Average Error: 28.7 → 28.8
Time: 29.4s
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 r69232 = x;
        double r69233 = y;
        double r69234 = r69232 * r69233;
        double r69235 = z;
        double r69236 = r69234 + r69235;
        double r69237 = r69236 * r69233;
        double r69238 = 27464.7644705;
        double r69239 = r69237 + r69238;
        double r69240 = r69239 * r69233;
        double r69241 = 230661.510616;
        double r69242 = r69240 + r69241;
        double r69243 = r69242 * r69233;
        double r69244 = t;
        double r69245 = r69243 + r69244;
        double r69246 = a;
        double r69247 = r69233 + r69246;
        double r69248 = r69247 * r69233;
        double r69249 = b;
        double r69250 = r69248 + r69249;
        double r69251 = r69250 * r69233;
        double r69252 = c;
        double r69253 = r69251 + r69252;
        double r69254 = r69253 * r69233;
        double r69255 = i;
        double r69256 = r69254 + r69255;
        double r69257 = r69245 / r69256;
        return r69257;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r69258 = x;
        double r69259 = y;
        double r69260 = r69258 * r69259;
        double r69261 = z;
        double r69262 = r69260 + r69261;
        double r69263 = r69262 * r69259;
        double r69264 = 27464.7644705;
        double r69265 = r69263 + r69264;
        double r69266 = r69265 * r69259;
        double r69267 = 230661.510616;
        double r69268 = r69266 + r69267;
        double r69269 = r69268 * r69259;
        double r69270 = t;
        double r69271 = r69269 + r69270;
        double r69272 = 1.0;
        double r69273 = a;
        double r69274 = r69259 + r69273;
        double r69275 = r69274 * r69259;
        double r69276 = b;
        double r69277 = r69275 + r69276;
        double r69278 = r69277 * r69259;
        double r69279 = c;
        double r69280 = r69278 + r69279;
        double r69281 = r69280 * r69259;
        double r69282 = i;
        double r69283 = r69281 + r69282;
        double r69284 = r69272 / r69283;
        double r69285 = r69271 * r69284;
        return r69285;
}

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 28.7

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

  3. Applied div-inv28.8

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

  4. Final simplification28.8

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

Reproduce

herbie shell --seed 2019323 
(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)))