Average Error: 29.1 → 29.2
Time: 11.8s
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 r69093 = x;
        double r69094 = y;
        double r69095 = r69093 * r69094;
        double r69096 = z;
        double r69097 = r69095 + r69096;
        double r69098 = r69097 * r69094;
        double r69099 = 27464.7644705;
        double r69100 = r69098 + r69099;
        double r69101 = r69100 * r69094;
        double r69102 = 230661.510616;
        double r69103 = r69101 + r69102;
        double r69104 = r69103 * r69094;
        double r69105 = t;
        double r69106 = r69104 + r69105;
        double r69107 = a;
        double r69108 = r69094 + r69107;
        double r69109 = r69108 * r69094;
        double r69110 = b;
        double r69111 = r69109 + r69110;
        double r69112 = r69111 * r69094;
        double r69113 = c;
        double r69114 = r69112 + r69113;
        double r69115 = r69114 * r69094;
        double r69116 = i;
        double r69117 = r69115 + r69116;
        double r69118 = r69106 / r69117;
        return r69118;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r69119 = x;
        double r69120 = y;
        double r69121 = r69119 * r69120;
        double r69122 = z;
        double r69123 = r69121 + r69122;
        double r69124 = r69123 * r69120;
        double r69125 = 27464.7644705;
        double r69126 = r69124 + r69125;
        double r69127 = r69126 * r69120;
        double r69128 = 230661.510616;
        double r69129 = r69127 + r69128;
        double r69130 = r69129 * r69120;
        double r69131 = t;
        double r69132 = r69130 + r69131;
        double r69133 = 1.0;
        double r69134 = a;
        double r69135 = r69120 + r69134;
        double r69136 = r69135 * r69120;
        double r69137 = b;
        double r69138 = r69136 + r69137;
        double r69139 = r69138 * r69120;
        double r69140 = c;
        double r69141 = r69139 + r69140;
        double r69142 = r69141 * r69120;
        double r69143 = i;
        double r69144 = r69142 + r69143;
        double r69145 = r69133 / r69144;
        double r69146 = r69132 * r69145;
        return r69146;
}

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 29.1

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

  3. Applied div-inv29.2

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

  4. Final simplification29.2

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

Reproduce

herbie shell --seed 2020001 
(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)))