Average Error: 29.2 → 28.5
Time: 9.4s
Precision: 64
\[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.764470499998\right) \cdot y + 230661.510616000014\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\]
↓
\[\begin{array}{l} \mathbf{if}\;\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.764470499998\right) \cdot y + 230661.510616000014\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \le 2.9235959509009306 \cdot 10^{289}:\\ \;\;\;\;\frac{\left(\left(\left(\sqrt[3]{\left(x \cdot y + z\right) \cdot y} \cdot \sqrt[3]{\left(x \cdot y + z\right) \cdot y}\right) \cdot \sqrt[3]{\left(x \cdot y + z\right) \cdot y} + 27464.764470499998\right) \cdot y + 230661.510616000014\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\\ \mathbf{else}:\\ \;\;\;\;0\\ \end{array}\]
\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}
↓
\begin{array}{l}
\mathbf{if}\;\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} \le 2.9235959509009306 \cdot 10^{289}:\\
\;\;\;\;\frac{\left(\left(\left(\sqrt[3]{\left(x \cdot y + z\right) \cdot y} \cdot \sqrt[3]{\left(x \cdot y + z\right) \cdot y}\right) \cdot \sqrt[3]{\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}\\

\mathbf{else}:\\
\;\;\;\;0\\

\end{array}
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r69975 = x;
        double r69976 = y;
        double r69977 = r69975 * r69976;
        double r69978 = z;
        double r69979 = r69977 + r69978;
        double r69980 = r69979 * r69976;
        double r69981 = 27464.7644705;
        double r69982 = r69980 + r69981;
        double r69983 = r69982 * r69976;
        double r69984 = 230661.510616;
        double r69985 = r69983 + r69984;
        double r69986 = r69985 * r69976;
        double r69987 = t;
        double r69988 = r69986 + r69987;
        double r69989 = a;
        double r69990 = r69976 + r69989;
        double r69991 = r69990 * r69976;
        double r69992 = b;
        double r69993 = r69991 + r69992;
        double r69994 = r69993 * r69976;
        double r69995 = c;
        double r69996 = r69994 + r69995;
        double r69997 = r69996 * r69976;
        double r69998 = i;
        double r69999 = r69997 + r69998;
        double r70000 = r69988 / r69999;
        return r70000;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r70001 = x;
        double r70002 = y;
        double r70003 = r70001 * r70002;
        double r70004 = z;
        double r70005 = r70003 + r70004;
        double r70006 = r70005 * r70002;
        double r70007 = 27464.7644705;
        double r70008 = r70006 + r70007;
        double r70009 = r70008 * r70002;
        double r70010 = 230661.510616;
        double r70011 = r70009 + r70010;
        double r70012 = r70011 * r70002;
        double r70013 = t;
        double r70014 = r70012 + r70013;
        double r70015 = a;
        double r70016 = r70002 + r70015;
        double r70017 = r70016 * r70002;
        double r70018 = b;
        double r70019 = r70017 + r70018;
        double r70020 = r70019 * r70002;
        double r70021 = c;
        double r70022 = r70020 + r70021;
        double r70023 = r70022 * r70002;
        double r70024 = i;
        double r70025 = r70023 + r70024;
        double r70026 = r70014 / r70025;
        double r70027 = 2.9235959509009306e+289;
        bool r70028 = r70026 <= r70027;
        double r70029 = cbrt(r70006);
        double r70030 = r70029 * r70029;
        double r70031 = r70030 * r70029;
        double r70032 = r70031 + r70007;
        double r70033 = r70032 * r70002;
        double r70034 = r70033 + r70010;
        double r70035 = r70034 * r70002;
        double r70036 = r70035 + r70013;
        double r70037 = r70036 / r70025;
        double r70038 = 0.0;
        double r70039 = r70028 ? r70037 : 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. Split input into 2 regimes

  2. if (/ (+ (* (+ (* (+ (* (+ (* x y) z) y) 27464.7644705) y) 230661.510616) y) t) (+ (* (+ (* (+ (* (+ y a) y) b) y) c) y) i)) < 2.9235959509009306e+289

    1. Initial program 5.6

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

    3. Applied add-cube-cbrt5.7

      \[\leadsto \frac{\left(\left(\color{blue}{\left(\sqrt[3]{\left(x \cdot y + z\right) \cdot y} \cdot \sqrt[3]{\left(x \cdot y + z\right) \cdot y}\right) \cdot \sqrt[3]{\left(x \cdot y + z\right) \cdot y}} + 27464.764470499998\right) \cdot y + 230661.510616000014\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\]

    if 2.9235959509009306e+289 < (/ (+ (* (+ (* (+ (* (+ (* x y) z) y) 27464.7644705) y) 230661.510616) y) t) (+ (* (+ (* (+ (* (+ y a) y) b) y) c) y) i))

    1. Initial program 63.7

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

    2. Taylor expanded around 0 61.7

      \[\leadsto \color{blue}{0}\]
  3. Recombined 2 regimes into one program.

  4. Final simplification28.5

    \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.764470499998\right) \cdot y + 230661.510616000014\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \le 2.9235959509009306 \cdot 10^{289}:\\ \;\;\;\;\frac{\left(\left(\left(\sqrt[3]{\left(x \cdot y + z\right) \cdot y} \cdot \sqrt[3]{\left(x \cdot y + z\right) \cdot y}\right) \cdot \sqrt[3]{\left(x \cdot y + z\right) \cdot y} + 27464.764470499998\right) \cdot y + 230661.510616000014\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\\ \mathbf{else}:\\ \;\;\;\;0\\ \end{array}\]

Reproduce

herbie shell --seed 2020081 +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)))