Average Error: 29.1 → 28.7
Time: 8.5s
Precision: 64
\[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.764470499998\right) \cdot y + 230661.510616000014\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\]
↓
\[\begin{array}{l} \mathbf{if}\;y \le -1.69974851560525037 \cdot 10^{72}:\\ \;\;\;\;0\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.764470499998\right) \cdot y + 230661.510616000014\right) \cdot y + t}{\left(\left(\sqrt[3]{\left(y + a\right) \cdot y + b} \cdot \sqrt[3]{\left(y + a\right) \cdot y + b}\right) \cdot \left(\sqrt[3]{\left(y + a\right) \cdot y + b} \cdot y\right) + c\right) \cdot y + i}\\ \end{array}\]
\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}\;y \le -1.69974851560525037 \cdot 10^{72}:\\
\;\;\;\;0\\

\mathbf{else}:\\
\;\;\;\;\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.764470499998\right) \cdot y + 230661.510616000014\right) \cdot y + t}{\left(\left(\sqrt[3]{\left(y + a\right) \cdot y + b} \cdot \sqrt[3]{\left(y + a\right) \cdot y + b}\right) \cdot \left(\sqrt[3]{\left(y + a\right) \cdot y + b} \cdot y\right) + c\right) \cdot y + i}\\

\end{array}
double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	return (((((((((x * y) + z) * y) + 27464.7644705) * y) + 230661.510616) * y) + t) / (((((((y + a) * y) + b) * y) + c) * y) + i));
}
↓
double code(double x, double y, double z, double t, double a, double b, double c, double i) {
	double temp;
	if ((y <= -1.6997485156052504e+72)) {
		temp = 0.0;
	} else {
		temp = (((((((((x * y) + z) * y) + 27464.7644705) * y) + 230661.510616) * y) + t) / (((((cbrt((((y + a) * y) + b)) * cbrt((((y + a) * y) + b))) * (cbrt((((y + a) * y) + b)) * y)) + c) * y) + i));
	}
	return temp;
}

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 y < -1.6997485156052504e+72

    1. Initial program 63.4

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

    3. Applied add-cube-cbrt63.4

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

    4. Applied associate-*l*63.4

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

    5. Taylor expanded around 0 61.4

      \[\leadsto \color{blue}{0}\]

    if -1.6997485156052504e+72 < y

    1. Initial program 20.4

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

    3. Applied add-cube-cbrt20.6

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

    4. Applied associate-*l*20.6

      \[\leadsto \frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.764470499998\right) \cdot y + 230661.510616000014\right) \cdot y + t}{\left(\color{blue}{\left(\sqrt[3]{\left(y + a\right) \cdot y + b} \cdot \sqrt[3]{\left(y + a\right) \cdot y + b}\right) \cdot \left(\sqrt[3]{\left(y + a\right) \cdot y + b} \cdot y\right)} + c\right) \cdot y + i}\]
  3. Recombined 2 regimes into one program.

  4. Final simplification28.7

    \[\leadsto \begin{array}{l} \mathbf{if}\;y \le -1.69974851560525037 \cdot 10^{72}:\\ \;\;\;\;0\\ \mathbf{else}:\\ \;\;\;\;\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.764470499998\right) \cdot y + 230661.510616000014\right) \cdot y + t}{\left(\left(\sqrt[3]{\left(y + a\right) \cdot y + b} \cdot \sqrt[3]{\left(y + a\right) \cdot y + b}\right) \cdot \left(\sqrt[3]{\left(y + a\right) \cdot y + b} \cdot y\right) + c\right) \cdot y + i}\\ \end{array}\]

Reproduce

herbie shell --seed 2020049 +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)))