Average Error: 29.0 → 28.2
Time: 10.2s
Precision: 64
\[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.764470499998\right) \cdot y + 230661.510616000014\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\]
↓
\[\begin{array}{l} \mathbf{if}\;\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.764470499998\right) \cdot y + 230661.510616000014\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \le 5.142889239312206 \cdot 10^{306}:\\ \;\;\;\;\left(\left(\left(\sqrt[3]{\left(x \cdot y + z\right) \cdot y + 27464.764470499998} \cdot \sqrt[3]{\left(x \cdot y + z\right) \cdot y + 27464.764470499998}\right) \cdot \left(\sqrt[3]{\left(x \cdot y + z\right) \cdot y + 27464.764470499998} \cdot y\right) + 230661.510616000014\right) \cdot y + t\right) \cdot \frac{1}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\\ \mathbf{else}:\\ \;\;\;\;0\\ \end{array}\]
\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 5.142889239312206 \cdot 10^{306}:\\
\;\;\;\;\left(\left(\left(\sqrt[3]{\left(x \cdot y + z\right) \cdot y + 27464.764470499998} \cdot \sqrt[3]{\left(x \cdot y + z\right) \cdot y + 27464.764470499998}\right) \cdot \left(\sqrt[3]{\left(x \cdot y + z\right) \cdot y + 27464.764470499998} \cdot y\right) + 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}\\

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

\end{array}
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r73207 = x;
        double r73208 = y;
        double r73209 = r73207 * r73208;
        double r73210 = z;
        double r73211 = r73209 + r73210;
        double r73212 = r73211 * r73208;
        double r73213 = 27464.7644705;
        double r73214 = r73212 + r73213;
        double r73215 = r73214 * r73208;
        double r73216 = 230661.510616;
        double r73217 = r73215 + r73216;
        double r73218 = r73217 * r73208;
        double r73219 = t;
        double r73220 = r73218 + r73219;
        double r73221 = a;
        double r73222 = r73208 + r73221;
        double r73223 = r73222 * r73208;
        double r73224 = b;
        double r73225 = r73223 + r73224;
        double r73226 = r73225 * r73208;
        double r73227 = c;
        double r73228 = r73226 + r73227;
        double r73229 = r73228 * r73208;
        double r73230 = i;
        double r73231 = r73229 + r73230;
        double r73232 = r73220 / r73231;
        return r73232;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r73233 = x;
        double r73234 = y;
        double r73235 = r73233 * r73234;
        double r73236 = z;
        double r73237 = r73235 + r73236;
        double r73238 = r73237 * r73234;
        double r73239 = 27464.7644705;
        double r73240 = r73238 + r73239;
        double r73241 = r73240 * r73234;
        double r73242 = 230661.510616;
        double r73243 = r73241 + r73242;
        double r73244 = r73243 * r73234;
        double r73245 = t;
        double r73246 = r73244 + r73245;
        double r73247 = a;
        double r73248 = r73234 + r73247;
        double r73249 = r73248 * r73234;
        double r73250 = b;
        double r73251 = r73249 + r73250;
        double r73252 = r73251 * r73234;
        double r73253 = c;
        double r73254 = r73252 + r73253;
        double r73255 = r73254 * r73234;
        double r73256 = i;
        double r73257 = r73255 + r73256;
        double r73258 = r73246 / r73257;
        double r73259 = 5.142889239312206e+306;
        bool r73260 = r73258 <= r73259;
        double r73261 = cbrt(r73240);
        double r73262 = r73261 * r73261;
        double r73263 = r73261 * r73234;
        double r73264 = r73262 * r73263;
        double r73265 = r73264 + r73242;
        double r73266 = r73265 * r73234;
        double r73267 = r73266 + r73245;
        double r73268 = 1.0;
        double r73269 = r73268 / r73257;
        double r73270 = r73267 * r73269;
        double r73271 = 0.0;
        double r73272 = r73260 ? r73270 : r73271;
        return r73272;
}

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)) < 5.142889239312206e+306

    1. Initial program 5.2

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

    3. Applied div-inv5.4

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

    5. Applied add-cube-cbrt5.5

      \[\leadsto \left(\left(\color{blue}{\left(\left(\sqrt[3]{\left(x \cdot y + z\right) \cdot y + 27464.764470499998} \cdot \sqrt[3]{\left(x \cdot y + z\right) \cdot y + 27464.764470499998}\right) \cdot \sqrt[3]{\left(x \cdot y + z\right) \cdot y + 27464.764470499998}\right)} \cdot y + 230661.510616000014\right) \cdot y + t\right) \cdot \frac{1}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\]

    6. Applied associate-*l*5.5

      \[\leadsto \left(\left(\color{blue}{\left(\sqrt[3]{\left(x \cdot y + z\right) \cdot y + 27464.764470499998} \cdot \sqrt[3]{\left(x \cdot y + z\right) \cdot y + 27464.764470499998}\right) \cdot \left(\sqrt[3]{\left(x \cdot y + z\right) \cdot y + 27464.764470499998} \cdot y\right)} + 230661.510616000014\right) \cdot y + t\right) \cdot \frac{1}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\]

    if 5.142889239312206e+306 < (/ (+ (* (+ (* (+ (* (+ (* x y) z) y) 27464.7644705) y) 230661.510616) y) t) (+ (* (+ (* (+ (* (+ y a) y) b) y) c) y) i))

    1. Initial program 64.0

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

    2. Taylor expanded around 0 61.8

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

  4. Final simplification28.2

    \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.764470499998\right) \cdot y + 230661.510616000014\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \le 5.142889239312206 \cdot 10^{306}:\\ \;\;\;\;\left(\left(\left(\sqrt[3]{\left(x \cdot y + z\right) \cdot y + 27464.764470499998} \cdot \sqrt[3]{\left(x \cdot y + z\right) \cdot y + 27464.764470499998}\right) \cdot \left(\sqrt[3]{\left(x \cdot y + z\right) \cdot y + 27464.764470499998} \cdot y\right) + 230661.510616000014\right) \cdot y + t\right) \cdot \frac{1}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\\ \mathbf{else}:\\ \;\;\;\;0\\ \end{array}\]

Reproduce

herbie shell --seed 2020036 
(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)))