Average Error: 28.7 → 28.8
Time: 30.9s
Precision: 64
\[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644704999984242022037506103515625\right) \cdot y + 230661.5106160000141244381666183471679688\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\]
↓
\[\left(\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644704999984242022037506103515625\right) \cdot y + 230661.5106160000141244381666183471679688\right) \cdot y + t\right) \cdot \frac{1}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\]
\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644704999984242022037506103515625\right) \cdot y + 230661.5106160000141244381666183471679688\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}
↓
\left(\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644704999984242022037506103515625\right) \cdot y + 230661.5106160000141244381666183471679688\right) \cdot y + t\right) \cdot \frac{1}{\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 r59097 = x;
        double r59098 = y;
        double r59099 = r59097 * r59098;
        double r59100 = z;
        double r59101 = r59099 + r59100;
        double r59102 = r59101 * r59098;
        double r59103 = 27464.7644705;
        double r59104 = r59102 + r59103;
        double r59105 = r59104 * r59098;
        double r59106 = 230661.510616;
        double r59107 = r59105 + r59106;
        double r59108 = r59107 * r59098;
        double r59109 = t;
        double r59110 = r59108 + r59109;
        double r59111 = a;
        double r59112 = r59098 + r59111;
        double r59113 = r59112 * r59098;
        double r59114 = b;
        double r59115 = r59113 + r59114;
        double r59116 = r59115 * r59098;
        double r59117 = c;
        double r59118 = r59116 + r59117;
        double r59119 = r59118 * r59098;
        double r59120 = i;
        double r59121 = r59119 + r59120;
        double r59122 = r59110 / r59121;
        return r59122;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r59123 = x;
        double r59124 = y;
        double r59125 = r59123 * r59124;
        double r59126 = z;
        double r59127 = r59125 + r59126;
        double r59128 = r59127 * r59124;
        double r59129 = 27464.7644705;
        double r59130 = r59128 + r59129;
        double r59131 = r59130 * r59124;
        double r59132 = 230661.510616;
        double r59133 = r59131 + r59132;
        double r59134 = r59133 * r59124;
        double r59135 = t;
        double r59136 = r59134 + r59135;
        double r59137 = 1.0;
        double r59138 = a;
        double r59139 = r59124 + r59138;
        double r59140 = r59139 * r59124;
        double r59141 = b;
        double r59142 = r59140 + r59141;
        double r59143 = r59142 * r59124;
        double r59144 = c;
        double r59145 = r59143 + r59144;
        double r59146 = r59145 * r59124;
        double r59147 = i;
        double r59148 = r59146 + r59147;
        double r59149 = r59137 / r59148;
        double r59150 = r59136 * r59149;
        return r59150;
}

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 28.7

    \[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644704999984242022037506103515625\right) \cdot y + 230661.5106160000141244381666183471679688\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\]
  2. Using strategy rm

  3. Applied div-inv28.8

    \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644704999984242022037506103515625\right) \cdot y + 230661.5106160000141244381666183471679688\right) \cdot y + t\right) \cdot \frac{1}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}}\]

  4. Final simplification28.8

    \[\leadsto \left(\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644704999984242022037506103515625\right) \cdot y + 230661.5106160000141244381666183471679688\right) \cdot y + t\right) \cdot \frac{1}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\]

Reproduce

herbie shell --seed 2019323 
(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)))