Average Error: 29.0 → 29.0
Time: 8.3s
Precision: 64
\[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.764470499998\right) \cdot y + 230661.510616000014\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\]
↓
\[\left(\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.764470499998\right) \cdot y + 230661.510616000014\right) \cdot y + t\right) \cdot \frac{1}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(y + a, y, b\right), y, c\right), y, i\right) \cdot 1}\]
\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}
↓
\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}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(y + a, y, b\right), y, c\right), y, i\right) \cdot 1}
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r69224 = x;
        double r69225 = y;
        double r69226 = r69224 * r69225;
        double r69227 = z;
        double r69228 = r69226 + r69227;
        double r69229 = r69228 * r69225;
        double r69230 = 27464.7644705;
        double r69231 = r69229 + r69230;
        double r69232 = r69231 * r69225;
        double r69233 = 230661.510616;
        double r69234 = r69232 + r69233;
        double r69235 = r69234 * r69225;
        double r69236 = t;
        double r69237 = r69235 + r69236;
        double r69238 = a;
        double r69239 = r69225 + r69238;
        double r69240 = r69239 * r69225;
        double r69241 = b;
        double r69242 = r69240 + r69241;
        double r69243 = r69242 * r69225;
        double r69244 = c;
        double r69245 = r69243 + r69244;
        double r69246 = r69245 * r69225;
        double r69247 = i;
        double r69248 = r69246 + r69247;
        double r69249 = r69237 / r69248;
        return r69249;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r69250 = x;
        double r69251 = y;
        double r69252 = r69250 * r69251;
        double r69253 = z;
        double r69254 = r69252 + r69253;
        double r69255 = r69254 * r69251;
        double r69256 = 27464.7644705;
        double r69257 = r69255 + r69256;
        double r69258 = r69257 * r69251;
        double r69259 = 230661.510616;
        double r69260 = r69258 + r69259;
        double r69261 = r69260 * r69251;
        double r69262 = t;
        double r69263 = r69261 + r69262;
        double r69264 = 1.0;
        double r69265 = a;
        double r69266 = r69251 + r69265;
        double r69267 = b;
        double r69268 = fma(r69266, r69251, r69267);
        double r69269 = c;
        double r69270 = fma(r69268, r69251, r69269);
        double r69271 = i;
        double r69272 = fma(r69270, r69251, r69271);
        double r69273 = r69272 * r69264;
        double r69274 = r69264 / r69273;
        double r69275 = r69263 * r69274;
        return r69275;
}

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

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-inv29.0

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

  4. Simplified29.0

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

  5. Final simplification29.0

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

Reproduce

herbie shell --seed 2020089 +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)))