Average Error: 29.5 → 29.5
Time: 15.4s
Precision: 64
\[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.764470499998\right) \cdot y + 230661.510616000014\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\]
↓
\[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.764470499998\right) \cdot y + 230661.510616000014\right) \cdot y + t}{\left(\left(y \cdot b + \left({y}^{3} + a \cdot {y}^{2}\right)\right) + c\right) \cdot y + i}\]
\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.764470499998\right) \cdot y + 230661.510616000014\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 + 27464.764470499998\right) \cdot y + 230661.510616000014\right) \cdot y + t}{\left(\left(y \cdot b + \left({y}^{3} + a \cdot {y}^{2}\right)\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 r73480 = x;
        double r73481 = y;
        double r73482 = r73480 * r73481;
        double r73483 = z;
        double r73484 = r73482 + r73483;
        double r73485 = r73484 * r73481;
        double r73486 = 27464.7644705;
        double r73487 = r73485 + r73486;
        double r73488 = r73487 * r73481;
        double r73489 = 230661.510616;
        double r73490 = r73488 + r73489;
        double r73491 = r73490 * r73481;
        double r73492 = t;
        double r73493 = r73491 + r73492;
        double r73494 = a;
        double r73495 = r73481 + r73494;
        double r73496 = r73495 * r73481;
        double r73497 = b;
        double r73498 = r73496 + r73497;
        double r73499 = r73498 * r73481;
        double r73500 = c;
        double r73501 = r73499 + r73500;
        double r73502 = r73501 * r73481;
        double r73503 = i;
        double r73504 = r73502 + r73503;
        double r73505 = r73493 / r73504;
        return r73505;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r73506 = x;
        double r73507 = y;
        double r73508 = r73506 * r73507;
        double r73509 = z;
        double r73510 = r73508 + r73509;
        double r73511 = r73510 * r73507;
        double r73512 = 27464.7644705;
        double r73513 = r73511 + r73512;
        double r73514 = r73513 * r73507;
        double r73515 = 230661.510616;
        double r73516 = r73514 + r73515;
        double r73517 = r73516 * r73507;
        double r73518 = t;
        double r73519 = r73517 + r73518;
        double r73520 = b;
        double r73521 = r73507 * r73520;
        double r73522 = 3.0;
        double r73523 = pow(r73507, r73522);
        double r73524 = a;
        double r73525 = 2.0;
        double r73526 = pow(r73507, r73525);
        double r73527 = r73524 * r73526;
        double r73528 = r73523 + r73527;
        double r73529 = r73521 + r73528;
        double r73530 = c;
        double r73531 = r73529 + r73530;
        double r73532 = r73531 * r73507;
        double r73533 = i;
        double r73534 = r73532 + r73533;
        double r73535 = r73519 / r73534;
        return r73535;
}

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

    \[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.764470499998\right) \cdot y + 230661.510616000014\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\]

  2. Taylor expanded around inf 29.5

    \[\leadsto \frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.764470499998\right) \cdot y + 230661.510616000014\right) \cdot y + t}{\left(\color{blue}{\left(y \cdot b + \left({y}^{3} + a \cdot {y}^{2}\right)\right)} + c\right) \cdot y + i}\]

  3. Final simplification29.5

    \[\leadsto \frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.764470499998\right) \cdot y + 230661.510616000014\right) \cdot y + t}{\left(\left(y \cdot b + \left({y}^{3} + a \cdot {y}^{2}\right)\right) + c\right) \cdot y + i}\]

Reproduce

herbie shell --seed 2020046 
(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)))