Average Error: 28.6 → 28.6
Time: 30.9s
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 r78229 = x;
        double r78230 = y;
        double r78231 = r78229 * r78230;
        double r78232 = z;
        double r78233 = r78231 + r78232;
        double r78234 = r78233 * r78230;
        double r78235 = 27464.7644705;
        double r78236 = r78234 + r78235;
        double r78237 = r78236 * r78230;
        double r78238 = 230661.510616;
        double r78239 = r78237 + r78238;
        double r78240 = r78239 * r78230;
        double r78241 = t;
        double r78242 = r78240 + r78241;
        double r78243 = a;
        double r78244 = r78230 + r78243;
        double r78245 = r78244 * r78230;
        double r78246 = b;
        double r78247 = r78245 + r78246;
        double r78248 = r78247 * r78230;
        double r78249 = c;
        double r78250 = r78248 + r78249;
        double r78251 = r78250 * r78230;
        double r78252 = i;
        double r78253 = r78251 + r78252;
        double r78254 = r78242 / r78253;
        return r78254;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r78255 = x;
        double r78256 = y;
        double r78257 = r78255 * r78256;
        double r78258 = z;
        double r78259 = r78257 + r78258;
        double r78260 = r78259 * r78256;
        double r78261 = 27464.7644705;
        double r78262 = r78260 + r78261;
        double r78263 = r78262 * r78256;
        double r78264 = 230661.510616;
        double r78265 = r78263 + r78264;
        double r78266 = r78265 * r78256;
        double r78267 = t;
        double r78268 = r78266 + r78267;
        double r78269 = 1.0;
        double r78270 = a;
        double r78271 = r78256 + r78270;
        double r78272 = r78271 * r78256;
        double r78273 = b;
        double r78274 = r78272 + r78273;
        double r78275 = r78274 * r78256;
        double r78276 = c;
        double r78277 = r78275 + r78276;
        double r78278 = r78277 * r78256;
        double r78279 = i;
        double r78280 = r78278 + r78279;
        double r78281 = r78269 / r78280;
        double r78282 = r78268 * r78281;
        return r78282;
}

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)))