Average Error: 29.2 → 29.3
Time: 9.3s
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 r58195 = x;
        double r58196 = y;
        double r58197 = r58195 * r58196;
        double r58198 = z;
        double r58199 = r58197 + r58198;
        double r58200 = r58199 * r58196;
        double r58201 = 27464.7644705;
        double r58202 = r58200 + r58201;
        double r58203 = r58202 * r58196;
        double r58204 = 230661.510616;
        double r58205 = r58203 + r58204;
        double r58206 = r58205 * r58196;
        double r58207 = t;
        double r58208 = r58206 + r58207;
        double r58209 = a;
        double r58210 = r58196 + r58209;
        double r58211 = r58210 * r58196;
        double r58212 = b;
        double r58213 = r58211 + r58212;
        double r58214 = r58213 * r58196;
        double r58215 = c;
        double r58216 = r58214 + r58215;
        double r58217 = r58216 * r58196;
        double r58218 = i;
        double r58219 = r58217 + r58218;
        double r58220 = r58208 / r58219;
        return r58220;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r58221 = x;
        double r58222 = y;
        double r58223 = r58221 * r58222;
        double r58224 = z;
        double r58225 = r58223 + r58224;
        double r58226 = r58225 * r58222;
        double r58227 = 27464.7644705;
        double r58228 = r58226 + r58227;
        double r58229 = r58228 * r58222;
        double r58230 = 230661.510616;
        double r58231 = r58229 + r58230;
        double r58232 = r58231 * r58222;
        double r58233 = t;
        double r58234 = r58232 + r58233;
        double r58235 = 1.0;
        double r58236 = a;
        double r58237 = r58222 + r58236;
        double r58238 = b;
        double r58239 = fma(r58237, r58222, r58238);
        double r58240 = c;
        double r58241 = fma(r58239, r58222, r58240);
        double r58242 = i;
        double r58243 = fma(r58241, r58222, r58242);
        double r58244 = r58243 * r58235;
        double r58245 = r58235 / r58244;
        double r58246 = r58234 * r58245;
        return r58246;
}

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 29.2

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

  3. Applied div-inv29.3

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

  4. Simplified29.3

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

  5. Final simplification29.3

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

Reproduce

herbie shell --seed 2020003 +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)))