Average Error: 28.6 → 28.6
Time: 29.2s
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 r66221 = x;
        double r66222 = y;
        double r66223 = r66221 * r66222;
        double r66224 = z;
        double r66225 = r66223 + r66224;
        double r66226 = r66225 * r66222;
        double r66227 = 27464.7644705;
        double r66228 = r66226 + r66227;
        double r66229 = r66228 * r66222;
        double r66230 = 230661.510616;
        double r66231 = r66229 + r66230;
        double r66232 = r66231 * r66222;
        double r66233 = t;
        double r66234 = r66232 + r66233;
        double r66235 = a;
        double r66236 = r66222 + r66235;
        double r66237 = r66236 * r66222;
        double r66238 = b;
        double r66239 = r66237 + r66238;
        double r66240 = r66239 * r66222;
        double r66241 = c;
        double r66242 = r66240 + r66241;
        double r66243 = r66242 * r66222;
        double r66244 = i;
        double r66245 = r66243 + r66244;
        double r66246 = r66234 / r66245;
        return r66246;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r66247 = x;
        double r66248 = y;
        double r66249 = z;
        double r66250 = fma(r66247, r66248, r66249);
        double r66251 = 27464.7644705;
        double r66252 = fma(r66250, r66248, r66251);
        double r66253 = 230661.510616;
        double r66254 = fma(r66252, r66248, r66253);
        double r66255 = t;
        double r66256 = fma(r66254, r66248, r66255);
        double r66257 = 1.0;
        double r66258 = a;
        double r66259 = r66248 + r66258;
        double r66260 = b;
        double r66261 = fma(r66259, r66248, r66260);
        double r66262 = c;
        double r66263 = fma(r66261, r66248, r66262);
        double r66264 = i;
        double r66265 = fma(r66263, r66248, r66264);
        double r66266 = r66257 / r66265;
        double r66267 = r66256 * r66266;
        return r66267;
}

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 28.6

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

  2. Simplified28.6

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

  4. Applied div-inv28.6

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

  5. Final simplification28.6

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

Reproduce

herbie shell --seed 2019195 +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)))