Average Error: 28.3 → 28.4
Time: 33.2s
Precision: 64
\[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\]
↓
\[\frac{y \cdot \left(230661.510616 + \left(\sqrt[3]{y \cdot \left(z + x \cdot y\right) + 27464.7644705} \cdot \sqrt[3]{y \cdot \left(z + x \cdot y\right) + 27464.7644705}\right) \cdot \left(\sqrt[3]{y \cdot \left(z + x \cdot y\right) + 27464.7644705} \cdot y\right)\right) + t}{y \cdot \left(c + \left(b + y \cdot \left(y + a\right)\right) \cdot y\right) + i}\]
\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(\sqrt[3]{y \cdot \left(z + x \cdot y\right) + 27464.7644705} \cdot \sqrt[3]{y \cdot \left(z + x \cdot y\right) + 27464.7644705}\right) \cdot \left(\sqrt[3]{y \cdot \left(z + x \cdot y\right) + 27464.7644705} \cdot y\right)\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 r2554137 = x;
        double r2554138 = y;
        double r2554139 = r2554137 * r2554138;
        double r2554140 = z;
        double r2554141 = r2554139 + r2554140;
        double r2554142 = r2554141 * r2554138;
        double r2554143 = 27464.7644705;
        double r2554144 = r2554142 + r2554143;
        double r2554145 = r2554144 * r2554138;
        double r2554146 = 230661.510616;
        double r2554147 = r2554145 + r2554146;
        double r2554148 = r2554147 * r2554138;
        double r2554149 = t;
        double r2554150 = r2554148 + r2554149;
        double r2554151 = a;
        double r2554152 = r2554138 + r2554151;
        double r2554153 = r2554152 * r2554138;
        double r2554154 = b;
        double r2554155 = r2554153 + r2554154;
        double r2554156 = r2554155 * r2554138;
        double r2554157 = c;
        double r2554158 = r2554156 + r2554157;
        double r2554159 = r2554158 * r2554138;
        double r2554160 = i;
        double r2554161 = r2554159 + r2554160;
        double r2554162 = r2554150 / r2554161;
        return r2554162;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r2554163 = y;
        double r2554164 = 230661.510616;
        double r2554165 = z;
        double r2554166 = x;
        double r2554167 = r2554166 * r2554163;
        double r2554168 = r2554165 + r2554167;
        double r2554169 = r2554163 * r2554168;
        double r2554170 = 27464.7644705;
        double r2554171 = r2554169 + r2554170;
        double r2554172 = cbrt(r2554171);
        double r2554173 = r2554172 * r2554172;
        double r2554174 = r2554172 * r2554163;
        double r2554175 = r2554173 * r2554174;
        double r2554176 = r2554164 + r2554175;
        double r2554177 = r2554163 * r2554176;
        double r2554178 = t;
        double r2554179 = r2554177 + r2554178;
        double r2554180 = c;
        double r2554181 = b;
        double r2554182 = a;
        double r2554183 = r2554163 + r2554182;
        double r2554184 = r2554163 * r2554183;
        double r2554185 = r2554181 + r2554184;
        double r2554186 = r2554185 * r2554163;
        double r2554187 = r2554180 + r2554186;
        double r2554188 = r2554163 * r2554187;
        double r2554189 = i;
        double r2554190 = r2554188 + r2554189;
        double r2554191 = r2554179 / r2554190;
        return r2554191;
}

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 28.3

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

  3. Applied add-cube-cbrt28.4

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

  4. Applied associate-*l*28.4

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

  5. Final simplification28.4

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

Reproduce

herbie shell --seed 2019135 
(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)))