Average Error: 28.6 → 28.6
Time: 32.4s
Precision: 64
\[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644704999984242022037506103515625\right) \cdot y + 230661.5106160000141244381666183471679688\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\]
↓
\[\left(\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644704999984242022037506103515625\right) \cdot y + 230661.5106160000141244381666183471679688\right) \cdot y + t\right) \cdot \frac{1}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\]
\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}
↓
\left(\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644704999984242022037506103515625\right) \cdot y + 230661.5106160000141244381666183471679688\right) \cdot y + t\right) \cdot \frac{1}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r59242 = x;
        double r59243 = y;
        double r59244 = r59242 * r59243;
        double r59245 = z;
        double r59246 = r59244 + r59245;
        double r59247 = r59246 * r59243;
        double r59248 = 27464.7644705;
        double r59249 = r59247 + r59248;
        double r59250 = r59249 * r59243;
        double r59251 = 230661.510616;
        double r59252 = r59250 + r59251;
        double r59253 = r59252 * r59243;
        double r59254 = t;
        double r59255 = r59253 + r59254;
        double r59256 = a;
        double r59257 = r59243 + r59256;
        double r59258 = r59257 * r59243;
        double r59259 = b;
        double r59260 = r59258 + r59259;
        double r59261 = r59260 * r59243;
        double r59262 = c;
        double r59263 = r59261 + r59262;
        double r59264 = r59263 * r59243;
        double r59265 = i;
        double r59266 = r59264 + r59265;
        double r59267 = r59255 / r59266;
        return r59267;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r59268 = x;
        double r59269 = y;
        double r59270 = r59268 * r59269;
        double r59271 = z;
        double r59272 = r59270 + r59271;
        double r59273 = r59272 * r59269;
        double r59274 = 27464.7644705;
        double r59275 = r59273 + r59274;
        double r59276 = r59275 * r59269;
        double r59277 = 230661.510616;
        double r59278 = r59276 + r59277;
        double r59279 = r59278 * r59269;
        double r59280 = t;
        double r59281 = r59279 + r59280;
        double r59282 = 1.0;
        double r59283 = a;
        double r59284 = r59269 + r59283;
        double r59285 = r59284 * r59269;
        double r59286 = b;
        double r59287 = r59285 + r59286;
        double r59288 = r59287 * r59269;
        double r59289 = c;
        double r59290 = r59288 + r59289;
        double r59291 = r59290 * r59269;
        double r59292 = i;
        double r59293 = r59291 + r59292;
        double r59294 = r59282 / r59293;
        double r59295 = r59281 * r59294;
        return r59295;
}

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

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 28.6

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

  3. Applied div-inv28.6

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

  4. Final simplification28.6

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

Reproduce

herbie shell --seed 2019325 
(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)))