Average Error: 29.1 → 29.5
Time: 8.4s
Precision: 64
\[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.764470499998\right) \cdot y + 230661.510616000014\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\]
↓
\[\frac{1}{\left(\left(i + y \cdot c\right) + y \cdot {\left(\sqrt[3]{\left(\left(y + a\right) \cdot y + b\right) \cdot y}\right)}^{3}\right) \cdot \frac{1}{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.764470499998\right) \cdot y + 230661.510616000014\right) \cdot y + t}}\]
\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}
↓
\frac{1}{\left(\left(i + y \cdot c\right) + y \cdot {\left(\sqrt[3]{\left(\left(y + a\right) \cdot y + b\right) \cdot y}\right)}^{3}\right) \cdot \frac{1}{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.764470499998\right) \cdot y + 230661.510616000014\right) \cdot y + t}}
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r68233 = x;
        double r68234 = y;
        double r68235 = r68233 * r68234;
        double r68236 = z;
        double r68237 = r68235 + r68236;
        double r68238 = r68237 * r68234;
        double r68239 = 27464.7644705;
        double r68240 = r68238 + r68239;
        double r68241 = r68240 * r68234;
        double r68242 = 230661.510616;
        double r68243 = r68241 + r68242;
        double r68244 = r68243 * r68234;
        double r68245 = t;
        double r68246 = r68244 + r68245;
        double r68247 = a;
        double r68248 = r68234 + r68247;
        double r68249 = r68248 * r68234;
        double r68250 = b;
        double r68251 = r68249 + r68250;
        double r68252 = r68251 * r68234;
        double r68253 = c;
        double r68254 = r68252 + r68253;
        double r68255 = r68254 * r68234;
        double r68256 = i;
        double r68257 = r68255 + r68256;
        double r68258 = r68246 / r68257;
        return r68258;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r68259 = 1.0;
        double r68260 = i;
        double r68261 = y;
        double r68262 = c;
        double r68263 = r68261 * r68262;
        double r68264 = r68260 + r68263;
        double r68265 = a;
        double r68266 = r68261 + r68265;
        double r68267 = r68266 * r68261;
        double r68268 = b;
        double r68269 = r68267 + r68268;
        double r68270 = r68269 * r68261;
        double r68271 = cbrt(r68270);
        double r68272 = 3.0;
        double r68273 = pow(r68271, r68272);
        double r68274 = r68261 * r68273;
        double r68275 = r68264 + r68274;
        double r68276 = x;
        double r68277 = r68276 * r68261;
        double r68278 = z;
        double r68279 = r68277 + r68278;
        double r68280 = r68279 * r68261;
        double r68281 = 27464.7644705;
        double r68282 = r68280 + r68281;
        double r68283 = r68282 * r68261;
        double r68284 = 230661.510616;
        double r68285 = r68283 + r68284;
        double r68286 = r68285 * r68261;
        double r68287 = t;
        double r68288 = r68286 + r68287;
        double r68289 = r68259 / r68288;
        double r68290 = r68275 * r68289;
        double r68291 = r68259 / r68290;
        return r68291;
}

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 29.1

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

  3. Applied add-cube-cbrt29.2

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

  5. Applied clear-num29.4

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

  6. Simplified29.5

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

  7. Final simplification29.5

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

Reproduce

herbie shell --seed 2020083 
(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)))