right) \cdot \frac{1}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\]

Reproduce

herbie shell --seed 2019323 
(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)))