Average Error: 29.2 → 29.3
Time: 8.4s
Precision: 64
\[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.764470499998\right) \cdot y + 230661.510616000014\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\]
↓
\[\frac{\left(\left(\sqrt[3]{\left(\left(x \cdot y + z\right) \cdot y + 27464.764470499998\right) \cdot y} \cdot \sqrt[3]{\left(\left(x \cdot y + z\right) \cdot y + 27464.764470499998\right) \cdot y}\right) \cdot \sqrt[3]{\left(\left(x \cdot y + z\right) \cdot y + 27464.764470499998\right) \cdot y} + 230661.510616000014\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\]
\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(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 + 27464.764470499998\right) \cdot y} \cdot \sqrt[3]{\left(\left(x \cdot y + z\right) \cdot y + 27464.764470499998\right) \cdot y}\right) \cdot \sqrt[3]{\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}
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r64152 = x;
        double r64153 = y;
        double r64154 = r64152 * r64153;
        double r64155 = z;
        double r64156 = r64154 + r64155;
        double r64157 = r64156 * r64153;
        double r64158 = 27464.7644705;
        double r64159 = r64157 + r64158;
        double r64160 = r64159 * r64153;
        double r64161 = 230661.510616;
        double r64162 = r64160 + r64161;
        double r64163 = r64162 * r64153;
        double r64164 = t;
        double r64165 = r64163 + r64164;
        double r64166 = a;
        double r64167 = r64153 + r64166;
        double r64168 = r64167 * r64153;
        double r64169 = b;
        double r64170 = r64168 + r64169;
        double r64171 = r64170 * r64153;
        double r64172 = c;
        double r64173 = r64171 + r64172;
        double r64174 = r64173 * r64153;
        double r64175 = i;
        double r64176 = r64174 + r64175;
        double r64177 = r64165 / r64176;
        return r64177;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r64178 = x;
        double r64179 = y;
        double r64180 = r64178 * r64179;
        double r64181 = z;
        double r64182 = r64180 + r64181;
        double r64183 = r64182 * r64179;
        double r64184 = 27464.7644705;
        double r64185 = r64183 + r64184;
        double r64186 = r64185 * r64179;
        double r64187 = cbrt(r64186);
        double r64188 = r64187 * r64187;
        double r64189 = r64188 * r64187;
        double r64190 = 230661.510616;
        double r64191 = r64189 + r64190;
        double r64192 = r64191 * r64179;
        double r64193 = t;
        double r64194 = r64192 + r64193;
        double r64195 = a;
        double r64196 = r64179 + r64195;
        double r64197 = r64196 * r64179;
        double r64198 = b;
        double r64199 = r64197 + r64198;
        double r64200 = r64199 * r64179;
        double r64201 = c;
        double r64202 = r64200 + r64201;
        double r64203 = r64202 * r64179;
        double r64204 = i;
        double r64205 = r64203 + r64204;
        double r64206 = r64194 / r64205;
        return r64206;
}

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 29.2

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

  3. Applied add-cube-cbrt29.3

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

  4. Final simplification29.3

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

Reproduce

herbie shell --seed 2020020 +o rules:numerics
(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)))