Average Error: 29.1 → 29.2
Time: 11.5s
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 r118432 = x;
        double r118433 = y;
        double r118434 = r118432 * r118433;
        double r118435 = z;
        double r118436 = r118434 + r118435;
        double r118437 = r118436 * r118433;
        double r118438 = 27464.7644705;
        double r118439 = r118437 + r118438;
        double r118440 = r118439 * r118433;
        double r118441 = 230661.510616;
        double r118442 = r118440 + r118441;
        double r118443 = r118442 * r118433;
        double r118444 = t;
        double r118445 = r118443 + r118444;
        double r118446 = a;
        double r118447 = r118433 + r118446;
        double r118448 = r118447 * r118433;
        double r118449 = b;
        double r118450 = r118448 + r118449;
        double r118451 = r118450 * r118433;
        double r118452 = c;
        double r118453 = r118451 + r118452;
        double r118454 = r118453 * r118433;
        double r118455 = i;
        double r118456 = r118454 + r118455;
        double r118457 = r118445 / r118456;
        return r118457;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r118458 = x;
        double r118459 = y;
        double r118460 = r118458 * r118459;
        double r118461 = z;
        double r118462 = r118460 + r118461;
        double r118463 = r118462 * r118459;
        double r118464 = 27464.7644705;
        double r118465 = r118463 + r118464;
        double r118466 = r118465 * r118459;
        double r118467 = 230661.510616;
        double r118468 = r118466 + r118467;
        double r118469 = r118468 * r118459;
        double r118470 = t;
        double r118471 = r118469 + r118470;
        double r118472 = 1.0;
        double r118473 = a;
        double r118474 = r118459 + r118473;
        double r118475 = r118474 * r118459;
        double r118476 = b;
        double r118477 = r118475 + r118476;
        double r118478 = r118477 * r118459;
        double r118479 = c;
        double r118480 = r118478 + r118479;
        double r118481 = r118480 * r118459;
        double r118482 = i;
        double r118483 = r118481 + r118482;
        double r118484 = r118472 / r118483;
        double r118485 = r118471 * r118484;
        return r118485;
}

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 29.1

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

  3. Applied div-inv29.2

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

  4. Final simplification29.2

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

Reproduce

herbie shell --seed 2020001 
(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)))