Average Error: 28.4 → 28.5
Time: 9.8s
Precision: 64
\[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.764470499998\right) \cdot y + 230661.510616000014\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\]
↓
\[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.764470499998\right) \cdot y + 230661.510616000014\right) \cdot y + t}{\left(\left(\sqrt[3]{\left(y + a\right) \cdot y + b} \cdot \sqrt[3]{\left(y + a\right) \cdot y + b}\right) \cdot \left(\sqrt[3]{\left(y + a\right) \cdot y + b} \cdot y\right) + c\right) \cdot y + i}\]
\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(\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}
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r84247 = x;
        double r84248 = y;
        double r84249 = r84247 * r84248;
        double r84250 = z;
        double r84251 = r84249 + r84250;
        double r84252 = r84251 * r84248;
        double r84253 = 27464.7644705;
        double r84254 = r84252 + r84253;
        double r84255 = r84254 * r84248;
        double r84256 = 230661.510616;
        double r84257 = r84255 + r84256;
        double r84258 = r84257 * r84248;
        double r84259 = t;
        double r84260 = r84258 + r84259;
        double r84261 = a;
        double r84262 = r84248 + r84261;
        double r84263 = r84262 * r84248;
        double r84264 = b;
        double r84265 = r84263 + r84264;
        double r84266 = r84265 * r84248;
        double r84267 = c;
        double r84268 = r84266 + r84267;
        double r84269 = r84268 * r84248;
        double r84270 = i;
        double r84271 = r84269 + r84270;
        double r84272 = r84260 / r84271;
        return r84272;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r84273 = x;
        double r84274 = y;
        double r84275 = r84273 * r84274;
        double r84276 = z;
        double r84277 = r84275 + r84276;
        double r84278 = r84277 * r84274;
        double r84279 = 27464.7644705;
        double r84280 = r84278 + r84279;
        double r84281 = r84280 * r84274;
        double r84282 = 230661.510616;
        double r84283 = r84281 + r84282;
        double r84284 = r84283 * r84274;
        double r84285 = t;
        double r84286 = r84284 + r84285;
        double r84287 = a;
        double r84288 = r84274 + r84287;
        double r84289 = r84288 * r84274;
        double r84290 = b;
        double r84291 = r84289 + r84290;
        double r84292 = cbrt(r84291);
        double r84293 = r84292 * r84292;
        double r84294 = r84292 * r84274;
        double r84295 = r84293 * r84294;
        double r84296 = c;
        double r84297 = r84295 + r84296;
        double r84298 = r84297 * r84274;
        double r84299 = i;
        double r84300 = r84298 + r84299;
        double r84301 = r84286 / r84300;
        return r84301;
}

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 28.4

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

  3. Applied add-cube-cbrt28.5

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

  4. Applied associate-*l*28.5

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

  5. Final simplification28.5

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

Reproduce

herbie shell --seed 2020035 +o rules:numerics
(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)))