Average Error: 29.5 → 29.5
Time: 14.2s
Precision: 64
\[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.764470499998\right) \cdot y + 230661.510616000014\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\]
↓
\[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.764470499998\right) \cdot y + 230661.510616000014\right) \cdot y + t}{\left(\left(y \cdot b + \left({y}^{3} + a \cdot {y}^{2}\right)\right) + c\right) \cdot y + i}\]
\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.764470499998\right) \cdot y + 230661.510616000014\right) \cdot y + t}{\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 + 27464.764470499998\right) \cdot y + 230661.510616000014\right) \cdot y + t}{\left(\left(y \cdot b + \left({y}^{3} + a \cdot {y}^{2}\right)\right) + c\right) \cdot y + i}
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r68283 = x;
        double r68284 = y;
        double r68285 = r68283 * r68284;
        double r68286 = z;
        double r68287 = r68285 + r68286;
        double r68288 = r68287 * r68284;
        double r68289 = 27464.7644705;
        double r68290 = r68288 + r68289;
        double r68291 = r68290 * r68284;
        double r68292 = 230661.510616;
        double r68293 = r68291 + r68292;
        double r68294 = r68293 * r68284;
        double r68295 = t;
        double r68296 = r68294 + r68295;
        double r68297 = a;
        double r68298 = r68284 + r68297;
        double r68299 = r68298 * r68284;
        double r68300 = b;
        double r68301 = r68299 + r68300;
        double r68302 = r68301 * r68284;
        double r68303 = c;
        double r68304 = r68302 + r68303;
        double r68305 = r68304 * r68284;
        double r68306 = i;
        double r68307 = r68305 + r68306;
        double r68308 = r68296 / r68307;
        return r68308;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r68309 = x;
        double r68310 = y;
        double r68311 = r68309 * r68310;
        double r68312 = z;
        double r68313 = r68311 + r68312;
        double r68314 = r68313 * r68310;
        double r68315 = 27464.7644705;
        double r68316 = r68314 + r68315;
        double r68317 = r68316 * r68310;
        double r68318 = 230661.510616;
        double r68319 = r68317 + r68318;
        double r68320 = r68319 * r68310;
        double r68321 = t;
        double r68322 = r68320 + r68321;
        double r68323 = b;
        double r68324 = r68310 * r68323;
        double r68325 = 3.0;
        double r68326 = pow(r68310, r68325);
        double r68327 = a;
        double r68328 = 2.0;
        double r68329 = pow(r68310, r68328);
        double r68330 = r68327 * r68329;
        double r68331 = r68326 + r68330;
        double r68332 = r68324 + r68331;
        double r68333 = c;
        double r68334 = r68332 + r68333;
        double r68335 = r68334 * r68310;
        double r68336 = i;
        double r68337 = r68335 + r68336;
        double r68338 = r68322 / r68337;
        return r68338;
}

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 29.5

    \[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.764470499998\right) \cdot y + 230661.510616000014\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\]

  2. Taylor expanded around inf 29.5

    \[\leadsto \frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.764470499998\right) \cdot y + 230661.510616000014\right) \cdot y + t}{\left(\color{blue}{\left(y \cdot b + \left({y}^{3} + a \cdot {y}^{2}\right)\right)} + c\right) \cdot y + i}\]

  3. Final simplification29.5

    \[\leadsto \frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.764470499998\right) \cdot y + 230661.510616000014\right) \cdot y + t}{\left(\left(y \cdot b + \left({y}^{3} + a \cdot {y}^{2}\right)\right) + c\right) \cdot y + i}\]

Reproduce

herbie shell --seed 2020046 
(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)))