Average Error: 28.7 → 28.8
Time: 29.4s
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 r71089 = x;
        double r71090 = y;
        double r71091 = r71089 * r71090;
        double r71092 = z;
        double r71093 = r71091 + r71092;
        double r71094 = r71093 * r71090;
        double r71095 = 27464.7644705;
        double r71096 = r71094 + r71095;
        double r71097 = r71096 * r71090;
        double r71098 = 230661.510616;
        double r71099 = r71097 + r71098;
        double r71100 = r71099 * r71090;
        double r71101 = t;
        double r71102 = r71100 + r71101;
        double r71103 = a;
        double r71104 = r71090 + r71103;
        double r71105 = r71104 * r71090;
        double r71106 = b;
        double r71107 = r71105 + r71106;
        double r71108 = r71107 * r71090;
        double r71109 = c;
        double r71110 = r71108 + r71109;
        double r71111 = r71110 * r71090;
        double r71112 = i;
        double r71113 = r71111 + r71112;
        double r71114 = r71102 / r71113;
        return r71114;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r71115 = x;
        double r71116 = y;
        double r71117 = r71115 * r71116;
        double r71118 = z;
        double r71119 = r71117 + r71118;
        double r71120 = r71119 * r71116;
        double r71121 = 27464.7644705;
        double r71122 = r71120 + r71121;
        double r71123 = r71122 * r71116;
        double r71124 = 230661.510616;
        double r71125 = r71123 + r71124;
        double r71126 = r71125 * r71116;
        double r71127 = t;
        double r71128 = r71126 + r71127;
        double r71129 = 1.0;
        double r71130 = a;
        double r71131 = r71116 + r71130;
        double r71132 = r71131 * r71116;
        double r71133 = b;
        double r71134 = r71132 + r71133;
        double r71135 = r71134 * r71116;
        double r71136 = c;
        double r71137 = r71135 + r71136;
        double r71138 = r71137 * r71116;
        double r71139 = i;
        double r71140 = r71138 + r71139;
        double r71141 = r71129 / r71140;
        double r71142 = r71128 * r71141;
        return r71142;
}

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)))