Average Error: 29.0 → 29.1
Time: 8.6s
Precision: 64
\[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.764470499998\right) \cdot y + 230661.510616000014\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\]
↓
\[\left(\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.764470499998\right) \cdot y + 230661.510616000014\right) \cdot y + t\right) \cdot \frac{1}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\]
\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}
↓
\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}
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r59260 = x;
        double r59261 = y;
        double r59262 = r59260 * r59261;
        double r59263 = z;
        double r59264 = r59262 + r59263;
        double r59265 = r59264 * r59261;
        double r59266 = 27464.7644705;
        double r59267 = r59265 + r59266;
        double r59268 = r59267 * r59261;
        double r59269 = 230661.510616;
        double r59270 = r59268 + r59269;
        double r59271 = r59270 * r59261;
        double r59272 = t;
        double r59273 = r59271 + r59272;
        double r59274 = a;
        double r59275 = r59261 + r59274;
        double r59276 = r59275 * r59261;
        double r59277 = b;
        double r59278 = r59276 + r59277;
        double r59279 = r59278 * r59261;
        double r59280 = c;
        double r59281 = r59279 + r59280;
        double r59282 = r59281 * r59261;
        double r59283 = i;
        double r59284 = r59282 + r59283;
        double r59285 = r59273 / r59284;
        return r59285;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r59286 = x;
        double r59287 = y;
        double r59288 = r59286 * r59287;
        double r59289 = z;
        double r59290 = r59288 + r59289;
        double r59291 = r59290 * r59287;
        double r59292 = 27464.7644705;
        double r59293 = r59291 + r59292;
        double r59294 = r59293 * r59287;
        double r59295 = 230661.510616;
        double r59296 = r59294 + r59295;
        double r59297 = r59296 * r59287;
        double r59298 = t;
        double r59299 = r59297 + r59298;
        double r59300 = 1.0;
        double r59301 = a;
        double r59302 = r59287 + r59301;
        double r59303 = r59302 * r59287;
        double r59304 = b;
        double r59305 = r59303 + r59304;
        double r59306 = r59305 * r59287;
        double r59307 = c;
        double r59308 = r59306 + r59307;
        double r59309 = r59308 * r59287;
        double r59310 = i;
        double r59311 = r59309 + r59310;
        double r59312 = r59300 / r59311;
        double r59313 = r59299 * r59312;
        return r59313;
}

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 29.0

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

  3. Applied div-inv29.1

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

  4. Final simplification29.1

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

Reproduce

herbie shell --seed 2020100 
(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)))