Average Error: 27.7 → 27.8
Time: 22.5s
Precision: 64
\[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\]
↓
\[\frac{1}{i + y \cdot \left(\left(b + \left(y + a\right) \cdot y\right) \cdot y + c\right)} \cdot \left(t + y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + \left(y \cdot x + z\right) \cdot y\right)\right)\right)\]
\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}{i + y \cdot \left(\left(b + \left(y + a\right) \cdot y\right) \cdot y + c\right)} \cdot \left(t + y \cdot \left(230661.510616 + y \cdot \left(27464.7644705 + \left(y \cdot x + z\right) \cdot y\right)\right)\right)
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r1606066 = x;
        double r1606067 = y;
        double r1606068 = r1606066 * r1606067;
        double r1606069 = z;
        double r1606070 = r1606068 + r1606069;
        double r1606071 = r1606070 * r1606067;
        double r1606072 = 27464.7644705;
        double r1606073 = r1606071 + r1606072;
        double r1606074 = r1606073 * r1606067;
        double r1606075 = 230661.510616;
        double r1606076 = r1606074 + r1606075;
        double r1606077 = r1606076 * r1606067;
        double r1606078 = t;
        double r1606079 = r1606077 + r1606078;
        double r1606080 = a;
        double r1606081 = r1606067 + r1606080;
        double r1606082 = r1606081 * r1606067;
        double r1606083 = b;
        double r1606084 = r1606082 + r1606083;
        double r1606085 = r1606084 * r1606067;
        double r1606086 = c;
        double r1606087 = r1606085 + r1606086;
        double r1606088 = r1606087 * r1606067;
        double r1606089 = i;
        double r1606090 = r1606088 + r1606089;
        double r1606091 = r1606079 / r1606090;
        return r1606091;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r1606092 = 1.0;
        double r1606093 = i;
        double r1606094 = y;
        double r1606095 = b;
        double r1606096 = a;
        double r1606097 = r1606094 + r1606096;
        double r1606098 = r1606097 * r1606094;
        double r1606099 = r1606095 + r1606098;
        double r1606100 = r1606099 * r1606094;
        double r1606101 = c;
        double r1606102 = r1606100 + r1606101;
        double r1606103 = r1606094 * r1606102;
        double r1606104 = r1606093 + r1606103;
        double r1606105 = r1606092 / r1606104;
        double r1606106 = t;
        double r1606107 = 230661.510616;
        double r1606108 = 27464.7644705;
        double r1606109 = x;
        double r1606110 = r1606094 * r1606109;
        double r1606111 = z;
        double r1606112 = r1606110 + r1606111;
        double r1606113 = r1606112 * r1606094;
        double r1606114 = r1606108 + r1606113;
        double r1606115 = r1606094 * r1606114;
        double r1606116 = r1606107 + r1606115;
        double r1606117 = r1606094 * r1606116;
        double r1606118 = r1606106 + r1606117;
        double r1606119 = r1606105 * r1606118;
        return r1606119;
}

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 27.7

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

  3. Applied clear-num28.0

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

  5. Applied associate-/r/27.8

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

  6. Final simplification27.8

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

Reproduce

herbie shell --seed 2019156 
(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)))