Average Error: 28.0 → 28.2
Time: 34.2s
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 r3803688 = x;
        double r3803689 = y;
        double r3803690 = r3803688 * r3803689;
        double r3803691 = z;
        double r3803692 = r3803690 + r3803691;
        double r3803693 = r3803692 * r3803689;
        double r3803694 = 27464.7644705;
        double r3803695 = r3803693 + r3803694;
        double r3803696 = r3803695 * r3803689;
        double r3803697 = 230661.510616;
        double r3803698 = r3803696 + r3803697;
        double r3803699 = r3803698 * r3803689;
        double r3803700 = t;
        double r3803701 = r3803699 + r3803700;
        double r3803702 = a;
        double r3803703 = r3803689 + r3803702;
        double r3803704 = r3803703 * r3803689;
        double r3803705 = b;
        double r3803706 = r3803704 + r3803705;
        double r3803707 = r3803706 * r3803689;
        double r3803708 = c;
        double r3803709 = r3803707 + r3803708;
        double r3803710 = r3803709 * r3803689;
        double r3803711 = i;
        double r3803712 = r3803710 + r3803711;
        double r3803713 = r3803701 / r3803712;
        return r3803713;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r3803714 = 1.0;
        double r3803715 = y;
        double r3803716 = a;
        double r3803717 = r3803715 + r3803716;
        double r3803718 = b;
        double r3803719 = fma(r3803717, r3803715, r3803718);
        double r3803720 = c;
        double r3803721 = fma(r3803715, r3803719, r3803720);
        double r3803722 = i;
        double r3803723 = fma(r3803721, r3803715, r3803722);
        double r3803724 = x;
        double r3803725 = z;
        double r3803726 = fma(r3803715, r3803724, r3803725);
        double r3803727 = 27464.7644705;
        double r3803728 = fma(r3803715, r3803726, r3803727);
        double r3803729 = 230661.510616;
        double r3803730 = fma(r3803715, r3803728, r3803729);
        double r3803731 = t;
        double r3803732 = fma(r3803715, r3803730, r3803731);
        double r3803733 = r3803723 / r3803732;
        double r3803734 = r3803714 / r3803733;
        return r3803734;
}

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 28.0

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

  2. Simplified28.0

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

  4. Applied clear-num28.2

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

  5. Final simplification28.2

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

Reproduce

herbie shell --seed 2019164 +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)))