Average Error: 29.1 → 29.2
Time: 3.8m
Precision: 64
\[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644704999984242022037506103515625\right) \cdot y + 230661.5106160000141244381666183471679688\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\]
↓
\[\frac{\left(\left(\sqrt[3]{\left(\left(x \cdot y + z\right) \cdot y + 27464.7644704999984242022037506103515625\right) \cdot y} \cdot \sqrt[3]{\left(\left(x \cdot y + z\right) \cdot y + 27464.7644704999984242022037506103515625\right) \cdot y}\right) \cdot \sqrt[3]{\left(\left(x \cdot y + z\right) \cdot y + 27464.7644704999984242022037506103515625\right) \cdot y} + 230661.5106160000141244381666183471679688\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\]
\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(\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}
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r1450148 = x;
        double r1450149 = y;
        double r1450150 = r1450148 * r1450149;
        double r1450151 = z;
        double r1450152 = r1450150 + r1450151;
        double r1450153 = r1450152 * r1450149;
        double r1450154 = 27464.7644705;
        double r1450155 = r1450153 + r1450154;
        double r1450156 = r1450155 * r1450149;
        double r1450157 = 230661.510616;
        double r1450158 = r1450156 + r1450157;
        double r1450159 = r1450158 * r1450149;
        double r1450160 = t;
        double r1450161 = r1450159 + r1450160;
        double r1450162 = a;
        double r1450163 = r1450149 + r1450162;
        double r1450164 = r1450163 * r1450149;
        double r1450165 = b;
        double r1450166 = r1450164 + r1450165;
        double r1450167 = r1450166 * r1450149;
        double r1450168 = c;
        double r1450169 = r1450167 + r1450168;
        double r1450170 = r1450169 * r1450149;
        double r1450171 = i;
        double r1450172 = r1450170 + r1450171;
        double r1450173 = r1450161 / r1450172;
        return r1450173;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r1450174 = x;
        double r1450175 = y;
        double r1450176 = r1450174 * r1450175;
        double r1450177 = z;
        double r1450178 = r1450176 + r1450177;
        double r1450179 = r1450178 * r1450175;
        double r1450180 = 27464.7644705;
        double r1450181 = r1450179 + r1450180;
        double r1450182 = r1450181 * r1450175;
        double r1450183 = cbrt(r1450182);
        double r1450184 = r1450183 * r1450183;
        double r1450185 = r1450184 * r1450183;
        double r1450186 = 230661.510616;
        double r1450187 = r1450185 + r1450186;
        double r1450188 = r1450187 * r1450175;
        double r1450189 = t;
        double r1450190 = r1450188 + r1450189;
        double r1450191 = a;
        double r1450192 = r1450175 + r1450191;
        double r1450193 = r1450192 * r1450175;
        double r1450194 = b;
        double r1450195 = r1450193 + r1450194;
        double r1450196 = r1450195 * r1450175;
        double r1450197 = c;
        double r1450198 = r1450196 + r1450197;
        double r1450199 = r1450198 * r1450175;
        double r1450200 = i;
        double r1450201 = r1450199 + r1450200;
        double r1450202 = r1450190 / r1450201;
        return r1450202;
}

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. Final simplification29.2

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

Reproduce

herbie shell --seed 2019235 
(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) 27464.764470499998) y) 230661.510616000014) y) t) (+ (* (+ (* (+ (* (+ y a) y) b) y) c) y) i)))