Average Error: 29.2 → 29.3
Time: 37.6s
Precision: 64
\[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644704999984242022037506103515625\right) \cdot y + 230661.5106160000141244381666183471679688\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\]
↓
\[\frac{\frac{1}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}}{\frac{1}{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644704999984242022037506103515625\right) \cdot y + 230661.5106160000141244381666183471679688\right) \cdot y + t}}\]
\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{\frac{1}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}}{\frac{1}{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644704999984242022037506103515625\right) \cdot y + 230661.5106160000141244381666183471679688\right) \cdot y + t}}
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r6974339 = x;
        double r6974340 = y;
        double r6974341 = r6974339 * r6974340;
        double r6974342 = z;
        double r6974343 = r6974341 + r6974342;
        double r6974344 = r6974343 * r6974340;
        double r6974345 = 27464.7644705;
        double r6974346 = r6974344 + r6974345;
        double r6974347 = r6974346 * r6974340;
        double r6974348 = 230661.510616;
        double r6974349 = r6974347 + r6974348;
        double r6974350 = r6974349 * r6974340;
        double r6974351 = t;
        double r6974352 = r6974350 + r6974351;
        double r6974353 = a;
        double r6974354 = r6974340 + r6974353;
        double r6974355 = r6974354 * r6974340;
        double r6974356 = b;
        double r6974357 = r6974355 + r6974356;
        double r6974358 = r6974357 * r6974340;
        double r6974359 = c;
        double r6974360 = r6974358 + r6974359;
        double r6974361 = r6974360 * r6974340;
        double r6974362 = i;
        double r6974363 = r6974361 + r6974362;
        double r6974364 = r6974352 / r6974363;
        return r6974364;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r6974365 = 1.0;
        double r6974366 = y;
        double r6974367 = a;
        double r6974368 = r6974366 + r6974367;
        double r6974369 = r6974368 * r6974366;
        double r6974370 = b;
        double r6974371 = r6974369 + r6974370;
        double r6974372 = r6974371 * r6974366;
        double r6974373 = c;
        double r6974374 = r6974372 + r6974373;
        double r6974375 = r6974374 * r6974366;
        double r6974376 = i;
        double r6974377 = r6974375 + r6974376;
        double r6974378 = r6974365 / r6974377;
        double r6974379 = x;
        double r6974380 = r6974379 * r6974366;
        double r6974381 = z;
        double r6974382 = r6974380 + r6974381;
        double r6974383 = r6974382 * r6974366;
        double r6974384 = 27464.7644705;
        double r6974385 = r6974383 + r6974384;
        double r6974386 = r6974385 * r6974366;
        double r6974387 = 230661.510616;
        double r6974388 = r6974386 + r6974387;
        double r6974389 = r6974388 * r6974366;
        double r6974390 = t;
        double r6974391 = r6974389 + r6974390;
        double r6974392 = r6974365 / r6974391;
        double r6974393 = r6974378 / r6974392;
        return r6974393;
}

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 29.2

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

  3. Applied clear-num29.4

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

  5. Applied div-inv29.5

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

  6. Applied associate-/r*29.3

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

  7. Final simplification29.3

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

Reproduce

herbie shell --seed 2019174 
(FPCore (x y z t a b c i)
  :name "Numeric.SpecFunctions:logGamma from math-functions-0.1.5.2"
  (/ (+ (* (+ (* (+ (* (+ (* x y) z) y) 27464.7644705) y) 230661.510616) y) t) (+ (* (+ (* (+ (* (+ y a) y) b) y) c) y) i)))