Average Error: 29.0 → 29.1
Time: 39.2s
Precision: 64
\[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644704999984242022037506103515625\right) \cdot y + 230661.5106160000141244381666183471679688\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\]
↓
\[\frac{1}{\frac{\mathsf{fma}\left(\mathsf{fma}\left(y, \mathsf{fma}\left(y + a, y, b\right), c\right), y, i\right)}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, x, z\right), 27464.7644704999984242022037506103515625\right), 230661.5106160000141244381666183471679688\right), t\right)}}\]
\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}{\frac{\mathsf{fma}\left(\mathsf{fma}\left(y, \mathsf{fma}\left(y + a, y, b\right), c\right), y, i\right)}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, x, z\right), 27464.7644704999984242022037506103515625\right), 230661.5106160000141244381666183471679688\right), t\right)}}
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r2517248 = x;
        double r2517249 = y;
        double r2517250 = r2517248 * r2517249;
        double r2517251 = z;
        double r2517252 = r2517250 + r2517251;
        double r2517253 = r2517252 * r2517249;
        double r2517254 = 27464.7644705;
        double r2517255 = r2517253 + r2517254;
        double r2517256 = r2517255 * r2517249;
        double r2517257 = 230661.510616;
        double r2517258 = r2517256 + r2517257;
        double r2517259 = r2517258 * r2517249;
        double r2517260 = t;
        double r2517261 = r2517259 + r2517260;
        double r2517262 = a;
        double r2517263 = r2517249 + r2517262;
        double r2517264 = r2517263 * r2517249;
        double r2517265 = b;
        double r2517266 = r2517264 + r2517265;
        double r2517267 = r2517266 * r2517249;
        double r2517268 = c;
        double r2517269 = r2517267 + r2517268;
        double r2517270 = r2517269 * r2517249;
        double r2517271 = i;
        double r2517272 = r2517270 + r2517271;
        double r2517273 = r2517261 / r2517272;
        return r2517273;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r2517274 = 1.0;
        double r2517275 = y;
        double r2517276 = a;
        double r2517277 = r2517275 + r2517276;
        double r2517278 = b;
        double r2517279 = fma(r2517277, r2517275, r2517278);
        double r2517280 = c;
        double r2517281 = fma(r2517275, r2517279, r2517280);
        double r2517282 = i;
        double r2517283 = fma(r2517281, r2517275, r2517282);
        double r2517284 = x;
        double r2517285 = z;
        double r2517286 = fma(r2517275, r2517284, r2517285);
        double r2517287 = 27464.7644705;
        double r2517288 = fma(r2517275, r2517286, r2517287);
        double r2517289 = 230661.510616;
        double r2517290 = fma(r2517275, r2517288, r2517289);
        double r2517291 = t;
        double r2517292 = fma(r2517275, r2517290, r2517291);
        double r2517293 = r2517283 / r2517292;
        double r2517294 = r2517274 / r2517293;
        return r2517294;
}

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 29.0

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

  2. Simplified29.0

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

  4. Applied clear-num29.1

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

  5. Final simplification29.1

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

Reproduce

herbie shell --seed 2019170 +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)))