Average Error: 28.1 → 28.1
Time: 37.6s
Precision: 64
\[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\]
↓
\[\frac{y \cdot \left(230661.510616 + \left(\left(\sqrt[3]{z + x \cdot y} \cdot y\right) \cdot \left(\sqrt[3]{z + x \cdot y} \cdot \sqrt[3]{z + x \cdot y}\right) + 27464.7644705\right) \cdot y\right) + t}{y \cdot \left(c + \left(b + y \cdot \left(y + a\right)\right) \cdot y\right) + i}\]
\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}
↓
\frac{y \cdot \left(230661.510616 + \left(\left(\sqrt[3]{z + x \cdot y} \cdot y\right) \cdot \left(\sqrt[3]{z + x \cdot y} \cdot \sqrt[3]{z + x \cdot y}\right) + 27464.7644705\right) \cdot y\right) + t}{y \cdot \left(c + \left(b + y \cdot \left(y + a\right)\right) \cdot y\right) + i}
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r2904118 = x;
        double r2904119 = y;
        double r2904120 = r2904118 * r2904119;
        double r2904121 = z;
        double r2904122 = r2904120 + r2904121;
        double r2904123 = r2904122 * r2904119;
        double r2904124 = 27464.7644705;
        double r2904125 = r2904123 + r2904124;
        double r2904126 = r2904125 * r2904119;
        double r2904127 = 230661.510616;
        double r2904128 = r2904126 + r2904127;
        double r2904129 = r2904128 * r2904119;
        double r2904130 = t;
        double r2904131 = r2904129 + r2904130;
        double r2904132 = a;
        double r2904133 = r2904119 + r2904132;
        double r2904134 = r2904133 * r2904119;
        double r2904135 = b;
        double r2904136 = r2904134 + r2904135;
        double r2904137 = r2904136 * r2904119;
        double r2904138 = c;
        double r2904139 = r2904137 + r2904138;
        double r2904140 = r2904139 * r2904119;
        double r2904141 = i;
        double r2904142 = r2904140 + r2904141;
        double r2904143 = r2904131 / r2904142;
        return r2904143;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r2904144 = y;
        double r2904145 = 230661.510616;
        double r2904146 = z;
        double r2904147 = x;
        double r2904148 = r2904147 * r2904144;
        double r2904149 = r2904146 + r2904148;
        double r2904150 = cbrt(r2904149);
        double r2904151 = r2904150 * r2904144;
        double r2904152 = r2904150 * r2904150;
        double r2904153 = r2904151 * r2904152;
        double r2904154 = 27464.7644705;
        double r2904155 = r2904153 + r2904154;
        double r2904156 = r2904155 * r2904144;
        double r2904157 = r2904145 + r2904156;
        double r2904158 = r2904144 * r2904157;
        double r2904159 = t;
        double r2904160 = r2904158 + r2904159;
        double r2904161 = c;
        double r2904162 = b;
        double r2904163 = a;
        double r2904164 = r2904144 + r2904163;
        double r2904165 = r2904144 * r2904164;
        double r2904166 = r2904162 + r2904165;
        double r2904167 = r2904166 * r2904144;
        double r2904168 = r2904161 + r2904167;
        double r2904169 = r2904144 * r2904168;
        double r2904170 = i;
        double r2904171 = r2904169 + r2904170;
        double r2904172 = r2904160 / r2904171;
        return r2904172;
}

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 28.1

    \[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\]
  2. Using strategy rm

  3. Applied add-cube-cbrt28.1

    \[\leadsto \frac{\left(\left(\color{blue}{\left(\left(\sqrt[3]{x \cdot y + z} \cdot \sqrt[3]{x \cdot y + z}\right) \cdot \sqrt[3]{x \cdot y + z}\right)} \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\]

  4. Applied associate-*l*28.1

    \[\leadsto \frac{\left(\left(\color{blue}{\left(\sqrt[3]{x \cdot y + z} \cdot \sqrt[3]{x \cdot y + z}\right) \cdot \left(\sqrt[3]{x \cdot y + z} \cdot y\right)} + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\]

  5. Final simplification28.1

    \[\leadsto \frac{y \cdot \left(230661.510616 + \left(\left(\sqrt[3]{z + x \cdot y} \cdot y\right) \cdot \left(\sqrt[3]{z + x \cdot y} \cdot \sqrt[3]{z + x \cdot y}\right) + 27464.7644705\right) \cdot y\right) + t}{y \cdot \left(c + \left(b + y \cdot \left(y + a\right)\right) \cdot y\right) + i}\]

Reproduce

herbie shell --seed 2019143 
(FPCore (x y z t a b c i)
  :name "Numeric.SpecFunctions:logGamma from math-functions-0.1.5.2"
  (/ (+ (* (+ (* (+ (* (+ (* x y) z) y) 27464.7644705) y) 230661.510616) y) t) (+ (* (+ (* (+ (* (+ y a) y) b) y) c) y) i)))