Average Error: 28.8 → 28.9
Time: 28.2s
Precision: 64
\[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644704999984242022037506103515625\right) \cdot y + 230661.5106160000141244381666183471679688\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\]
↓
\[\frac{1}{\mathsf{fma}\left(\mathsf{fma}\left(y, \mathsf{fma}\left(y + a, y, b\right), c\right), y, i\right)} \cdot \mathsf{fma}\left(\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, x, z\right), 27464.7644704999984242022037506103515625\right), 230661.5106160000141244381666183471679688\right), y, t\right)\]
\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{1}{\mathsf{fma}\left(\mathsf{fma}\left(y, \mathsf{fma}\left(y + a, y, b\right), c\right), y, i\right)} \cdot \mathsf{fma}\left(\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, x, z\right), 27464.7644704999984242022037506103515625\right), 230661.5106160000141244381666183471679688\right), y, t\right)
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r2975674 = x;
        double r2975675 = y;
        double r2975676 = r2975674 * r2975675;
        double r2975677 = z;
        double r2975678 = r2975676 + r2975677;
        double r2975679 = r2975678 * r2975675;
        double r2975680 = 27464.7644705;
        double r2975681 = r2975679 + r2975680;
        double r2975682 = r2975681 * r2975675;
        double r2975683 = 230661.510616;
        double r2975684 = r2975682 + r2975683;
        double r2975685 = r2975684 * r2975675;
        double r2975686 = t;
        double r2975687 = r2975685 + r2975686;
        double r2975688 = a;
        double r2975689 = r2975675 + r2975688;
        double r2975690 = r2975689 * r2975675;
        double r2975691 = b;
        double r2975692 = r2975690 + r2975691;
        double r2975693 = r2975692 * r2975675;
        double r2975694 = c;
        double r2975695 = r2975693 + r2975694;
        double r2975696 = r2975695 * r2975675;
        double r2975697 = i;
        double r2975698 = r2975696 + r2975697;
        double r2975699 = r2975687 / r2975698;
        return r2975699;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r2975700 = 1.0;
        double r2975701 = y;
        double r2975702 = a;
        double r2975703 = r2975701 + r2975702;
        double r2975704 = b;
        double r2975705 = fma(r2975703, r2975701, r2975704);
        double r2975706 = c;
        double r2975707 = fma(r2975701, r2975705, r2975706);
        double r2975708 = i;
        double r2975709 = fma(r2975707, r2975701, r2975708);
        double r2975710 = r2975700 / r2975709;
        double r2975711 = x;
        double r2975712 = z;
        double r2975713 = fma(r2975701, r2975711, r2975712);
        double r2975714 = 27464.7644705;
        double r2975715 = fma(r2975701, r2975713, r2975714);
        double r2975716 = 230661.510616;
        double r2975717 = fma(r2975701, r2975715, r2975716);
        double r2975718 = t;
        double r2975719 = fma(r2975717, r2975701, r2975718);
        double r2975720 = r2975710 * r2975719;
        return r2975720;
}

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 28.8

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

  2. Simplified28.8

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

  4. Applied div-inv28.9

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

  5. Final simplification28.9

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

Reproduce

herbie shell --seed 2019172 +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)))