Average Error: 29.1 → 29.2
Time: 29.3s
Precision: 64
\[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644704999984242022037506103515625\right) \cdot y + 230661.5106160000141244381666183471679688\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\]
↓
\[\frac{t + y \cdot \left(230661.5106160000141244381666183471679688 + \left(\sqrt[3]{\left(27464.7644704999984242022037506103515625 + \left(z + y \cdot x\right) \cdot y\right) \cdot y} \cdot \sqrt[3]{\left(27464.7644704999984242022037506103515625 + \left(z + y \cdot x\right) \cdot y\right) \cdot y}\right) \cdot \left(\sqrt[3]{\sqrt[3]{\left(27464.7644704999984242022037506103515625 + \left(z + y \cdot x\right) \cdot y\right) \cdot y}} \cdot \left(\sqrt[3]{\sqrt[3]{\left(27464.7644704999984242022037506103515625 + \left(z + y \cdot x\right) \cdot y\right) \cdot y}} \cdot \sqrt[3]{\sqrt[3]{\left(27464.7644704999984242022037506103515625 + \left(z + y \cdot x\right) \cdot y\right) \cdot y}}\right)\right)\right)}{i + \left(y \cdot \left(b + y \cdot \left(a + y\right)\right) + c\right) \cdot y}\]
\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{t + y \cdot \left(230661.5106160000141244381666183471679688 + \left(\sqrt[3]{\left(27464.7644704999984242022037506103515625 + \left(z + y \cdot x\right) \cdot y\right) \cdot y} \cdot \sqrt[3]{\left(27464.7644704999984242022037506103515625 + \left(z + y \cdot x\right) \cdot y\right) \cdot y}\right) \cdot \left(\sqrt[3]{\sqrt[3]{\left(27464.7644704999984242022037506103515625 + \left(z + y \cdot x\right) \cdot y\right) \cdot y}} \cdot \left(\sqrt[3]{\sqrt[3]{\left(27464.7644704999984242022037506103515625 + \left(z + y \cdot x\right) \cdot y\right) \cdot y}} \cdot \sqrt[3]{\sqrt[3]{\left(27464.7644704999984242022037506103515625 + \left(z + y \cdot x\right) \cdot y\right) \cdot y}}\right)\right)\right)}{i + \left(y \cdot \left(b + y \cdot \left(a + y\right)\right) + c\right) \cdot y}
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r91267 = x;
        double r91268 = y;
        double r91269 = r91267 * r91268;
        double r91270 = z;
        double r91271 = r91269 + r91270;
        double r91272 = r91271 * r91268;
        double r91273 = 27464.7644705;
        double r91274 = r91272 + r91273;
        double r91275 = r91274 * r91268;
        double r91276 = 230661.510616;
        double r91277 = r91275 + r91276;
        double r91278 = r91277 * r91268;
        double r91279 = t;
        double r91280 = r91278 + r91279;
        double r91281 = a;
        double r91282 = r91268 + r91281;
        double r91283 = r91282 * r91268;
        double r91284 = b;
        double r91285 = r91283 + r91284;
        double r91286 = r91285 * r91268;
        double r91287 = c;
        double r91288 = r91286 + r91287;
        double r91289 = r91288 * r91268;
        double r91290 = i;
        double r91291 = r91289 + r91290;
        double r91292 = r91280 / r91291;
        return r91292;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r91293 = t;
        double r91294 = y;
        double r91295 = 230661.510616;
        double r91296 = 27464.7644705;
        double r91297 = z;
        double r91298 = x;
        double r91299 = r91294 * r91298;
        double r91300 = r91297 + r91299;
        double r91301 = r91300 * r91294;
        double r91302 = r91296 + r91301;
        double r91303 = r91302 * r91294;
        double r91304 = cbrt(r91303);
        double r91305 = r91304 * r91304;
        double r91306 = cbrt(r91304);
        double r91307 = r91306 * r91306;
        double r91308 = r91306 * r91307;
        double r91309 = r91305 * r91308;
        double r91310 = r91295 + r91309;
        double r91311 = r91294 * r91310;
        double r91312 = r91293 + r91311;
        double r91313 = i;
        double r91314 = b;
        double r91315 = a;
        double r91316 = r91315 + r91294;
        double r91317 = r91294 * r91316;
        double r91318 = r91314 + r91317;
        double r91319 = r91294 * r91318;
        double r91320 = c;
        double r91321 = r91319 + r91320;
        double r91322 = r91321 * r91294;
        double r91323 = r91313 + r91322;
        double r91324 = r91312 / r91323;
        return r91324;
}

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

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

  4. Simplified29.2

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

  5. Simplified29.2

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

  7. Applied add-cube-cbrt29.2

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

  8. Simplified29.2

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

  9. Simplified29.2

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

  10. Final simplification29.2

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

Reproduce

herbie shell --seed 2019194 
(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)))