Average Error: 28.4 → 28.5
Time: 8.6s
Precision: 64
\[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.764470499998\right) \cdot y + 230661.510616000014\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\]
↓
\[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.764470499998\right) \cdot y + 230661.510616000014\right) \cdot y + t}{\left(\left(\sqrt[3]{\left(y + a\right) \cdot y + b} \cdot \sqrt[3]{\left(y + a\right) \cdot y + b}\right) \cdot \left(\sqrt[3]{\left(y + a\right) \cdot y + b} \cdot y\right) + c\right) \cdot y + i}\]
\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.764470499998\right) \cdot y + 230661.510616000014\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 + 27464.764470499998\right) \cdot y + 230661.510616000014\right) \cdot y + t}{\left(\left(\sqrt[3]{\left(y + a\right) \cdot y + b} \cdot \sqrt[3]{\left(y + a\right) \cdot y + b}\right) \cdot \left(\sqrt[3]{\left(y + a\right) \cdot y + b} \cdot y\right) + c\right) \cdot y + i}
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r80159 = x;
        double r80160 = y;
        double r80161 = r80159 * r80160;
        double r80162 = z;
        double r80163 = r80161 + r80162;
        double r80164 = r80163 * r80160;
        double r80165 = 27464.7644705;
        double r80166 = r80164 + r80165;
        double r80167 = r80166 * r80160;
        double r80168 = 230661.510616;
        double r80169 = r80167 + r80168;
        double r80170 = r80169 * r80160;
        double r80171 = t;
        double r80172 = r80170 + r80171;
        double r80173 = a;
        double r80174 = r80160 + r80173;
        double r80175 = r80174 * r80160;
        double r80176 = b;
        double r80177 = r80175 + r80176;
        double r80178 = r80177 * r80160;
        double r80179 = c;
        double r80180 = r80178 + r80179;
        double r80181 = r80180 * r80160;
        double r80182 = i;
        double r80183 = r80181 + r80182;
        double r80184 = r80172 / r80183;
        return r80184;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r80185 = x;
        double r80186 = y;
        double r80187 = r80185 * r80186;
        double r80188 = z;
        double r80189 = r80187 + r80188;
        double r80190 = r80189 * r80186;
        double r80191 = 27464.7644705;
        double r80192 = r80190 + r80191;
        double r80193 = r80192 * r80186;
        double r80194 = 230661.510616;
        double r80195 = r80193 + r80194;
        double r80196 = r80195 * r80186;
        double r80197 = t;
        double r80198 = r80196 + r80197;
        double r80199 = a;
        double r80200 = r80186 + r80199;
        double r80201 = r80200 * r80186;
        double r80202 = b;
        double r80203 = r80201 + r80202;
        double r80204 = cbrt(r80203);
        double r80205 = r80204 * r80204;
        double r80206 = r80204 * r80186;
        double r80207 = r80205 * r80206;
        double r80208 = c;
        double r80209 = r80207 + r80208;
        double r80210 = r80209 * r80186;
        double r80211 = i;
        double r80212 = r80210 + r80211;
        double r80213 = r80198 / r80212;
        return r80213;
}

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 28.4

    \[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.764470499998\right) \cdot y + 230661.510616000014\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\]
  2. Using strategy rm

  3. Applied add-cube-cbrt28.5

    \[\leadsto \frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.764470499998\right) \cdot y + 230661.510616000014\right) \cdot y + t}{\left(\color{blue}{\left(\left(\sqrt[3]{\left(y + a\right) \cdot y + b} \cdot \sqrt[3]{\left(y + a\right) \cdot y + b}\right) \cdot \sqrt[3]{\left(y + a\right) \cdot y + b}\right)} \cdot y + c\right) \cdot y + i}\]

  4. Applied associate-*l*28.5

    \[\leadsto \frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.764470499998\right) \cdot y + 230661.510616000014\right) \cdot y + t}{\left(\color{blue}{\left(\sqrt[3]{\left(y + a\right) \cdot y + b} \cdot \sqrt[3]{\left(y + a\right) \cdot y + b}\right) \cdot \left(\sqrt[3]{\left(y + a\right) \cdot y + b} \cdot y\right)} + c\right) \cdot y + i}\]

  5. Final simplification28.5

    \[\leadsto \frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.764470499998\right) \cdot y + 230661.510616000014\right) \cdot y + t}{\left(\left(\sqrt[3]{\left(y + a\right) \cdot y + b} \cdot \sqrt[3]{\left(y + a\right) \cdot y + b}\right) \cdot \left(\sqrt[3]{\left(y + a\right) \cdot y + b} \cdot y\right) + c\right) \cdot y + i}\]

Reproduce

herbie shell --seed 2020035 
(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)))