Average Error: 29.1 → 29.2
Time: 30.8s
Precision: 64
\[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644704999984242022037506103515625\right) \cdot y + 230661.5106160000141244381666183471679688\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\]
↓
\[\frac{1}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y + a, y, b\right), c\right), i\right)} \cdot \mathsf{fma}\left(\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, x, z\right), 27464.7644704999984242022037506103515625\right), 230661.5106160000141244381666183471679688\right), y, t\right)\]
\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644704999984242022037506103515625\right) \cdot y + 230661.5106160000141244381666183471679688\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(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y + a, y, b\right), c\right), i\right)} \cdot \mathsf{fma}\left(\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, x, z\right), 27464.7644704999984242022037506103515625\right), 230661.5106160000141244381666183471679688\right), y, t\right)
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r61195 = x;
        double r61196 = y;
        double r61197 = r61195 * r61196;
        double r61198 = z;
        double r61199 = r61197 + r61198;
        double r61200 = r61199 * r61196;
        double r61201 = 27464.7644705;
        double r61202 = r61200 + r61201;
        double r61203 = r61202 * r61196;
        double r61204 = 230661.510616;
        double r61205 = r61203 + r61204;
        double r61206 = r61205 * r61196;
        double r61207 = t;
        double r61208 = r61206 + r61207;
        double r61209 = a;
        double r61210 = r61196 + r61209;
        double r61211 = r61210 * r61196;
        double r61212 = b;
        double r61213 = r61211 + r61212;
        double r61214 = r61213 * r61196;
        double r61215 = c;
        double r61216 = r61214 + r61215;
        double r61217 = r61216 * r61196;
        double r61218 = i;
        double r61219 = r61217 + r61218;
        double r61220 = r61208 / r61219;
        return r61220;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r61221 = 1.0;
        double r61222 = y;
        double r61223 = a;
        double r61224 = r61222 + r61223;
        double r61225 = b;
        double r61226 = fma(r61224, r61222, r61225);
        double r61227 = c;
        double r61228 = fma(r61222, r61226, r61227);
        double r61229 = i;
        double r61230 = fma(r61222, r61228, r61229);
        double r61231 = r61221 / r61230;
        double r61232 = x;
        double r61233 = z;
        double r61234 = fma(r61222, r61232, r61233);
        double r61235 = 27464.7644705;
        double r61236 = fma(r61222, r61234, r61235);
        double r61237 = 230661.510616;
        double r61238 = fma(r61222, r61236, r61237);
        double r61239 = t;
        double r61240 = fma(r61238, r61222, r61239);
        double r61241 = r61231 * r61240;
        return r61241;
}

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 29.1

    \[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644704999984242022037506103515625\right) \cdot y + 230661.5106160000141244381666183471679688\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\]

  2. Simplified29.1

    \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, x, z\right), 27464.7644704999984242022037506103515625\right), 230661.5106160000141244381666183471679688\right), y, t\right)}{\mathsf{fma}\left(\mathsf{fma}\left(y, \mathsf{fma}\left(y + a, y, b\right), c\right), y, i\right)}}\]
  3. Using strategy rm

  4. Applied div-inv29.2

    \[\leadsto \color{blue}{\mathsf{fma}\left(\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, x, z\right), 27464.7644704999984242022037506103515625\right), 230661.5106160000141244381666183471679688\right), y, t\right) \cdot \frac{1}{\mathsf{fma}\left(\mathsf{fma}\left(y, \mathsf{fma}\left(y + a, y, b\right), c\right), y, i\right)}}\]

  5. Simplified29.2

    \[\leadsto \mathsf{fma}\left(\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, x, z\right), 27464.7644704999984242022037506103515625\right), 230661.5106160000141244381666183471679688\right), y, t\right) \cdot \color{blue}{\frac{1}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y + a, y, b\right), c\right), i\right)}}\]

  6. Final simplification29.2

    \[\leadsto \frac{1}{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y + a, y, b\right), c\right), i\right)} \cdot \mathsf{fma}\left(\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, x, z\right), 27464.7644704999984242022037506103515625\right), 230661.5106160000141244381666183471679688\right), y, t\right)\]

Reproduce

herbie shell --seed 2019194 +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)))