Average Error: 28.7 → 28.8
Time: 9.2s
Precision: 64
\[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644704999984242022037506103515625\right) \cdot y + 230661.5106160000141244381666183471679688\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\]
↓
\[\frac{\left(\left(\sqrt[3]{\left(x \cdot y + z\right) \cdot y + 27464.7644704999984242022037506103515625} \cdot \sqrt[3]{\left(x \cdot y + z\right) \cdot y + 27464.7644704999984242022037506103515625}\right) \cdot \left(\sqrt[3]{\left(x \cdot y + z\right) \cdot y + 27464.7644704999984242022037506103515625} \cdot y\right) + 230661.5106160000141244381666183471679688\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\]
\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(x \cdot y + z\right) \cdot y + 27464.7644704999984242022037506103515625} \cdot \sqrt[3]{\left(x \cdot y + z\right) \cdot y + 27464.7644704999984242022037506103515625}\right) \cdot \left(\sqrt[3]{\left(x \cdot y + z\right) \cdot y + 27464.7644704999984242022037506103515625} \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}
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r60154 = x;
        double r60155 = y;
        double r60156 = r60154 * r60155;
        double r60157 = z;
        double r60158 = r60156 + r60157;
        double r60159 = r60158 * r60155;
        double r60160 = 27464.7644705;
        double r60161 = r60159 + r60160;
        double r60162 = r60161 * r60155;
        double r60163 = 230661.510616;
        double r60164 = r60162 + r60163;
        double r60165 = r60164 * r60155;
        double r60166 = t;
        double r60167 = r60165 + r60166;
        double r60168 = a;
        double r60169 = r60155 + r60168;
        double r60170 = r60169 * r60155;
        double r60171 = b;
        double r60172 = r60170 + r60171;
        double r60173 = r60172 * r60155;
        double r60174 = c;
        double r60175 = r60173 + r60174;
        double r60176 = r60175 * r60155;
        double r60177 = i;
        double r60178 = r60176 + r60177;
        double r60179 = r60167 / r60178;
        return r60179;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r60180 = x;
        double r60181 = y;
        double r60182 = r60180 * r60181;
        double r60183 = z;
        double r60184 = r60182 + r60183;
        double r60185 = r60184 * r60181;
        double r60186 = 27464.7644705;
        double r60187 = r60185 + r60186;
        double r60188 = cbrt(r60187);
        double r60189 = r60188 * r60188;
        double r60190 = r60188 * r60181;
        double r60191 = r60189 * r60190;
        double r60192 = 230661.510616;
        double r60193 = r60191 + r60192;
        double r60194 = r60193 * r60181;
        double r60195 = t;
        double r60196 = r60194 + r60195;
        double r60197 = a;
        double r60198 = r60181 + r60197;
        double r60199 = r60198 * r60181;
        double r60200 = b;
        double r60201 = r60199 + r60200;
        double r60202 = r60201 * r60181;
        double r60203 = c;
        double r60204 = r60202 + r60203;
        double r60205 = r60204 * r60181;
        double r60206 = i;
        double r60207 = r60205 + r60206;
        double r60208 = r60196 / r60207;
        return r60208;
}

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 28.7

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

  3. Applied add-cube-cbrt28.8

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

  4. Applied associate-*l*28.8

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

  5. Final simplification28.8

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

Reproduce

herbie shell --seed 2019353 
(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)))