Average Error: 28.3 → 28.3
Time: 35.1s
Precision: 64
\[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\]
↓
\[\frac{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, x, z\right), 27464.7644705\right), 230661.510616\right), t\right)}{\mathsf{fma}\left(\mathsf{fma}\left(y, \mathsf{fma}\left(y + a, y, b\right), c\right), y, i\right)}\]
\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}
↓
\frac{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, x, z\right), 27464.7644705\right), 230661.510616\right), t\right)}{\mathsf{fma}\left(\mathsf{fma}\left(y, \mathsf{fma}\left(y + a, y, b\right), c\right), y, i\right)}
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r2630240 = x;
        double r2630241 = y;
        double r2630242 = r2630240 * r2630241;
        double r2630243 = z;
        double r2630244 = r2630242 + r2630243;
        double r2630245 = r2630244 * r2630241;
        double r2630246 = 27464.7644705;
        double r2630247 = r2630245 + r2630246;
        double r2630248 = r2630247 * r2630241;
        double r2630249 = 230661.510616;
        double r2630250 = r2630248 + r2630249;
        double r2630251 = r2630250 * r2630241;
        double r2630252 = t;
        double r2630253 = r2630251 + r2630252;
        double r2630254 = a;
        double r2630255 = r2630241 + r2630254;
        double r2630256 = r2630255 * r2630241;
        double r2630257 = b;
        double r2630258 = r2630256 + r2630257;
        double r2630259 = r2630258 * r2630241;
        double r2630260 = c;
        double r2630261 = r2630259 + r2630260;
        double r2630262 = r2630261 * r2630241;
        double r2630263 = i;
        double r2630264 = r2630262 + r2630263;
        double r2630265 = r2630253 / r2630264;
        return r2630265;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r2630266 = y;
        double r2630267 = x;
        double r2630268 = z;
        double r2630269 = fma(r2630266, r2630267, r2630268);
        double r2630270 = 27464.7644705;
        double r2630271 = fma(r2630266, r2630269, r2630270);
        double r2630272 = 230661.510616;
        double r2630273 = fma(r2630266, r2630271, r2630272);
        double r2630274 = t;
        double r2630275 = fma(r2630266, r2630273, r2630274);
        double r2630276 = a;
        double r2630277 = r2630266 + r2630276;
        double r2630278 = b;
        double r2630279 = fma(r2630277, r2630266, r2630278);
        double r2630280 = c;
        double r2630281 = fma(r2630266, r2630279, r2630280);
        double r2630282 = i;
        double r2630283 = fma(r2630281, r2630266, r2630282);
        double r2630284 = r2630275 / r2630283;
        return r2630284;
}

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 28.3

    \[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\]

  2. Simplified28.3

    \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, x, z\right), 27464.7644705\right), 230661.510616\right), t\right)}{\mathsf{fma}\left(\mathsf{fma}\left(y, \mathsf{fma}\left(y + a, y, b\right), c\right), y, i\right)}}\]

  3. Final simplification28.3

    \[\leadsto \frac{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, x, z\right), 27464.7644705\right), 230661.510616\right), t\right)}{\mathsf{fma}\left(\mathsf{fma}\left(y, \mathsf{fma}\left(y + a, y, b\right), c\right), y, i\right)}\]

Reproduce

herbie shell --seed 2019162 +o rules:numerics
(FPCore (x y z t a b c i)
  :name "Numeric.SpecFunctions:logGamma from math-functions-0.1.5.2"
  (/ (+ (* (+ (* (+ (* (+ (* x y) z) y) 27464.7644705) y) 230661.510616) y) t) (+ (* (+ (* (+ (* (+ y a) y) b) y) c) y) i)))