Average Error: 28.3 → 28.3
Time: 35.9s
Precision: 64
\[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\]
↓
\[\frac{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, x, z\right), 27464.7644705\right), 230661.510616\right), t\right)}{\mathsf{fma}\left(\mathsf{fma}\left(y, \mathsf{fma}\left(y + a, y, b\right), c\right), y, i\right)}\]
\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}
↓
\frac{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, x, z\right), 27464.7644705\right), 230661.510616\right), t\right)}{\mathsf{fma}\left(\mathsf{fma}\left(y, \mathsf{fma}\left(y + a, y, b\right), c\right), y, i\right)}
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r4279431 = x;
        double r4279432 = y;
        double r4279433 = r4279431 * r4279432;
        double r4279434 = z;
        double r4279435 = r4279433 + r4279434;
        double r4279436 = r4279435 * r4279432;
        double r4279437 = 27464.7644705;
        double r4279438 = r4279436 + r4279437;
        double r4279439 = r4279438 * r4279432;
        double r4279440 = 230661.510616;
        double r4279441 = r4279439 + r4279440;
        double r4279442 = r4279441 * r4279432;
        double r4279443 = t;
        double r4279444 = r4279442 + r4279443;
        double r4279445 = a;
        double r4279446 = r4279432 + r4279445;
        double r4279447 = r4279446 * r4279432;
        double r4279448 = b;
        double r4279449 = r4279447 + r4279448;
        double r4279450 = r4279449 * r4279432;
        double r4279451 = c;
        double r4279452 = r4279450 + r4279451;
        double r4279453 = r4279452 * r4279432;
        double r4279454 = i;
        double r4279455 = r4279453 + r4279454;
        double r4279456 = r4279444 / r4279455;
        return r4279456;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r4279457 = y;
        double r4279458 = x;
        double r4279459 = z;
        double r4279460 = fma(r4279457, r4279458, r4279459);
        double r4279461 = 27464.7644705;
        double r4279462 = fma(r4279457, r4279460, r4279461);
        double r4279463 = 230661.510616;
        double r4279464 = fma(r4279457, r4279462, r4279463);
        double r4279465 = t;
        double r4279466 = fma(r4279457, r4279464, r4279465);
        double r4279467 = a;
        double r4279468 = r4279457 + r4279467;
        double r4279469 = b;
        double r4279470 = fma(r4279468, r4279457, r4279469);
        double r4279471 = c;
        double r4279472 = fma(r4279457, r4279470, r4279471);
        double r4279473 = i;
        double r4279474 = fma(r4279472, r4279457, r4279473);
        double r4279475 = r4279466 / r4279474;
        return r4279475;
}

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

Derivation

  1. Initial program 28.3

    \[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\]

  2. Simplified28.3

    \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, x, z\right), 27464.7644705\right), 230661.510616\right), t\right)}{\mathsf{fma}\left(\mathsf{fma}\left(y, \mathsf{fma}\left(y + a, y, b\right), c\right), y, i\right)}}\]

  3. Final simplification28.3

    \[\leadsto \frac{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, x, z\right), 27464.7644705\right), 230661.510616\right), t\right)}{\mathsf{fma}\left(\mathsf{fma}\left(y, \mathsf{fma}\left(y + a, y, b\right), c\right), y, i\right)}\]

Reproduce

herbie shell --seed 2019162 +o rules:numerics
(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)))