Average Error: 28.8 → 29.0
Time: 40.1s
Precision: 64
\[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\]
↓
\[\frac{1}{\frac{1}{t + y \cdot \left(\left(\left(y \cdot x + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right)} \cdot \left(i + y \cdot \left(\left(b + \left(y + a\right) \cdot y\right) \cdot y + c\right)\right)}\]
\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{1}{\frac{1}{t + y \cdot \left(\left(\left(y \cdot x + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right)} \cdot \left(i + y \cdot \left(\left(b + \left(y + a\right) \cdot y\right) \cdot y + c\right)\right)}
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r2245146 = x;
        double r2245147 = y;
        double r2245148 = r2245146 * r2245147;
        double r2245149 = z;
        double r2245150 = r2245148 + r2245149;
        double r2245151 = r2245150 * r2245147;
        double r2245152 = 27464.7644705;
        double r2245153 = r2245151 + r2245152;
        double r2245154 = r2245153 * r2245147;
        double r2245155 = 230661.510616;
        double r2245156 = r2245154 + r2245155;
        double r2245157 = r2245156 * r2245147;
        double r2245158 = t;
        double r2245159 = r2245157 + r2245158;
        double r2245160 = a;
        double r2245161 = r2245147 + r2245160;
        double r2245162 = r2245161 * r2245147;
        double r2245163 = b;
        double r2245164 = r2245162 + r2245163;
        double r2245165 = r2245164 * r2245147;
        double r2245166 = c;
        double r2245167 = r2245165 + r2245166;
        double r2245168 = r2245167 * r2245147;
        double r2245169 = i;
        double r2245170 = r2245168 + r2245169;
        double r2245171 = r2245159 / r2245170;
        return r2245171;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r2245172 = 1.0;
        double r2245173 = t;
        double r2245174 = y;
        double r2245175 = x;
        double r2245176 = r2245174 * r2245175;
        double r2245177 = z;
        double r2245178 = r2245176 + r2245177;
        double r2245179 = r2245178 * r2245174;
        double r2245180 = 27464.7644705;
        double r2245181 = r2245179 + r2245180;
        double r2245182 = r2245181 * r2245174;
        double r2245183 = 230661.510616;
        double r2245184 = r2245182 + r2245183;
        double r2245185 = r2245174 * r2245184;
        double r2245186 = r2245173 + r2245185;
        double r2245187 = r2245172 / r2245186;
        double r2245188 = i;
        double r2245189 = b;
        double r2245190 = a;
        double r2245191 = r2245174 + r2245190;
        double r2245192 = r2245191 * r2245174;
        double r2245193 = r2245189 + r2245192;
        double r2245194 = r2245193 * r2245174;
        double r2245195 = c;
        double r2245196 = r2245194 + r2245195;
        double r2245197 = r2245174 * r2245196;
        double r2245198 = r2245188 + r2245197;
        double r2245199 = r2245187 * r2245198;
        double r2245200 = r2245172 / r2245199;
        return r2245200;
}

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 28.8

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

  3. Applied *-un-lft-identity28.8

    \[\leadsto \frac{\color{blue}{1 \cdot \left(\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t\right)}}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\]

  4. Applied associate-/l*29.0

    \[\leadsto \color{blue}{\frac{1}{\frac{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}}}\]
  5. Using strategy rm

  6. Applied div-inv29.0

    \[\leadsto \frac{1}{\color{blue}{\left(\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i\right) \cdot \frac{1}{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}}}\]

  7. Final simplification29.0

    \[\leadsto \frac{1}{\frac{1}{t + y \cdot \left(\left(\left(y \cdot x + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right)} \cdot \left(i + y \cdot \left(\left(b + \left(y + a\right) \cdot y\right) \cdot y + c\right)\right)}\]

Reproduce

herbie shell --seed 2019134 
(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)))