Average Error: 29.2 → 29.2
Time: 32.9s
Precision: 64
\[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644704999984242022037506103515625\right) \cdot y + 230661.5106160000141244381666183471679688\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\]
↓
\[\frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x, y, z\right), y, 27464.7644704999984242022037506103515625\right), y, 230661.5106160000141244381666183471679688\right), y, t\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(y + a, y, b\right), y, c\right), y, i\right)}\]
\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{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x, y, z\right), y, 27464.7644704999984242022037506103515625\right), y, 230661.5106160000141244381666183471679688\right), y, t\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(y + a, y, b\right), y, c\right), y, i\right)}
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r51405 = x;
        double r51406 = y;
        double r51407 = r51405 * r51406;
        double r51408 = z;
        double r51409 = r51407 + r51408;
        double r51410 = r51409 * r51406;
        double r51411 = 27464.7644705;
        double r51412 = r51410 + r51411;
        double r51413 = r51412 * r51406;
        double r51414 = 230661.510616;
        double r51415 = r51413 + r51414;
        double r51416 = r51415 * r51406;
        double r51417 = t;
        double r51418 = r51416 + r51417;
        double r51419 = a;
        double r51420 = r51406 + r51419;
        double r51421 = r51420 * r51406;
        double r51422 = b;
        double r51423 = r51421 + r51422;
        double r51424 = r51423 * r51406;
        double r51425 = c;
        double r51426 = r51424 + r51425;
        double r51427 = r51426 * r51406;
        double r51428 = i;
        double r51429 = r51427 + r51428;
        double r51430 = r51418 / r51429;
        return r51430;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r51431 = x;
        double r51432 = y;
        double r51433 = z;
        double r51434 = fma(r51431, r51432, r51433);
        double r51435 = 27464.7644705;
        double r51436 = fma(r51434, r51432, r51435);
        double r51437 = 230661.510616;
        double r51438 = fma(r51436, r51432, r51437);
        double r51439 = t;
        double r51440 = fma(r51438, r51432, r51439);
        double r51441 = a;
        double r51442 = r51432 + r51441;
        double r51443 = b;
        double r51444 = fma(r51442, r51432, r51443);
        double r51445 = c;
        double r51446 = fma(r51444, r51432, r51445);
        double r51447 = i;
        double r51448 = fma(r51446, r51432, r51447);
        double r51449 = r51440 / r51448;
        return r51449;
}

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 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. Simplified29.2

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

  3. Final simplification29.2

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

Reproduce

herbie shell --seed 2019326 +o rules:numerics
(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)))