Average Error: 29.0 → 29.1
Time: 31.3s
Precision: 64
\[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\]
↓
\[\frac{1}{\mathsf{fma}\left(\left(\mathsf{fma}\left(y, \left(\mathsf{fma}\left(\left(y + a\right), y, b\right)\right), c\right)\right), y, i\right)} \cdot \mathsf{fma}\left(y, \left(\mathsf{fma}\left(y, \left(\mathsf{fma}\left(y, \left(\mathsf{fma}\left(y, x, z\right)\right), 27464.7644705\right)\right), 230661.510616\right)\right), t\right)\]
\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}{\mathsf{fma}\left(\left(\mathsf{fma}\left(y, \left(\mathsf{fma}\left(\left(y + a\right), y, b\right)\right), c\right)\right), y, i\right)} \cdot \mathsf{fma}\left(y, \left(\mathsf{fma}\left(y, \left(\mathsf{fma}\left(y, \left(\mathsf{fma}\left(y, x, z\right)\right), 27464.7644705\right)\right), 230661.510616\right)\right), t\right)
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r2361163 = x;
        double r2361164 = y;
        double r2361165 = r2361163 * r2361164;
        double r2361166 = z;
        double r2361167 = r2361165 + r2361166;
        double r2361168 = r2361167 * r2361164;
        double r2361169 = 27464.7644705;
        double r2361170 = r2361168 + r2361169;
        double r2361171 = r2361170 * r2361164;
        double r2361172 = 230661.510616;
        double r2361173 = r2361171 + r2361172;
        double r2361174 = r2361173 * r2361164;
        double r2361175 = t;
        double r2361176 = r2361174 + r2361175;
        double r2361177 = a;
        double r2361178 = r2361164 + r2361177;
        double r2361179 = r2361178 * r2361164;
        double r2361180 = b;
        double r2361181 = r2361179 + r2361180;
        double r2361182 = r2361181 * r2361164;
        double r2361183 = c;
        double r2361184 = r2361182 + r2361183;
        double r2361185 = r2361184 * r2361164;
        double r2361186 = i;
        double r2361187 = r2361185 + r2361186;
        double r2361188 = r2361176 / r2361187;
        return r2361188;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r2361189 = 1.0;
        double r2361190 = y;
        double r2361191 = a;
        double r2361192 = r2361190 + r2361191;
        double r2361193 = b;
        double r2361194 = fma(r2361192, r2361190, r2361193);
        double r2361195 = c;
        double r2361196 = fma(r2361190, r2361194, r2361195);
        double r2361197 = i;
        double r2361198 = fma(r2361196, r2361190, r2361197);
        double r2361199 = r2361189 / r2361198;
        double r2361200 = x;
        double r2361201 = z;
        double r2361202 = fma(r2361190, r2361200, r2361201);
        double r2361203 = 27464.7644705;
        double r2361204 = fma(r2361190, r2361202, r2361203);
        double r2361205 = 230661.510616;
        double r2361206 = fma(r2361190, r2361204, r2361205);
        double r2361207 = t;
        double r2361208 = fma(r2361190, r2361206, r2361207);
        double r2361209 = r2361199 * r2361208;
        return r2361209;
}

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 29.0

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

  2. Simplified29.0

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

  4. Applied div-inv29.1

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

  5. Final simplification29.1

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

Reproduce

herbie shell --seed 2019130 +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)))