Average Error: 29.2 → 29.3
Time: 8.7s
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 r69986 = x;
        double r69987 = y;
        double r69988 = r69986 * r69987;
        double r69989 = z;
        double r69990 = r69988 + r69989;
        double r69991 = r69990 * r69987;
        double r69992 = 27464.7644705;
        double r69993 = r69991 + r69992;
        double r69994 = r69993 * r69987;
        double r69995 = 230661.510616;
        double r69996 = r69994 + r69995;
        double r69997 = r69996 * r69987;
        double r69998 = t;
        double r69999 = r69997 + r69998;
        double r70000 = a;
        double r70001 = r69987 + r70000;
        double r70002 = r70001 * r69987;
        double r70003 = b;
        double r70004 = r70002 + r70003;
        double r70005 = r70004 * r69987;
        double r70006 = c;
        double r70007 = r70005 + r70006;
        double r70008 = r70007 * r69987;
        double r70009 = i;
        double r70010 = r70008 + r70009;
        double r70011 = r69999 / r70010;
        return r70011;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r70012 = x;
        double r70013 = y;
        double r70014 = r70012 * r70013;
        double r70015 = z;
        double r70016 = r70014 + r70015;
        double r70017 = r70016 * r70013;
        double r70018 = 27464.7644705;
        double r70019 = r70017 + r70018;
        double r70020 = r70019 * r70013;
        double r70021 = 230661.510616;
        double r70022 = r70020 + r70021;
        double r70023 = r70022 * r70013;
        double r70024 = t;
        double r70025 = r70023 + r70024;
        double r70026 = 1.0;
        double r70027 = a;
        double r70028 = r70013 + r70027;
        double r70029 = r70028 * r70013;
        double r70030 = b;
        double r70031 = r70029 + r70030;
        double r70032 = r70031 * r70013;
        double r70033 = c;
        double r70034 = r70032 + r70033;
        double r70035 = r70034 * r70013;
        double r70036 = i;
        double r70037 = r70035 + r70036;
        double r70038 = r70026 / r70037;
        double r70039 = r70025 * r70038;
        return r70039;
}

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 29.2

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

  3. Applied div-inv29.3

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

  4. Final simplification29.3

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

Reproduce

herbie shell --seed 2020064 
(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)))