Average Error: 28.8 → 28.8
Time: 37.5s
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 r2261184 = x;
        double r2261185 = y;
        double r2261186 = r2261184 * r2261185;
        double r2261187 = z;
        double r2261188 = r2261186 + r2261187;
        double r2261189 = r2261188 * r2261185;
        double r2261190 = 27464.7644705;
        double r2261191 = r2261189 + r2261190;
        double r2261192 = r2261191 * r2261185;
        double r2261193 = 230661.510616;
        double r2261194 = r2261192 + r2261193;
        double r2261195 = r2261194 * r2261185;
        double r2261196 = t;
        double r2261197 = r2261195 + r2261196;
        double r2261198 = a;
        double r2261199 = r2261185 + r2261198;
        double r2261200 = r2261199 * r2261185;
        double r2261201 = b;
        double r2261202 = r2261200 + r2261201;
        double r2261203 = r2261202 * r2261185;
        double r2261204 = c;
        double r2261205 = r2261203 + r2261204;
        double r2261206 = r2261205 * r2261185;
        double r2261207 = i;
        double r2261208 = r2261206 + r2261207;
        double r2261209 = r2261197 / r2261208;
        return r2261209;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r2261210 = y;
        double r2261211 = x;
        double r2261212 = z;
        double r2261213 = fma(r2261210, r2261211, r2261212);
        double r2261214 = 27464.7644705;
        double r2261215 = fma(r2261210, r2261213, r2261214);
        double r2261216 = 230661.510616;
        double r2261217 = fma(r2261210, r2261215, r2261216);
        double r2261218 = t;
        double r2261219 = fma(r2261210, r2261217, r2261218);
        double r2261220 = a;
        double r2261221 = r2261210 + r2261220;
        double r2261222 = b;
        double r2261223 = fma(r2261221, r2261210, r2261222);
        double r2261224 = c;
        double r2261225 = fma(r2261210, r2261223, r2261224);
        double r2261226 = i;
        double r2261227 = fma(r2261225, r2261210, r2261226);
        double r2261228 = r2261219 / r2261227;
        return r2261228;
}

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 28.8

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

  2. Simplified28.8

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

  3. Final simplification28.8

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

Reproduce

herbie shell --seed 2019142 +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)))