Average Error: 29.2 → 29.8
Time: 33.4s
Precision: 64
\[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644704999984242022037506103515625\right) \cdot y + 230661.5106160000141244381666183471679688\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\]
↓
\[\frac{\frac{t + \left(y \cdot \left(y \cdot \left(z + x \cdot y\right) + 27464.7644704999984242022037506103515625\right) + 230661.5106160000141244381666183471679688\right) \cdot y}{\sqrt[3]{i + \left(c + y \cdot \left(b + \left(y + a\right) \cdot y\right)\right) \cdot y} \cdot \sqrt[3]{i + \left(c + y \cdot \left(b + \left(y + a\right) \cdot y\right)\right) \cdot y}}}{\sqrt[3]{i + \left(c + y \cdot \left(b + \left(y + a\right) \cdot y\right)\right) \cdot y}}\]
\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{\frac{t + \left(y \cdot \left(y \cdot \left(z + x \cdot y\right) + 27464.7644704999984242022037506103515625\right) + 230661.5106160000141244381666183471679688\right) \cdot y}{\sqrt[3]{i + \left(c + y \cdot \left(b + \left(y + a\right) \cdot y\right)\right) \cdot y} \cdot \sqrt[3]{i + \left(c + y \cdot \left(b + \left(y + a\right) \cdot y\right)\right) \cdot y}}}{\sqrt[3]{i + \left(c + y \cdot \left(b + \left(y + a\right) \cdot y\right)\right) \cdot y}}
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r3721267 = x;
        double r3721268 = y;
        double r3721269 = r3721267 * r3721268;
        double r3721270 = z;
        double r3721271 = r3721269 + r3721270;
        double r3721272 = r3721271 * r3721268;
        double r3721273 = 27464.7644705;
        double r3721274 = r3721272 + r3721273;
        double r3721275 = r3721274 * r3721268;
        double r3721276 = 230661.510616;
        double r3721277 = r3721275 + r3721276;
        double r3721278 = r3721277 * r3721268;
        double r3721279 = t;
        double r3721280 = r3721278 + r3721279;
        double r3721281 = a;
        double r3721282 = r3721268 + r3721281;
        double r3721283 = r3721282 * r3721268;
        double r3721284 = b;
        double r3721285 = r3721283 + r3721284;
        double r3721286 = r3721285 * r3721268;
        double r3721287 = c;
        double r3721288 = r3721286 + r3721287;
        double r3721289 = r3721288 * r3721268;
        double r3721290 = i;
        double r3721291 = r3721289 + r3721290;
        double r3721292 = r3721280 / r3721291;
        return r3721292;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r3721293 = t;
        double r3721294 = y;
        double r3721295 = z;
        double r3721296 = x;
        double r3721297 = r3721296 * r3721294;
        double r3721298 = r3721295 + r3721297;
        double r3721299 = r3721294 * r3721298;
        double r3721300 = 27464.7644705;
        double r3721301 = r3721299 + r3721300;
        double r3721302 = r3721294 * r3721301;
        double r3721303 = 230661.510616;
        double r3721304 = r3721302 + r3721303;
        double r3721305 = r3721304 * r3721294;
        double r3721306 = r3721293 + r3721305;
        double r3721307 = i;
        double r3721308 = c;
        double r3721309 = b;
        double r3721310 = a;
        double r3721311 = r3721294 + r3721310;
        double r3721312 = r3721311 * r3721294;
        double r3721313 = r3721309 + r3721312;
        double r3721314 = r3721294 * r3721313;
        double r3721315 = r3721308 + r3721314;
        double r3721316 = r3721315 * r3721294;
        double r3721317 = r3721307 + r3721316;
        double r3721318 = cbrt(r3721317);
        double r3721319 = r3721318 * r3721318;
        double r3721320 = r3721306 / r3721319;
        double r3721321 = r3721320 / r3721318;
        return r3721321;
}

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 29.2

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

  3. Applied add-cube-cbrt29.8

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

  4. Applied associate-/r*29.8

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

  5. Final simplification29.8

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

Reproduce

herbie shell --seed 2019171 
(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)))