Average Error: 28.7 → 28.8
Time: 19.4s
Precision: 64
\[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.764470499998\right) \cdot y + 230661.510616000014\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\]
↓
\[\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x, y, z\right), y, 27464.764470499998\right), y, 230661.510616000014\right), y, t\right) \cdot \frac{1}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(y + a, y, b\right), y, c\right), y, i\right)}\]
\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}
↓
\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x, y, z\right), y, 27464.764470499998\right), y, 230661.510616000014\right), 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 r79197 = x;
        double r79198 = y;
        double r79199 = r79197 * r79198;
        double r79200 = z;
        double r79201 = r79199 + r79200;
        double r79202 = r79201 * r79198;
        double r79203 = 27464.7644705;
        double r79204 = r79202 + r79203;
        double r79205 = r79204 * r79198;
        double r79206 = 230661.510616;
        double r79207 = r79205 + r79206;
        double r79208 = r79207 * r79198;
        double r79209 = t;
        double r79210 = r79208 + r79209;
        double r79211 = a;
        double r79212 = r79198 + r79211;
        double r79213 = r79212 * r79198;
        double r79214 = b;
        double r79215 = r79213 + r79214;
        double r79216 = r79215 * r79198;
        double r79217 = c;
        double r79218 = r79216 + r79217;
        double r79219 = r79218 * r79198;
        double r79220 = i;
        double r79221 = r79219 + r79220;
        double r79222 = r79210 / r79221;
        return r79222;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r79223 = x;
        double r79224 = y;
        double r79225 = z;
        double r79226 = fma(r79223, r79224, r79225);
        double r79227 = 27464.7644705;
        double r79228 = fma(r79226, r79224, r79227);
        double r79229 = 230661.510616;
        double r79230 = fma(r79228, r79224, r79229);
        double r79231 = t;
        double r79232 = fma(r79230, r79224, r79231);
        double r79233 = 1.0;
        double r79234 = a;
        double r79235 = r79224 + r79234;
        double r79236 = b;
        double r79237 = fma(r79235, r79224, r79236);
        double r79238 = c;
        double r79239 = fma(r79237, r79224, r79238);
        double r79240 = i;
        double r79241 = fma(r79239, r79224, r79240);
        double r79242 = r79233 / r79241;
        double r79243 = r79232 * r79242;
        return r79243;
}

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 28.7

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

  2. Simplified28.7

    \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x, y, z\right), y, 27464.764470499998\right), y, 230661.510616000014\right), y, t\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(y + a, y, b\right), y, c\right), y, i\right)}}\]
  3. Using strategy rm

  4. Applied div-inv28.8

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

  5. Final simplification28.8

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

Reproduce

herbie shell --seed 2020047 +o rules:numerics
(FPCore (x y z t a b c i)
  :name "Numeric.SpecFunctions:logGamma from math-functions-0.1.5.2"
  :precision binary64
  (/ (+ (* (+ (* (+ (* (+ (* x y) z) y) 27464.7644705) y) 230661.510616) y) t) (+ (* (+ (* (+ (* (+ y a) y) b) y) c) y) i)))