Average Error: 29.0 → 29.0
Time: 54.7s
Precision: 64
\[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644704999984242022037506103515625\right) \cdot y + 230661.5106160000141244381666183471679688\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\]
↓
\[\frac{t + \left(230661.5106160000141244381666183471679688 + \left(\left(\left(y \cdot x + z\right) \cdot y + 27464.7644704999984242022037506103515625\right) \cdot \left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right)\right) \cdot \sqrt[3]{y}\right) \cdot y}{y \cdot \left(y \cdot \left(b + y \cdot \left(a + y\right)\right) + c\right) + i}\]
\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(230661.5106160000141244381666183471679688 + \left(\left(\left(y \cdot x + z\right) \cdot y + 27464.7644704999984242022037506103515625\right) \cdot \left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right)\right) \cdot \sqrt[3]{y}\right) \cdot y}{y \cdot \left(y \cdot \left(b + y \cdot \left(a + y\right)\right) + c\right) + i}
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r3554208 = x;
        double r3554209 = y;
        double r3554210 = r3554208 * r3554209;
        double r3554211 = z;
        double r3554212 = r3554210 + r3554211;
        double r3554213 = r3554212 * r3554209;
        double r3554214 = 27464.7644705;
        double r3554215 = r3554213 + r3554214;
        double r3554216 = r3554215 * r3554209;
        double r3554217 = 230661.510616;
        double r3554218 = r3554216 + r3554217;
        double r3554219 = r3554218 * r3554209;
        double r3554220 = t;
        double r3554221 = r3554219 + r3554220;
        double r3554222 = a;
        double r3554223 = r3554209 + r3554222;
        double r3554224 = r3554223 * r3554209;
        double r3554225 = b;
        double r3554226 = r3554224 + r3554225;
        double r3554227 = r3554226 * r3554209;
        double r3554228 = c;
        double r3554229 = r3554227 + r3554228;
        double r3554230 = r3554229 * r3554209;
        double r3554231 = i;
        double r3554232 = r3554230 + r3554231;
        double r3554233 = r3554221 / r3554232;
        return r3554233;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r3554234 = t;
        double r3554235 = 230661.510616;
        double r3554236 = y;
        double r3554237 = x;
        double r3554238 = r3554236 * r3554237;
        double r3554239 = z;
        double r3554240 = r3554238 + r3554239;
        double r3554241 = r3554240 * r3554236;
        double r3554242 = 27464.7644705;
        double r3554243 = r3554241 + r3554242;
        double r3554244 = cbrt(r3554236);
        double r3554245 = r3554244 * r3554244;
        double r3554246 = r3554243 * r3554245;
        double r3554247 = r3554246 * r3554244;
        double r3554248 = r3554235 + r3554247;
        double r3554249 = r3554248 * r3554236;
        double r3554250 = r3554234 + r3554249;
        double r3554251 = b;
        double r3554252 = a;
        double r3554253 = r3554252 + r3554236;
        double r3554254 = r3554236 * r3554253;
        double r3554255 = r3554251 + r3554254;
        double r3554256 = r3554236 * r3554255;
        double r3554257 = c;
        double r3554258 = r3554256 + r3554257;
        double r3554259 = r3554236 * r3554258;
        double r3554260 = i;
        double r3554261 = r3554259 + r3554260;
        double r3554262 = r3554250 / r3554261;
        return r3554262;
}

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 29.0

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

  3. Applied add-cube-cbrt29.0

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

  4. Applied associate-*r*29.0

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

  5. Final simplification29.0

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

Reproduce

herbie shell --seed 2019200 
(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)))