Average Error: 28.8 → 28.9
Time: 37.1s
Precision: 64
\[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644704999984242022037506103515625\right) \cdot y + 230661.5106160000141244381666183471679688\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\]
↓
\[\frac{1}{\mathsf{fma}\left(\mathsf{fma}\left(y, \mathsf{fma}\left(y + a, y, b\right), c\right), y, i\right)} \cdot \mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, x, z\right), 27464.7644704999984242022037506103515625\right), 230661.5106160000141244381666183471679688\right), t\right)\]
\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}{\mathsf{fma}\left(\mathsf{fma}\left(y, \mathsf{fma}\left(y + a, y, b\right), c\right), y, i\right)} \cdot \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 r3592291 = x;
        double r3592292 = y;
        double r3592293 = r3592291 * r3592292;
        double r3592294 = z;
        double r3592295 = r3592293 + r3592294;
        double r3592296 = r3592295 * r3592292;
        double r3592297 = 27464.7644705;
        double r3592298 = r3592296 + r3592297;
        double r3592299 = r3592298 * r3592292;
        double r3592300 = 230661.510616;
        double r3592301 = r3592299 + r3592300;
        double r3592302 = r3592301 * r3592292;
        double r3592303 = t;
        double r3592304 = r3592302 + r3592303;
        double r3592305 = a;
        double r3592306 = r3592292 + r3592305;
        double r3592307 = r3592306 * r3592292;
        double r3592308 = b;
        double r3592309 = r3592307 + r3592308;
        double r3592310 = r3592309 * r3592292;
        double r3592311 = c;
        double r3592312 = r3592310 + r3592311;
        double r3592313 = r3592312 * r3592292;
        double r3592314 = i;
        double r3592315 = r3592313 + r3592314;
        double r3592316 = r3592304 / r3592315;
        return r3592316;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r3592317 = 1.0;
        double r3592318 = y;
        double r3592319 = a;
        double r3592320 = r3592318 + r3592319;
        double r3592321 = b;
        double r3592322 = fma(r3592320, r3592318, r3592321);
        double r3592323 = c;
        double r3592324 = fma(r3592318, r3592322, r3592323);
        double r3592325 = i;
        double r3592326 = fma(r3592324, r3592318, r3592325);
        double r3592327 = r3592317 / r3592326;
        double r3592328 = x;
        double r3592329 = z;
        double r3592330 = fma(r3592318, r3592328, r3592329);
        double r3592331 = 27464.7644705;
        double r3592332 = fma(r3592318, r3592330, r3592331);
        double r3592333 = 230661.510616;
        double r3592334 = fma(r3592318, r3592332, r3592333);
        double r3592335 = t;
        double r3592336 = fma(r3592318, r3592334, r3592335);
        double r3592337 = r3592327 * r3592336;
        return r3592337;
}

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 28.8

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

  2. Simplified28.8

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

  4. Applied div-inv28.9

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

  5. Final simplification28.9

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

Reproduce

herbie shell --seed 2019172 +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)))