Average Error: 28.5 → 28.6
Time: 8.4s
Precision: 64
\[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.764470499998\right) \cdot y + 230661.510616000014\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\]
↓
\[\left(\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.764470499998\right) \cdot y + 230661.510616000014\right) \cdot y + t\right) \cdot \frac{1}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\]
\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.764470499998\right) \cdot y + 230661.510616000014\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 + 27464.764470499998\right) \cdot y + 230661.510616000014\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 r66064 = x;
        double r66065 = y;
        double r66066 = r66064 * r66065;
        double r66067 = z;
        double r66068 = r66066 + r66067;
        double r66069 = r66068 * r66065;
        double r66070 = 27464.7644705;
        double r66071 = r66069 + r66070;
        double r66072 = r66071 * r66065;
        double r66073 = 230661.510616;
        double r66074 = r66072 + r66073;
        double r66075 = r66074 * r66065;
        double r66076 = t;
        double r66077 = r66075 + r66076;
        double r66078 = a;
        double r66079 = r66065 + r66078;
        double r66080 = r66079 * r66065;
        double r66081 = b;
        double r66082 = r66080 + r66081;
        double r66083 = r66082 * r66065;
        double r66084 = c;
        double r66085 = r66083 + r66084;
        double r66086 = r66085 * r66065;
        double r66087 = i;
        double r66088 = r66086 + r66087;
        double r66089 = r66077 / r66088;
        return r66089;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r66090 = x;
        double r66091 = y;
        double r66092 = r66090 * r66091;
        double r66093 = z;
        double r66094 = r66092 + r66093;
        double r66095 = r66094 * r66091;
        double r66096 = 27464.7644705;
        double r66097 = r66095 + r66096;
        double r66098 = r66097 * r66091;
        double r66099 = 230661.510616;
        double r66100 = r66098 + r66099;
        double r66101 = r66100 * r66091;
        double r66102 = t;
        double r66103 = r66101 + r66102;
        double r66104 = 1.0;
        double r66105 = a;
        double r66106 = r66091 + r66105;
        double r66107 = r66106 * r66091;
        double r66108 = b;
        double r66109 = r66107 + r66108;
        double r66110 = r66109 * r66091;
        double r66111 = c;
        double r66112 = r66110 + r66111;
        double r66113 = r66112 * r66091;
        double r66114 = i;
        double r66115 = r66113 + r66114;
        double r66116 = r66104 / r66115;
        double r66117 = r66103 * r66116;
        return r66117;
}

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 28.5

    \[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.764470499998\right) \cdot y + 230661.510616000014\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\]
  2. Using strategy rm

  3. Applied div-inv28.6

    \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.764470499998\right) \cdot y + 230661.510616000014\right) \cdot y + t\right) \cdot \frac{1}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}}\]

  4. Final simplification28.6

    \[\leadsto \left(\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.764470499998\right) \cdot y + 230661.510616000014\right) \cdot y + t\right) \cdot \frac{1}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\]

Reproduce

herbie shell --seed 2020039 
(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)))