Average Error: 29.2 → 29.3
Time: 22.8s
Precision: 64
\[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.764470499998\right) \cdot y + 230661.510616000014\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\]
↓
\[\frac{\left(\left(\sqrt[3]{\left(\left(x \cdot y + z\right) \cdot y + 27464.764470499998\right) \cdot y} \cdot \sqrt[3]{\left(\left(x \cdot y + z\right) \cdot y + 27464.764470499998\right) \cdot y}\right) \cdot \sqrt[3]{\left(\left(x \cdot y + z\right) \cdot y + 27464.764470499998\right) \cdot y} + 230661.510616000014\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\]
\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{\left(\left(\sqrt[3]{\left(\left(x \cdot y + z\right) \cdot y + 27464.764470499998\right) \cdot y} \cdot \sqrt[3]{\left(\left(x \cdot y + z\right) \cdot y + 27464.764470499998\right) \cdot y}\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}
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r237 = x;
        double r238 = y;
        double r239 = r237 * r238;
        double r240 = z;
        double r241 = r239 + r240;
        double r242 = r241 * r238;
        double r243 = 27464.7644705;
        double r244 = r242 + r243;
        double r245 = r244 * r238;
        double r246 = 230661.510616;
        double r247 = r245 + r246;
        double r248 = r247 * r238;
        double r249 = t;
        double r250 = r248 + r249;
        double r251 = a;
        double r252 = r238 + r251;
        double r253 = r252 * r238;
        double r254 = b;
        double r255 = r253 + r254;
        double r256 = r255 * r238;
        double r257 = c;
        double r258 = r256 + r257;
        double r259 = r258 * r238;
        double r260 = i;
        double r261 = r259 + r260;
        double r262 = r250 / r261;
        return r262;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r263 = x;
        double r264 = y;
        double r265 = r263 * r264;
        double r266 = z;
        double r267 = r265 + r266;
        double r268 = r267 * r264;
        double r269 = 27464.7644705;
        double r270 = r268 + r269;
        double r271 = r270 * r264;
        double r272 = cbrt(r271);
        double r273 = r272 * r272;
        double r274 = r273 * r272;
        double r275 = 230661.510616;
        double r276 = r274 + r275;
        double r277 = r276 * r264;
        double r278 = t;
        double r279 = r277 + r278;
        double r280 = a;
        double r281 = r264 + r280;
        double r282 = r281 * r264;
        double r283 = b;
        double r284 = r282 + r283;
        double r285 = r284 * r264;
        double r286 = c;
        double r287 = r285 + r286;
        double r288 = r287 * r264;
        double r289 = i;
        double r290 = r288 + r289;
        double r291 = r279 / r290;
        return r291;
}

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 add-cube-cbrt29.3

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

  4. Final simplification29.3

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

Reproduce

herbie shell --seed 2020025 
(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)))