Average Error: 28.8 → 28.9
Time: 2.2m
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 r755949 = x;
        double r755950 = y;
        double r755951 = r755949 * r755950;
        double r755952 = z;
        double r755953 = r755951 + r755952;
        double r755954 = r755953 * r755950;
        double r755955 = 27464.7644705;
        double r755956 = r755954 + r755955;
        double r755957 = r755956 * r755950;
        double r755958 = 230661.510616;
        double r755959 = r755957 + r755958;
        double r755960 = r755959 * r755950;
        double r755961 = t;
        double r755962 = r755960 + r755961;
        double r755963 = a;
        double r755964 = r755950 + r755963;
        double r755965 = r755964 * r755950;
        double r755966 = b;
        double r755967 = r755965 + r755966;
        double r755968 = r755967 * r755950;
        double r755969 = c;
        double r755970 = r755968 + r755969;
        double r755971 = r755970 * r755950;
        double r755972 = i;
        double r755973 = r755971 + r755972;
        double r755974 = r755962 / r755973;
        return r755974;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r755975 = x;
        double r755976 = y;
        double r755977 = r755975 * r755976;
        double r755978 = z;
        double r755979 = r755977 + r755978;
        double r755980 = r755979 * r755976;
        double r755981 = 27464.7644705;
        double r755982 = r755980 + r755981;
        double r755983 = r755982 * r755976;
        double r755984 = 230661.510616;
        double r755985 = r755983 + r755984;
        double r755986 = r755985 * r755976;
        double r755987 = t;
        double r755988 = r755986 + r755987;
        double r755989 = 1.0;
        double r755990 = a;
        double r755991 = r755976 + r755990;
        double r755992 = r755991 * r755976;
        double r755993 = b;
        double r755994 = r755992 + r755993;
        double r755995 = r755994 * r755976;
        double r755996 = c;
        double r755997 = r755995 + r755996;
        double r755998 = r755997 * r755976;
        double r755999 = i;
        double r756000 = r755998 + r755999;
        double r756001 = r755989 / r756000;
        double r756002 = r755988 * r756001;
        return r756002;
}

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 28.8

    \[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644704999984242022037506103515625\right) \cdot y + 230661.5106160000141244381666183471679688\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\]
  2. Using strategy rm

  3. Applied div-inv28.9

    \[\leadsto \color{blue}{\left(\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644704999984242022037506103515625\right) \cdot y + 230661.5106160000141244381666183471679688\right) \cdot y + t\right) \cdot \frac{1}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}}\]

  4. Final simplification28.9

    \[\leadsto \left(\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644704999984242022037506103515625\right) \cdot y + 230661.5106160000141244381666183471679688\right) \cdot y + t\right) \cdot \frac{1}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\]

Reproduce

herbie shell --seed 2019303 
(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) 27464.764470499998) y) 230661.510616000014) y) t) (+ (* (+ (* (+ (* (+ y a) y) b) y) c) y) i)))