Average Error: 29.3 → 29.4
Time: 7.9s
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 r57156 = x;
        double r57157 = y;
        double r57158 = r57156 * r57157;
        double r57159 = z;
        double r57160 = r57158 + r57159;
        double r57161 = r57160 * r57157;
        double r57162 = 27464.7644705;
        double r57163 = r57161 + r57162;
        double r57164 = r57163 * r57157;
        double r57165 = 230661.510616;
        double r57166 = r57164 + r57165;
        double r57167 = r57166 * r57157;
        double r57168 = t;
        double r57169 = r57167 + r57168;
        double r57170 = a;
        double r57171 = r57157 + r57170;
        double r57172 = r57171 * r57157;
        double r57173 = b;
        double r57174 = r57172 + r57173;
        double r57175 = r57174 * r57157;
        double r57176 = c;
        double r57177 = r57175 + r57176;
        double r57178 = r57177 * r57157;
        double r57179 = i;
        double r57180 = r57178 + r57179;
        double r57181 = r57169 / r57180;
        return r57181;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r57182 = x;
        double r57183 = y;
        double r57184 = r57182 * r57183;
        double r57185 = z;
        double r57186 = r57184 + r57185;
        double r57187 = r57186 * r57183;
        double r57188 = 27464.7644705;
        double r57189 = r57187 + r57188;
        double r57190 = r57189 * r57183;
        double r57191 = 230661.510616;
        double r57192 = r57190 + r57191;
        double r57193 = r57192 * r57183;
        double r57194 = t;
        double r57195 = r57193 + r57194;
        double r57196 = 1.0;
        double r57197 = a;
        double r57198 = r57183 + r57197;
        double r57199 = b;
        double r57200 = fma(r57198, r57183, r57199);
        double r57201 = c;
        double r57202 = fma(r57200, r57183, r57201);
        double r57203 = i;
        double r57204 = fma(r57202, r57183, r57203);
        double r57205 = r57204 * r57196;
        double r57206 = r57196 / r57205;
        double r57207 = r57195 * r57206;
        return r57207;
}

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 29.3

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

  3. Applied div-inv29.4

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

  4. Simplified29.4

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

  5. Final simplification29.4

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

Reproduce

herbie shell --seed 2020024 +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)))