Average Error: 28.6 → 28.6
Time: 29.8s
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 r81424 = x;
        double r81425 = y;
        double r81426 = r81424 * r81425;
        double r81427 = z;
        double r81428 = r81426 + r81427;
        double r81429 = r81428 * r81425;
        double r81430 = 27464.7644705;
        double r81431 = r81429 + r81430;
        double r81432 = r81431 * r81425;
        double r81433 = 230661.510616;
        double r81434 = r81432 + r81433;
        double r81435 = r81434 * r81425;
        double r81436 = t;
        double r81437 = r81435 + r81436;
        double r81438 = a;
        double r81439 = r81425 + r81438;
        double r81440 = r81439 * r81425;
        double r81441 = b;
        double r81442 = r81440 + r81441;
        double r81443 = r81442 * r81425;
        double r81444 = c;
        double r81445 = r81443 + r81444;
        double r81446 = r81445 * r81425;
        double r81447 = i;
        double r81448 = r81446 + r81447;
        double r81449 = r81437 / r81448;
        return r81449;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r81450 = x;
        double r81451 = y;
        double r81452 = r81450 * r81451;
        double r81453 = z;
        double r81454 = r81452 + r81453;
        double r81455 = r81454 * r81451;
        double r81456 = 27464.7644705;
        double r81457 = r81455 + r81456;
        double r81458 = r81457 * r81451;
        double r81459 = 230661.510616;
        double r81460 = r81458 + r81459;
        double r81461 = r81460 * r81451;
        double r81462 = t;
        double r81463 = r81461 + r81462;
        double r81464 = 1.0;
        double r81465 = a;
        double r81466 = r81451 + r81465;
        double r81467 = r81466 * r81451;
        double r81468 = b;
        double r81469 = r81467 + r81468;
        double r81470 = r81469 * r81451;
        double r81471 = c;
        double r81472 = r81470 + r81471;
        double r81473 = r81472 * r81451;
        double r81474 = i;
        double r81475 = r81473 + r81474;
        double r81476 = r81464 / r81475;
        double r81477 = r81463 * r81476;
        return r81477;
}

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 28.6

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

  3. Applied div-inv28.6

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

  4. Final simplification28.6

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

Reproduce

herbie shell --seed 2019325 
(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)))