Average Error: 28.8 → 28.9
Time: 31.3s
Precision: 64
\[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644704999984242022037506103515625\right) \cdot y + 230661.5106160000141244381666183471679688\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\]
↓
\[\frac{t + \left(y \cdot \left(y \cdot \left(z + x \cdot y\right) + 27464.7644704999984242022037506103515625\right) + 230661.5106160000141244381666183471679688\right) \cdot y}{y \cdot \left(c + \left(\sqrt[3]{b + \left(y + a\right) \cdot y} \cdot \sqrt[3]{b + \left(y + a\right) \cdot y}\right) \cdot \left(\sqrt[3]{b + \left(y + a\right) \cdot y} \cdot y\right)\right) + i}\]
\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}
↓
\frac{t + \left(y \cdot \left(y \cdot \left(z + x \cdot y\right) + 27464.7644704999984242022037506103515625\right) + 230661.5106160000141244381666183471679688\right) \cdot y}{y \cdot \left(c + \left(\sqrt[3]{b + \left(y + a\right) \cdot y} \cdot \sqrt[3]{b + \left(y + a\right) \cdot y}\right) \cdot \left(\sqrt[3]{b + \left(y + a\right) \cdot y} \cdot y\right)\right) + i}
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r4549314 = x;
        double r4549315 = y;
        double r4549316 = r4549314 * r4549315;
        double r4549317 = z;
        double r4549318 = r4549316 + r4549317;
        double r4549319 = r4549318 * r4549315;
        double r4549320 = 27464.7644705;
        double r4549321 = r4549319 + r4549320;
        double r4549322 = r4549321 * r4549315;
        double r4549323 = 230661.510616;
        double r4549324 = r4549322 + r4549323;
        double r4549325 = r4549324 * r4549315;
        double r4549326 = t;
        double r4549327 = r4549325 + r4549326;
        double r4549328 = a;
        double r4549329 = r4549315 + r4549328;
        double r4549330 = r4549329 * r4549315;
        double r4549331 = b;
        double r4549332 = r4549330 + r4549331;
        double r4549333 = r4549332 * r4549315;
        double r4549334 = c;
        double r4549335 = r4549333 + r4549334;
        double r4549336 = r4549335 * r4549315;
        double r4549337 = i;
        double r4549338 = r4549336 + r4549337;
        double r4549339 = r4549327 / r4549338;
        return r4549339;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r4549340 = t;
        double r4549341 = y;
        double r4549342 = z;
        double r4549343 = x;
        double r4549344 = r4549343 * r4549341;
        double r4549345 = r4549342 + r4549344;
        double r4549346 = r4549341 * r4549345;
        double r4549347 = 27464.7644705;
        double r4549348 = r4549346 + r4549347;
        double r4549349 = r4549341 * r4549348;
        double r4549350 = 230661.510616;
        double r4549351 = r4549349 + r4549350;
        double r4549352 = r4549351 * r4549341;
        double r4549353 = r4549340 + r4549352;
        double r4549354 = c;
        double r4549355 = b;
        double r4549356 = a;
        double r4549357 = r4549341 + r4549356;
        double r4549358 = r4549357 * r4549341;
        double r4549359 = r4549355 + r4549358;
        double r4549360 = cbrt(r4549359);
        double r4549361 = r4549360 * r4549360;
        double r4549362 = r4549360 * r4549341;
        double r4549363 = r4549361 * r4549362;
        double r4549364 = r4549354 + r4549363;
        double r4549365 = r4549341 * r4549364;
        double r4549366 = i;
        double r4549367 = r4549365 + r4549366;
        double r4549368 = r4549353 / r4549367;
        return r4549368;
}

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 28.8

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

  3. Applied add-cube-cbrt28.9

    \[\leadsto \frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644704999984242022037506103515625\right) \cdot y + 230661.5106160000141244381666183471679688\right) \cdot y + t}{\left(\color{blue}{\left(\left(\sqrt[3]{\left(y + a\right) \cdot y + b} \cdot \sqrt[3]{\left(y + a\right) \cdot y + b}\right) \cdot \sqrt[3]{\left(y + a\right) \cdot y + b}\right)} \cdot y + c\right) \cdot y + i}\]

  4. Applied associate-*l*28.9

    \[\leadsto \frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644704999984242022037506103515625\right) \cdot y + 230661.5106160000141244381666183471679688\right) \cdot y + t}{\left(\color{blue}{\left(\sqrt[3]{\left(y + a\right) \cdot y + b} \cdot \sqrt[3]{\left(y + a\right) \cdot y + b}\right) \cdot \left(\sqrt[3]{\left(y + a\right) \cdot y + b} \cdot y\right)} + c\right) \cdot y + i}\]

  5. Final simplification28.9

    \[\leadsto \frac{t + \left(y \cdot \left(y \cdot \left(z + x \cdot y\right) + 27464.7644704999984242022037506103515625\right) + 230661.5106160000141244381666183471679688\right) \cdot y}{y \cdot \left(c + \left(\sqrt[3]{b + \left(y + a\right) \cdot y} \cdot \sqrt[3]{b + \left(y + a\right) \cdot y}\right) \cdot \left(\sqrt[3]{b + \left(y + a\right) \cdot y} \cdot y\right)\right) + i}\]

Reproduce

herbie shell --seed 2019172 
(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)))