Average Error: 28.5 → 28.7
Time: 28.3s
Precision: 64
\[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\]
↓
\[\frac{1}{\frac{\mathsf{fma}\left(\mathsf{fma}\left(y, \mathsf{fma}\left(y + a, y, b\right), c\right), y, i\right)}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, x, z\right), 27464.7644705\right), 230661.510616\right), t\right)}}\]
\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{1}{\frac{\mathsf{fma}\left(\mathsf{fma}\left(y, \mathsf{fma}\left(y + a, y, b\right), c\right), y, i\right)}{\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)}}
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r1147669 = x;
        double r1147670 = y;
        double r1147671 = r1147669 * r1147670;
        double r1147672 = z;
        double r1147673 = r1147671 + r1147672;
        double r1147674 = r1147673 * r1147670;
        double r1147675 = 27464.7644705;
        double r1147676 = r1147674 + r1147675;
        double r1147677 = r1147676 * r1147670;
        double r1147678 = 230661.510616;
        double r1147679 = r1147677 + r1147678;
        double r1147680 = r1147679 * r1147670;
        double r1147681 = t;
        double r1147682 = r1147680 + r1147681;
        double r1147683 = a;
        double r1147684 = r1147670 + r1147683;
        double r1147685 = r1147684 * r1147670;
        double r1147686 = b;
        double r1147687 = r1147685 + r1147686;
        double r1147688 = r1147687 * r1147670;
        double r1147689 = c;
        double r1147690 = r1147688 + r1147689;
        double r1147691 = r1147690 * r1147670;
        double r1147692 = i;
        double r1147693 = r1147691 + r1147692;
        double r1147694 = r1147682 / r1147693;
        return r1147694;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r1147695 = 1.0;
        double r1147696 = y;
        double r1147697 = a;
        double r1147698 = r1147696 + r1147697;
        double r1147699 = b;
        double r1147700 = fma(r1147698, r1147696, r1147699);
        double r1147701 = c;
        double r1147702 = fma(r1147696, r1147700, r1147701);
        double r1147703 = i;
        double r1147704 = fma(r1147702, r1147696, r1147703);
        double r1147705 = x;
        double r1147706 = z;
        double r1147707 = fma(r1147696, r1147705, r1147706);
        double r1147708 = 27464.7644705;
        double r1147709 = fma(r1147696, r1147707, r1147708);
        double r1147710 = 230661.510616;
        double r1147711 = fma(r1147696, r1147709, r1147710);
        double r1147712 = t;
        double r1147713 = fma(r1147696, r1147711, r1147712);
        double r1147714 = r1147704 / r1147713;
        double r1147715 = r1147695 / r1147714;
        return r1147715;
}

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 28.5

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

  2. Simplified28.5

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

  4. Applied clear-num28.7

    \[\leadsto \color{blue}{\frac{1}{\frac{\mathsf{fma}\left(\mathsf{fma}\left(y, \mathsf{fma}\left(y + a, y, b\right), c\right), y, i\right)}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, x, z\right), 27464.7644705\right), 230661.510616\right), t\right)}}}\]

  5. Final simplification28.7

    \[\leadsto \frac{1}{\frac{\mathsf{fma}\left(\mathsf{fma}\left(y, \mathsf{fma}\left(y + a, y, b\right), c\right), y, i\right)}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, x, z\right), 27464.7644705\right), 230661.510616\right), t\right)}}\]

Reproduce

herbie shell --seed 2019154 +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)))