Average Error: 29.5 → 29.6
Time: 7.8s
Precision: 64
\[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.764470499998\right) \cdot y + 230661.510616000014\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\]
↓
\[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.764470499998\right) \cdot y + 230661.510616000014\right) \cdot y + t}{\left(\left(\left(\left(y + a\right) \cdot y + b\right) \cdot \left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right)\right) \cdot \sqrt[3]{y} + c\right) \cdot y + i}\]
\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.764470499998\right) \cdot y + 230661.510616000014\right) \cdot y + t}{\left(\left(\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(\left(\left(y + a\right) \cdot y + b\right) \cdot \left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right)\right) \cdot \sqrt[3]{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 r55134 = x;
        double r55135 = y;
        double r55136 = r55134 * r55135;
        double r55137 = z;
        double r55138 = r55136 + r55137;
        double r55139 = r55138 * r55135;
        double r55140 = 27464.7644705;
        double r55141 = r55139 + r55140;
        double r55142 = r55141 * r55135;
        double r55143 = 230661.510616;
        double r55144 = r55142 + r55143;
        double r55145 = r55144 * r55135;
        double r55146 = t;
        double r55147 = r55145 + r55146;
        double r55148 = a;
        double r55149 = r55135 + r55148;
        double r55150 = r55149 * r55135;
        double r55151 = b;
        double r55152 = r55150 + r55151;
        double r55153 = r55152 * r55135;
        double r55154 = c;
        double r55155 = r55153 + r55154;
        double r55156 = r55155 * r55135;
        double r55157 = i;
        double r55158 = r55156 + r55157;
        double r55159 = r55147 / r55158;
        return r55159;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r55160 = x;
        double r55161 = y;
        double r55162 = r55160 * r55161;
        double r55163 = z;
        double r55164 = r55162 + r55163;
        double r55165 = r55164 * r55161;
        double r55166 = 27464.7644705;
        double r55167 = r55165 + r55166;
        double r55168 = r55167 * r55161;
        double r55169 = 230661.510616;
        double r55170 = r55168 + r55169;
        double r55171 = r55170 * r55161;
        double r55172 = t;
        double r55173 = r55171 + r55172;
        double r55174 = a;
        double r55175 = r55161 + r55174;
        double r55176 = r55175 * r55161;
        double r55177 = b;
        double r55178 = r55176 + r55177;
        double r55179 = cbrt(r55161);
        double r55180 = r55179 * r55179;
        double r55181 = r55178 * r55180;
        double r55182 = r55181 * r55179;
        double r55183 = c;
        double r55184 = r55182 + r55183;
        double r55185 = r55184 * r55161;
        double r55186 = i;
        double r55187 = r55185 + r55186;
        double r55188 = r55173 / r55187;
        return r55188;
}

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 29.5

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

  3. Applied add-cube-cbrt29.6

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

  4. Applied associate-*r*29.6

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

  5. Final simplification29.6

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

Reproduce

herbie shell --seed 2020046 
(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)))