Average Error: 28.9 → 28.9
Time: 8.9s
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 r54039 = x;
        double r54040 = y;
        double r54041 = r54039 * r54040;
        double r54042 = z;
        double r54043 = r54041 + r54042;
        double r54044 = r54043 * r54040;
        double r54045 = 27464.7644705;
        double r54046 = r54044 + r54045;
        double r54047 = r54046 * r54040;
        double r54048 = 230661.510616;
        double r54049 = r54047 + r54048;
        double r54050 = r54049 * r54040;
        double r54051 = t;
        double r54052 = r54050 + r54051;
        double r54053 = a;
        double r54054 = r54040 + r54053;
        double r54055 = r54054 * r54040;
        double r54056 = b;
        double r54057 = r54055 + r54056;
        double r54058 = r54057 * r54040;
        double r54059 = c;
        double r54060 = r54058 + r54059;
        double r54061 = r54060 * r54040;
        double r54062 = i;
        double r54063 = r54061 + r54062;
        double r54064 = r54052 / r54063;
        return r54064;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r54065 = x;
        double r54066 = y;
        double r54067 = r54065 * r54066;
        double r54068 = z;
        double r54069 = r54067 + r54068;
        double r54070 = r54069 * r54066;
        double r54071 = 27464.7644705;
        double r54072 = r54070 + r54071;
        double r54073 = r54072 * r54066;
        double r54074 = 230661.510616;
        double r54075 = r54073 + r54074;
        double r54076 = r54075 * r54066;
        double r54077 = t;
        double r54078 = r54076 + r54077;
        double r54079 = 1.0;
        double r54080 = a;
        double r54081 = r54066 + r54080;
        double r54082 = r54081 * r54066;
        double r54083 = b;
        double r54084 = r54082 + r54083;
        double r54085 = r54084 * r54066;
        double r54086 = c;
        double r54087 = r54085 + r54086;
        double r54088 = r54087 * r54066;
        double r54089 = i;
        double r54090 = r54088 + r54089;
        double r54091 = r54079 / r54090;
        double r54092 = r54078 * r54091;
        return r54092;
}

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 28.9

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

  3. Applied div-inv28.9

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

  4. Final simplification28.9

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

Reproduce

herbie shell --seed 2020021 
(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)))