Average Error: 29.1 → 29.2
Time: 29.0s
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 r75166 = x;
        double r75167 = y;
        double r75168 = r75166 * r75167;
        double r75169 = z;
        double r75170 = r75168 + r75169;
        double r75171 = r75170 * r75167;
        double r75172 = 27464.7644705;
        double r75173 = r75171 + r75172;
        double r75174 = r75173 * r75167;
        double r75175 = 230661.510616;
        double r75176 = r75174 + r75175;
        double r75177 = r75176 * r75167;
        double r75178 = t;
        double r75179 = r75177 + r75178;
        double r75180 = a;
        double r75181 = r75167 + r75180;
        double r75182 = r75181 * r75167;
        double r75183 = b;
        double r75184 = r75182 + r75183;
        double r75185 = r75184 * r75167;
        double r75186 = c;
        double r75187 = r75185 + r75186;
        double r75188 = r75187 * r75167;
        double r75189 = i;
        double r75190 = r75188 + r75189;
        double r75191 = r75179 / r75190;
        return r75191;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r75192 = t;
        double r75193 = y;
        double r75194 = 230661.510616;
        double r75195 = 27464.7644705;
        double r75196 = z;
        double r75197 = x;
        double r75198 = r75193 * r75197;
        double r75199 = r75196 + r75198;
        double r75200 = r75199 * r75193;
        double r75201 = r75195 + r75200;
        double r75202 = r75201 * r75193;
        double r75203 = cbrt(r75202);
        double r75204 = r75203 * r75203;
        double r75205 = cbrt(r75203);
        double r75206 = r75205 * r75205;
        double r75207 = r75205 * r75206;
        double r75208 = r75204 * r75207;
        double r75209 = r75194 + r75208;
        double r75210 = r75193 * r75209;
        double r75211 = r75192 + r75210;
        double r75212 = i;
        double r75213 = b;
        double r75214 = a;
        double r75215 = r75214 + r75193;
        double r75216 = r75193 * r75215;
        double r75217 = r75213 + r75216;
        double r75218 = r75193 * r75217;
        double r75219 = c;
        double r75220 = r75218 + r75219;
        double r75221 = r75220 * r75193;
        double r75222 = r75212 + r75221;
        double r75223 = r75211 / r75222;
        return r75223;
}

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)))