Average Error: 28.8 → 28.9
Time: 37.9s
Precision: 64
\[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644704999984242022037506103515625\right) \cdot y + 230661.5106160000141244381666183471679688\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\]
↓
\[\frac{1}{\mathsf{fma}\left(\mathsf{fma}\left(y, \mathsf{fma}\left(y + a, y, b\right), c\right), y, i\right)} \cdot \mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, x, z\right), 27464.7644704999984242022037506103515625\right), 230661.5106160000141244381666183471679688\right), t\right)\]
\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(\mathsf{fma}\left(y, \mathsf{fma}\left(y + a, y, b\right), c\right), y, i\right)} \cdot \mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, x, z\right), 27464.7644704999984242022037506103515625\right), 230661.5106160000141244381666183471679688\right), t\right)
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r2265020 = x;
        double r2265021 = y;
        double r2265022 = r2265020 * r2265021;
        double r2265023 = z;
        double r2265024 = r2265022 + r2265023;
        double r2265025 = r2265024 * r2265021;
        double r2265026 = 27464.7644705;
        double r2265027 = r2265025 + r2265026;
        double r2265028 = r2265027 * r2265021;
        double r2265029 = 230661.510616;
        double r2265030 = r2265028 + r2265029;
        double r2265031 = r2265030 * r2265021;
        double r2265032 = t;
        double r2265033 = r2265031 + r2265032;
        double r2265034 = a;
        double r2265035 = r2265021 + r2265034;
        double r2265036 = r2265035 * r2265021;
        double r2265037 = b;
        double r2265038 = r2265036 + r2265037;
        double r2265039 = r2265038 * r2265021;
        double r2265040 = c;
        double r2265041 = r2265039 + r2265040;
        double r2265042 = r2265041 * r2265021;
        double r2265043 = i;
        double r2265044 = r2265042 + r2265043;
        double r2265045 = r2265033 / r2265044;
        return r2265045;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r2265046 = 1.0;
        double r2265047 = y;
        double r2265048 = a;
        double r2265049 = r2265047 + r2265048;
        double r2265050 = b;
        double r2265051 = fma(r2265049, r2265047, r2265050);
        double r2265052 = c;
        double r2265053 = fma(r2265047, r2265051, r2265052);
        double r2265054 = i;
        double r2265055 = fma(r2265053, r2265047, r2265054);
        double r2265056 = r2265046 / r2265055;
        double r2265057 = x;
        double r2265058 = z;
        double r2265059 = fma(r2265047, r2265057, r2265058);
        double r2265060 = 27464.7644705;
        double r2265061 = fma(r2265047, r2265059, r2265060);
        double r2265062 = 230661.510616;
        double r2265063 = fma(r2265047, r2265061, r2265062);
        double r2265064 = t;
        double r2265065 = fma(r2265047, r2265063, r2265064);
        double r2265066 = r2265056 * r2265065;
        return r2265066;
}

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 28.8

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

  2. Simplified28.8

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

  4. Applied div-inv28.9

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

  5. Final simplification28.9

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

Reproduce

herbie shell --seed 2019172 +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)))