Average Error: 28.9 → 29.1
Time: 10.5s
Precision: 64
\[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644704999984242022037506103515625\right) \cdot y + 230661.5106160000141244381666183471679688\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\]
↓
\[\frac{1}{\frac{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644704999984242022037506103515625\right) \cdot y + 230661.5106160000141244381666183471679688\right) \cdot y + t}}\]
\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}
↓
\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 + 27464.7644704999984242022037506103515625\right) \cdot y + 230661.5106160000141244381666183471679688\right) \cdot y + t}}
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r73968 = x;
        double r73969 = y;
        double r73970 = r73968 * r73969;
        double r73971 = z;
        double r73972 = r73970 + r73971;
        double r73973 = r73972 * r73969;
        double r73974 = 27464.7644705;
        double r73975 = r73973 + r73974;
        double r73976 = r73975 * r73969;
        double r73977 = 230661.510616;
        double r73978 = r73976 + r73977;
        double r73979 = r73978 * r73969;
        double r73980 = t;
        double r73981 = r73979 + r73980;
        double r73982 = a;
        double r73983 = r73969 + r73982;
        double r73984 = r73983 * r73969;
        double r73985 = b;
        double r73986 = r73984 + r73985;
        double r73987 = r73986 * r73969;
        double r73988 = c;
        double r73989 = r73987 + r73988;
        double r73990 = r73989 * r73969;
        double r73991 = i;
        double r73992 = r73990 + r73991;
        double r73993 = r73981 / r73992;
        return r73993;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r73994 = 1.0;
        double r73995 = y;
        double r73996 = a;
        double r73997 = r73995 + r73996;
        double r73998 = r73997 * r73995;
        double r73999 = b;
        double r74000 = r73998 + r73999;
        double r74001 = r74000 * r73995;
        double r74002 = c;
        double r74003 = r74001 + r74002;
        double r74004 = r74003 * r73995;
        double r74005 = i;
        double r74006 = r74004 + r74005;
        double r74007 = x;
        double r74008 = r74007 * r73995;
        double r74009 = z;
        double r74010 = r74008 + r74009;
        double r74011 = r74010 * r73995;
        double r74012 = 27464.7644705;
        double r74013 = r74011 + r74012;
        double r74014 = r74013 * r73995;
        double r74015 = 230661.510616;
        double r74016 = r74014 + r74015;
        double r74017 = r74016 * r73995;
        double r74018 = t;
        double r74019 = r74017 + r74018;
        double r74020 = r74006 / r74019;
        double r74021 = r73994 / r74020;
        return r74021;
}

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

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

  3. Applied clear-num29.1

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

  4. Final simplification29.1

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

Reproduce

herbie shell --seed 2019346 +o rules:numerics
(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)))