Average Error: 28.2 → 28.4
Time: 2.0m
Precision: 64
\[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\]
↓
\[\frac{1}{\frac{i + y \cdot \left(\left(b + \left(y + a\right) \cdot y\right) \cdot y + c\right)}{t + y \cdot \left(\left(\left(y \cdot x + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right)}}\]
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r12843246 = x;
        double r12843247 = y;
        double r12843248 = r12843246 * r12843247;
        double r12843249 = z;
        double r12843250 = r12843248 + r12843249;
        double r12843251 = r12843250 * r12843247;
        double r12843252 = 27464.7644705;
        double r12843253 = r12843251 + r12843252;
        double r12843254 = r12843253 * r12843247;
        double r12843255 = 230661.510616;
        double r12843256 = r12843254 + r12843255;
        double r12843257 = r12843256 * r12843247;
        double r12843258 = t;
        double r12843259 = r12843257 + r12843258;
        double r12843260 = a;
        double r12843261 = r12843247 + r12843260;
        double r12843262 = r12843261 * r12843247;
        double r12843263 = b;
        double r12843264 = r12843262 + r12843263;
        double r12843265 = r12843264 * r12843247;
        double r12843266 = c;
        double r12843267 = r12843265 + r12843266;
        double r12843268 = r12843267 * r12843247;
        double r12843269 = i;
        double r12843270 = r12843268 + r12843269;
        double r12843271 = r12843259 / r12843270;
        return r12843271;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r12843272 = 1.0;
        double r12843273 = i;
        double r12843274 = y;
        double r12843275 = b;
        double r12843276 = a;
        double r12843277 = r12843274 + r12843276;
        double r12843278 = r12843277 * r12843274;
        double r12843279 = r12843275 + r12843278;
        double r12843280 = r12843279 * r12843274;
        double r12843281 = c;
        double r12843282 = r12843280 + r12843281;
        double r12843283 = r12843274 * r12843282;
        double r12843284 = r12843273 + r12843283;
        double r12843285 = t;
        double r12843286 = x;
        double r12843287 = r12843274 * r12843286;
        double r12843288 = z;
        double r12843289 = r12843287 + r12843288;
        double r12843290 = r12843289 * r12843274;
        double r12843291 = 27464.7644705;
        double r12843292 = r12843290 + r12843291;
        double r12843293 = r12843292 * r12843274;
        double r12843294 = 230661.510616;
        double r12843295 = r12843293 + r12843294;
        double r12843296 = r12843274 * r12843295;
        double r12843297 = r12843285 + r12843296;
        double r12843298 = r12843284 / r12843297;
        double r12843299 = r12843272 / r12843298;
        return r12843299;
}


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

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 28.2

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

  3. Applied clear-num28.4

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

  4. Final simplification28.4

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

Reproduce

herbie shell --seed 2019101 
(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)))