Average Error: 29.0 → 29.1
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 r96018 = x;
        double r96019 = y;
        double r96020 = r96018 * r96019;
        double r96021 = z;
        double r96022 = r96020 + r96021;
        double r96023 = r96022 * r96019;
        double r96024 = 27464.7644705;
        double r96025 = r96023 + r96024;
        double r96026 = r96025 * r96019;
        double r96027 = 230661.510616;
        double r96028 = r96026 + r96027;
        double r96029 = r96028 * r96019;
        double r96030 = t;
        double r96031 = r96029 + r96030;
        double r96032 = a;
        double r96033 = r96019 + r96032;
        double r96034 = r96033 * r96019;
        double r96035 = b;
        double r96036 = r96034 + r96035;
        double r96037 = r96036 * r96019;
        double r96038 = c;
        double r96039 = r96037 + r96038;
        double r96040 = r96039 * r96019;
        double r96041 = i;
        double r96042 = r96040 + r96041;
        double r96043 = r96031 / r96042;
        return r96043;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r96044 = x;
        double r96045 = y;
        double r96046 = r96044 * r96045;
        double r96047 = z;
        double r96048 = r96046 + r96047;
        double r96049 = r96048 * r96045;
        double r96050 = 27464.7644705;
        double r96051 = r96049 + r96050;
        double r96052 = r96051 * r96045;
        double r96053 = 230661.510616;
        double r96054 = r96052 + r96053;
        double r96055 = r96054 * r96045;
        double r96056 = t;
        double r96057 = r96055 + r96056;
        double r96058 = 1.0;
        double r96059 = a;
        double r96060 = r96045 + r96059;
        double r96061 = r96060 * r96045;
        double r96062 = b;
        double r96063 = r96061 + r96062;
        double r96064 = r96063 * r96045;
        double r96065 = c;
        double r96066 = r96064 + r96065;
        double r96067 = r96066 * r96045;
        double r96068 = i;
        double r96069 = r96067 + r96068;
        double r96070 = r96058 / r96069;
        double r96071 = r96057 * r96070;
        return r96071;
}

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 29.0

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

  3. Applied div-inv29.1

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

  4. Final simplification29.1

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

Reproduce

herbie shell --seed 2020100 
(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)))