Average Error: 28.3 → 28.3
Time: 36.6s
Precision: 64
\[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\]
↓
\[\frac{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, x, z\right), 27464.7644705\right), 230661.510616\right), t\right)}{\mathsf{fma}\left(\mathsf{fma}\left(y, \mathsf{fma}\left(y + a, y, b\right), c\right), y, i\right)}\]
\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{\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)}
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r2641546 = x;
        double r2641547 = y;
        double r2641548 = r2641546 * r2641547;
        double r2641549 = z;
        double r2641550 = r2641548 + r2641549;
        double r2641551 = r2641550 * r2641547;
        double r2641552 = 27464.7644705;
        double r2641553 = r2641551 + r2641552;
        double r2641554 = r2641553 * r2641547;
        double r2641555 = 230661.510616;
        double r2641556 = r2641554 + r2641555;
        double r2641557 = r2641556 * r2641547;
        double r2641558 = t;
        double r2641559 = r2641557 + r2641558;
        double r2641560 = a;
        double r2641561 = r2641547 + r2641560;
        double r2641562 = r2641561 * r2641547;
        double r2641563 = b;
        double r2641564 = r2641562 + r2641563;
        double r2641565 = r2641564 * r2641547;
        double r2641566 = c;
        double r2641567 = r2641565 + r2641566;
        double r2641568 = r2641567 * r2641547;
        double r2641569 = i;
        double r2641570 = r2641568 + r2641569;
        double r2641571 = r2641559 / r2641570;
        return r2641571;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r2641572 = y;
        double r2641573 = x;
        double r2641574 = z;
        double r2641575 = fma(r2641572, r2641573, r2641574);
        double r2641576 = 27464.7644705;
        double r2641577 = fma(r2641572, r2641575, r2641576);
        double r2641578 = 230661.510616;
        double r2641579 = fma(r2641572, r2641577, r2641578);
        double r2641580 = t;
        double r2641581 = fma(r2641572, r2641579, r2641580);
        double r2641582 = a;
        double r2641583 = r2641572 + r2641582;
        double r2641584 = b;
        double r2641585 = fma(r2641583, r2641572, r2641584);
        double r2641586 = c;
        double r2641587 = fma(r2641572, r2641585, r2641586);
        double r2641588 = i;
        double r2641589 = fma(r2641587, r2641572, r2641588);
        double r2641590 = r2641581 / r2641589;
        return r2641590;
}

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 28.3

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

  2. Simplified28.3

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

  3. Final simplification28.3

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

Reproduce

herbie shell --seed 2019162 +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)))