Average Error: 29.5 → 29.5
Time: 23.6s
Precision: 64
\[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644704999984242022037506103515625\right) \cdot y + 230661.5106160000141244381666183471679688\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\]
↓
\[\left(\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644704999984242022037506103515625\right) \cdot y + 230661.5106160000141244381666183471679688\right) \cdot y + t\right) \cdot \frac{1}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(y + a, y, b\right), y, c\right), y, i\right)}\]
\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}
↓
\left(\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644704999984242022037506103515625\right) \cdot y + 230661.5106160000141244381666183471679688\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)}
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r68199 = x;
        double r68200 = y;
        double r68201 = r68199 * r68200;
        double r68202 = z;
        double r68203 = r68201 + r68202;
        double r68204 = r68203 * r68200;
        double r68205 = 27464.7644705;
        double r68206 = r68204 + r68205;
        double r68207 = r68206 * r68200;
        double r68208 = 230661.510616;
        double r68209 = r68207 + r68208;
        double r68210 = r68209 * r68200;
        double r68211 = t;
        double r68212 = r68210 + r68211;
        double r68213 = a;
        double r68214 = r68200 + r68213;
        double r68215 = r68214 * r68200;
        double r68216 = b;
        double r68217 = r68215 + r68216;
        double r68218 = r68217 * r68200;
        double r68219 = c;
        double r68220 = r68218 + r68219;
        double r68221 = r68220 * r68200;
        double r68222 = i;
        double r68223 = r68221 + r68222;
        double r68224 = r68212 / r68223;
        return r68224;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r68225 = x;
        double r68226 = y;
        double r68227 = r68225 * r68226;
        double r68228 = z;
        double r68229 = r68227 + r68228;
        double r68230 = r68229 * r68226;
        double r68231 = 27464.7644705;
        double r68232 = r68230 + r68231;
        double r68233 = r68232 * r68226;
        double r68234 = 230661.510616;
        double r68235 = r68233 + r68234;
        double r68236 = r68235 * r68226;
        double r68237 = t;
        double r68238 = r68236 + r68237;
        double r68239 = 1.0;
        double r68240 = a;
        double r68241 = r68226 + r68240;
        double r68242 = b;
        double r68243 = fma(r68241, r68226, r68242);
        double r68244 = c;
        double r68245 = fma(r68243, r68226, r68244);
        double r68246 = i;
        double r68247 = fma(r68245, r68226, r68246);
        double r68248 = r68239 / r68247;
        double r68249 = r68238 * r68248;
        return r68249;
}

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 29.5

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

  3. Applied div-inv29.5

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

  4. Simplified29.5

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

  5. Final simplification29.5

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

Reproduce

herbie shell --seed 2019209 +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) 27464.764470499998) y) 230661.510616000014) y) t) (+ (* (+ (* (+ (* (+ y a) y) b) y) c) y) i)))