Average Error: 29.0 → 29.0
Time: 58.6s
Precision: 64
\[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644704999984242022037506103515625\right) \cdot y + 230661.5106160000141244381666183471679688\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\]
↓
\[\mathsf{fma}\left(\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, x, z\right), 27464.7644704999984242022037506103515625\right), 230661.5106160000141244381666183471679688\right), y, t\right) \cdot \frac{1}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(a + y, y, b\right), y, c\right), y, i\right)}\]
\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}
↓
\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(\mathsf{fma}\left(a + y, 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 r2850659 = x;
        double r2850660 = y;
        double r2850661 = r2850659 * r2850660;
        double r2850662 = z;
        double r2850663 = r2850661 + r2850662;
        double r2850664 = r2850663 * r2850660;
        double r2850665 = 27464.7644705;
        double r2850666 = r2850664 + r2850665;
        double r2850667 = r2850666 * r2850660;
        double r2850668 = 230661.510616;
        double r2850669 = r2850667 + r2850668;
        double r2850670 = r2850669 * r2850660;
        double r2850671 = t;
        double r2850672 = r2850670 + r2850671;
        double r2850673 = a;
        double r2850674 = r2850660 + r2850673;
        double r2850675 = r2850674 * r2850660;
        double r2850676 = b;
        double r2850677 = r2850675 + r2850676;
        double r2850678 = r2850677 * r2850660;
        double r2850679 = c;
        double r2850680 = r2850678 + r2850679;
        double r2850681 = r2850680 * r2850660;
        double r2850682 = i;
        double r2850683 = r2850681 + r2850682;
        double r2850684 = r2850672 / r2850683;
        return r2850684;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r2850685 = y;
        double r2850686 = x;
        double r2850687 = z;
        double r2850688 = fma(r2850685, r2850686, r2850687);
        double r2850689 = 27464.7644705;
        double r2850690 = fma(r2850685, r2850688, r2850689);
        double r2850691 = 230661.510616;
        double r2850692 = fma(r2850685, r2850690, r2850691);
        double r2850693 = t;
        double r2850694 = fma(r2850692, r2850685, r2850693);
        double r2850695 = 1.0;
        double r2850696 = a;
        double r2850697 = r2850696 + r2850685;
        double r2850698 = b;
        double r2850699 = fma(r2850697, r2850685, r2850698);
        double r2850700 = c;
        double r2850701 = fma(r2850699, r2850685, r2850700);
        double r2850702 = i;
        double r2850703 = fma(r2850701, r2850685, r2850702);
        double r2850704 = r2850695 / r2850703;
        double r2850705 = r2850694 * r2850704;
        return r2850705;
}

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 29.0

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

  2. Simplified28.9

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

  4. Applied div-inv29.0

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

  5. Final simplification29.0

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

Reproduce

herbie shell --seed 2019200 +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)))