Average Error: 29.1 → 29.2
Time: 8.6s
Precision: 64
\[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644704999984242022037506103515625\right) \cdot y + 230661.5106160000141244381666183471679688\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\]
↓
\[\frac{\left(\left(\left(\sqrt[3]{x \cdot y + z} \cdot \sqrt[3]{x \cdot y + z}\right) \cdot \left(\sqrt[3]{x \cdot y + z} \cdot y\right) + 27464.7644704999984242022037506103515625\right) \cdot y + 230661.5106160000141244381666183471679688\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\]
\frac{\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{\left(\left(\left(\sqrt[3]{x \cdot y + z} \cdot \sqrt[3]{x \cdot y + z}\right) \cdot \left(\sqrt[3]{x \cdot y + z} \cdot y\right) + 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}
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r76283 = x;
        double r76284 = y;
        double r76285 = r76283 * r76284;
        double r76286 = z;
        double r76287 = r76285 + r76286;
        double r76288 = r76287 * r76284;
        double r76289 = 27464.7644705;
        double r76290 = r76288 + r76289;
        double r76291 = r76290 * r76284;
        double r76292 = 230661.510616;
        double r76293 = r76291 + r76292;
        double r76294 = r76293 * r76284;
        double r76295 = t;
        double r76296 = r76294 + r76295;
        double r76297 = a;
        double r76298 = r76284 + r76297;
        double r76299 = r76298 * r76284;
        double r76300 = b;
        double r76301 = r76299 + r76300;
        double r76302 = r76301 * r76284;
        double r76303 = c;
        double r76304 = r76302 + r76303;
        double r76305 = r76304 * r76284;
        double r76306 = i;
        double r76307 = r76305 + r76306;
        double r76308 = r76296 / r76307;
        return r76308;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r76309 = x;
        double r76310 = y;
        double r76311 = r76309 * r76310;
        double r76312 = z;
        double r76313 = r76311 + r76312;
        double r76314 = cbrt(r76313);
        double r76315 = r76314 * r76314;
        double r76316 = r76314 * r76310;
        double r76317 = r76315 * r76316;
        double r76318 = 27464.7644705;
        double r76319 = r76317 + r76318;
        double r76320 = r76319 * r76310;
        double r76321 = 230661.510616;
        double r76322 = r76320 + r76321;
        double r76323 = r76322 * r76310;
        double r76324 = t;
        double r76325 = r76323 + r76324;
        double r76326 = a;
        double r76327 = r76310 + r76326;
        double r76328 = r76327 * r76310;
        double r76329 = b;
        double r76330 = r76328 + r76329;
        double r76331 = r76330 * r76310;
        double r76332 = c;
        double r76333 = r76331 + r76332;
        double r76334 = r76333 * r76310;
        double r76335 = i;
        double r76336 = r76334 + r76335;
        double r76337 = r76325 / r76336;
        return r76337;
}

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 29.1

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

  3. Applied add-cube-cbrt29.2

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

  4. Applied associate-*l*29.2

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

  5. Final simplification29.2

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

Reproduce

herbie shell --seed 2020002 +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)))