Average Error: 29.0 → 29.1
Time: 30.0s
Precision: 64
\[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.764470499998\right) \cdot y + 230661.510616000014\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\]
↓
\[\left(\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.764470499998\right) \cdot y + 230661.510616000014\right) \cdot y + t\right) \cdot \frac{1}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(y + a, y, b\right), y, c\right), y, i\right)}\]
\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.764470499998\right) \cdot y + 230661.510616000014\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}
↓
\left(\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.764470499998\right) \cdot y + 230661.510616000014\right) \cdot y + t\right) \cdot \frac{1}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(y + a, 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 r49653 = x;
        double r49654 = y;
        double r49655 = r49653 * r49654;
        double r49656 = z;
        double r49657 = r49655 + r49656;
        double r49658 = r49657 * r49654;
        double r49659 = 27464.7644705;
        double r49660 = r49658 + r49659;
        double r49661 = r49660 * r49654;
        double r49662 = 230661.510616;
        double r49663 = r49661 + r49662;
        double r49664 = r49663 * r49654;
        double r49665 = t;
        double r49666 = r49664 + r49665;
        double r49667 = a;
        double r49668 = r49654 + r49667;
        double r49669 = r49668 * r49654;
        double r49670 = b;
        double r49671 = r49669 + r49670;
        double r49672 = r49671 * r49654;
        double r49673 = c;
        double r49674 = r49672 + r49673;
        double r49675 = r49674 * r49654;
        double r49676 = i;
        double r49677 = r49675 + r49676;
        double r49678 = r49666 / r49677;
        return r49678;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r49679 = x;
        double r49680 = y;
        double r49681 = r49679 * r49680;
        double r49682 = z;
        double r49683 = r49681 + r49682;
        double r49684 = r49683 * r49680;
        double r49685 = 27464.7644705;
        double r49686 = r49684 + r49685;
        double r49687 = r49686 * r49680;
        double r49688 = 230661.510616;
        double r49689 = r49687 + r49688;
        double r49690 = r49689 * r49680;
        double r49691 = t;
        double r49692 = r49690 + r49691;
        double r49693 = 1.0;
        double r49694 = a;
        double r49695 = r49680 + r49694;
        double r49696 = b;
        double r49697 = fma(r49695, r49680, r49696);
        double r49698 = c;
        double r49699 = fma(r49697, r49680, r49698);
        double r49700 = i;
        double r49701 = fma(r49699, r49680, r49700);
        double r49702 = r49693 / r49701;
        double r49703 = r49692 * r49702;
        return r49703;
}

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

    \[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.764470499998\right) \cdot y + 230661.510616000014\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\]
  2. Using strategy rm

  3. Applied div-inv29.1

    \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.764470499998\right) \cdot y + 230661.510616000014\right) \cdot y + t\right) \cdot \frac{1}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}}\]

  4. Simplified29.1

    \[\leadsto \left(\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.764470499998\right) \cdot y + 230661.510616000014\right) \cdot y + t\right) \cdot \color{blue}{\frac{1}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(y + a, y, b\right), y, c\right), y, i\right)}}\]

  5. Final simplification29.1

    \[\leadsto \left(\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.764470499998\right) \cdot y + 230661.510616000014\right) \cdot y + t\right) \cdot \frac{1}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(y + a, y, b\right), y, c\right), y, i\right)}\]

Reproduce

herbie shell --seed 2019198 +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)))