Average Error: 29.6 → 29.6
Time: 1.2m
Precision: 64
\[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644704999984242022037506103515625\right) \cdot y + 230661.5106160000141244381666183471679688\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\]
↓
\[\frac{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, x, z\right), 27464.7644704999984242022037506103515625\right), 230661.5106160000141244381666183471679688\right), t\right)}{\mathsf{fma}\left(\mathsf{fma}\left(y, \mathsf{fma}\left(y + a, y, b\right), c\right), y, i\right)}\]
\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644704999984242022037506103515625\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(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, x, z\right), 27464.7644704999984242022037506103515625\right), 230661.5106160000141244381666183471679688\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 r3237348 = x;
        double r3237349 = y;
        double r3237350 = r3237348 * r3237349;
        double r3237351 = z;
        double r3237352 = r3237350 + r3237351;
        double r3237353 = r3237352 * r3237349;
        double r3237354 = 27464.7644705;
        double r3237355 = r3237353 + r3237354;
        double r3237356 = r3237355 * r3237349;
        double r3237357 = 230661.510616;
        double r3237358 = r3237356 + r3237357;
        double r3237359 = r3237358 * r3237349;
        double r3237360 = t;
        double r3237361 = r3237359 + r3237360;
        double r3237362 = a;
        double r3237363 = r3237349 + r3237362;
        double r3237364 = r3237363 * r3237349;
        double r3237365 = b;
        double r3237366 = r3237364 + r3237365;
        double r3237367 = r3237366 * r3237349;
        double r3237368 = c;
        double r3237369 = r3237367 + r3237368;
        double r3237370 = r3237369 * r3237349;
        double r3237371 = i;
        double r3237372 = r3237370 + r3237371;
        double r3237373 = r3237361 / r3237372;
        return r3237373;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r3237374 = y;
        double r3237375 = x;
        double r3237376 = z;
        double r3237377 = fma(r3237374, r3237375, r3237376);
        double r3237378 = 27464.7644705;
        double r3237379 = fma(r3237374, r3237377, r3237378);
        double r3237380 = 230661.510616;
        double r3237381 = fma(r3237374, r3237379, r3237380);
        double r3237382 = t;
        double r3237383 = fma(r3237374, r3237381, r3237382);
        double r3237384 = a;
        double r3237385 = r3237374 + r3237384;
        double r3237386 = b;
        double r3237387 = fma(r3237385, r3237374, r3237386);
        double r3237388 = c;
        double r3237389 = fma(r3237374, r3237387, r3237388);
        double r3237390 = i;
        double r3237391 = fma(r3237389, r3237374, r3237390);
        double r3237392 = r3237383 / r3237391;
        return r3237392;
}

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 29.6

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

  2. Simplified29.6

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

  3. Final simplification29.6

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

Reproduce

herbie shell --seed 2019168 +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)))