Average Error: 27.9 → 28.1
Time: 39.2s
Precision: 64
\[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\]
↓
\[\frac{1}{\frac{\mathsf{fma}\left(\mathsf{fma}\left(y, \mathsf{fma}\left(y + a, y, b\right), c\right), y, i\right)}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, x, z\right), 27464.7644705\right), 230661.510616\right), t\right)}}\]
\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{1}{\frac{\mathsf{fma}\left(\mathsf{fma}\left(y, \mathsf{fma}\left(y + a, y, b\right), c\right), y, i\right)}{\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)}}
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r3332176 = x;
        double r3332177 = y;
        double r3332178 = r3332176 * r3332177;
        double r3332179 = z;
        double r3332180 = r3332178 + r3332179;
        double r3332181 = r3332180 * r3332177;
        double r3332182 = 27464.7644705;
        double r3332183 = r3332181 + r3332182;
        double r3332184 = r3332183 * r3332177;
        double r3332185 = 230661.510616;
        double r3332186 = r3332184 + r3332185;
        double r3332187 = r3332186 * r3332177;
        double r3332188 = t;
        double r3332189 = r3332187 + r3332188;
        double r3332190 = a;
        double r3332191 = r3332177 + r3332190;
        double r3332192 = r3332191 * r3332177;
        double r3332193 = b;
        double r3332194 = r3332192 + r3332193;
        double r3332195 = r3332194 * r3332177;
        double r3332196 = c;
        double r3332197 = r3332195 + r3332196;
        double r3332198 = r3332197 * r3332177;
        double r3332199 = i;
        double r3332200 = r3332198 + r3332199;
        double r3332201 = r3332189 / r3332200;
        return r3332201;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r3332202 = 1.0;
        double r3332203 = y;
        double r3332204 = a;
        double r3332205 = r3332203 + r3332204;
        double r3332206 = b;
        double r3332207 = fma(r3332205, r3332203, r3332206);
        double r3332208 = c;
        double r3332209 = fma(r3332203, r3332207, r3332208);
        double r3332210 = i;
        double r3332211 = fma(r3332209, r3332203, r3332210);
        double r3332212 = x;
        double r3332213 = z;
        double r3332214 = fma(r3332203, r3332212, r3332213);
        double r3332215 = 27464.7644705;
        double r3332216 = fma(r3332203, r3332214, r3332215);
        double r3332217 = 230661.510616;
        double r3332218 = fma(r3332203, r3332216, r3332217);
        double r3332219 = t;
        double r3332220 = fma(r3332203, r3332218, r3332219);
        double r3332221 = r3332211 / r3332220;
        double r3332222 = r3332202 / r3332221;
        return r3332222;
}

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 27.9

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

  2. Simplified27.9

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

  4. Applied clear-num28.1

    \[\leadsto \color{blue}{\frac{1}{\frac{\mathsf{fma}\left(\mathsf{fma}\left(y, \mathsf{fma}\left(y + a, y, b\right), c\right), y, i\right)}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, x, z\right), 27464.7644705\right), 230661.510616\right), t\right)}}}\]

  5. Final simplification28.1

    \[\leadsto \frac{1}{\frac{\mathsf{fma}\left(\mathsf{fma}\left(y, \mathsf{fma}\left(y + a, y, b\right), c\right), y, i\right)}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, x, z\right), 27464.7644705\right), 230661.510616\right), t\right)}}\]

Reproduce

herbie shell --seed 2019158 +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)))