Average Error: 28.8 → 28.9
Time: 30.2s
Precision: 64
\[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644704999984242022037506103515625\right) \cdot y + 230661.5106160000141244381666183471679688\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\]
↓
\[\frac{1}{\mathsf{fma}\left(\mathsf{fma}\left(y, \mathsf{fma}\left(y + a, y, b\right), c\right), y, i\right)} \cdot \mathsf{fma}\left(\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, x, z\right), 27464.7644704999984242022037506103515625\right), 230661.5106160000141244381666183471679688\right), y, t\right)\]
\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}
↓
\frac{1}{\mathsf{fma}\left(\mathsf{fma}\left(y, \mathsf{fma}\left(y + a, y, b\right), c\right), y, i\right)} \cdot \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)
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r2469633 = x;
        double r2469634 = y;
        double r2469635 = r2469633 * r2469634;
        double r2469636 = z;
        double r2469637 = r2469635 + r2469636;
        double r2469638 = r2469637 * r2469634;
        double r2469639 = 27464.7644705;
        double r2469640 = r2469638 + r2469639;
        double r2469641 = r2469640 * r2469634;
        double r2469642 = 230661.510616;
        double r2469643 = r2469641 + r2469642;
        double r2469644 = r2469643 * r2469634;
        double r2469645 = t;
        double r2469646 = r2469644 + r2469645;
        double r2469647 = a;
        double r2469648 = r2469634 + r2469647;
        double r2469649 = r2469648 * r2469634;
        double r2469650 = b;
        double r2469651 = r2469649 + r2469650;
        double r2469652 = r2469651 * r2469634;
        double r2469653 = c;
        double r2469654 = r2469652 + r2469653;
        double r2469655 = r2469654 * r2469634;
        double r2469656 = i;
        double r2469657 = r2469655 + r2469656;
        double r2469658 = r2469646 / r2469657;
        return r2469658;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r2469659 = 1.0;
        double r2469660 = y;
        double r2469661 = a;
        double r2469662 = r2469660 + r2469661;
        double r2469663 = b;
        double r2469664 = fma(r2469662, r2469660, r2469663);
        double r2469665 = c;
        double r2469666 = fma(r2469660, r2469664, r2469665);
        double r2469667 = i;
        double r2469668 = fma(r2469666, r2469660, r2469667);
        double r2469669 = r2469659 / r2469668;
        double r2469670 = x;
        double r2469671 = z;
        double r2469672 = fma(r2469660, r2469670, r2469671);
        double r2469673 = 27464.7644705;
        double r2469674 = fma(r2469660, r2469672, r2469673);
        double r2469675 = 230661.510616;
        double r2469676 = fma(r2469660, r2469674, r2469675);
        double r2469677 = t;
        double r2469678 = fma(r2469676, r2469660, r2469677);
        double r2469679 = r2469669 * r2469678;
        return r2469679;
}

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 28.8

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

  2. Simplified28.8

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

  4. Applied div-inv28.9

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

  5. Final simplification28.9

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

Reproduce

herbie shell --seed 2019172 +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)))