Average Error: 27.7 → 28.0
Time: 22.6s
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 r1039604 = x;
        double r1039605 = y;
        double r1039606 = r1039604 * r1039605;
        double r1039607 = z;
        double r1039608 = r1039606 + r1039607;
        double r1039609 = r1039608 * r1039605;
        double r1039610 = 27464.7644705;
        double r1039611 = r1039609 + r1039610;
        double r1039612 = r1039611 * r1039605;
        double r1039613 = 230661.510616;
        double r1039614 = r1039612 + r1039613;
        double r1039615 = r1039614 * r1039605;
        double r1039616 = t;
        double r1039617 = r1039615 + r1039616;
        double r1039618 = a;
        double r1039619 = r1039605 + r1039618;
        double r1039620 = r1039619 * r1039605;
        double r1039621 = b;
        double r1039622 = r1039620 + r1039621;
        double r1039623 = r1039622 * r1039605;
        double r1039624 = c;
        double r1039625 = r1039623 + r1039624;
        double r1039626 = r1039625 * r1039605;
        double r1039627 = i;
        double r1039628 = r1039626 + r1039627;
        double r1039629 = r1039617 / r1039628;
        return r1039629;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r1039630 = 1.0;
        double r1039631 = y;
        double r1039632 = a;
        double r1039633 = r1039631 + r1039632;
        double r1039634 = b;
        double r1039635 = fma(r1039633, r1039631, r1039634);
        double r1039636 = c;
        double r1039637 = fma(r1039631, r1039635, r1039636);
        double r1039638 = i;
        double r1039639 = fma(r1039637, r1039631, r1039638);
        double r1039640 = x;
        double r1039641 = z;
        double r1039642 = fma(r1039631, r1039640, r1039641);
        double r1039643 = 27464.7644705;
        double r1039644 = fma(r1039631, r1039642, r1039643);
        double r1039645 = 230661.510616;
        double r1039646 = fma(r1039631, r1039644, r1039645);
        double r1039647 = t;
        double r1039648 = fma(r1039631, r1039646, r1039647);
        double r1039649 = r1039639 / r1039648;
        double r1039650 = r1039630 / r1039649;
        return r1039650;
}

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 27.7

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

  2. Simplified27.7

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

  4. Applied clear-num28.0

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

  5. Final simplification28.0

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

Reproduce

herbie shell --seed 2019156 +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)))