Average Error: 28.8 → 28.9
Time: 37.8s
Precision: 64
\[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644704999984242022037506103515625\right) \cdot y + 230661.5106160000141244381666183471679688\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\]
↓
\[\frac{1}{\mathsf{fma}\left(\mathsf{fma}\left(y, \mathsf{fma}\left(y + a, y, b\right), c\right), y, i\right)} \cdot \mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, x, z\right), 27464.7644704999984242022037506103515625\right), 230661.5106160000141244381666183471679688\right), t\right)\]
\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 r2265022 = x;
        double r2265023 = y;
        double r2265024 = r2265022 * r2265023;
        double r2265025 = z;
        double r2265026 = r2265024 + r2265025;
        double r2265027 = r2265026 * r2265023;
        double r2265028 = 27464.7644705;
        double r2265029 = r2265027 + r2265028;
        double r2265030 = r2265029 * r2265023;
        double r2265031 = 230661.510616;
        double r2265032 = r2265030 + r2265031;
        double r2265033 = r2265032 * r2265023;
        double r2265034 = t;
        double r2265035 = r2265033 + r2265034;
        double r2265036 = a;
        double r2265037 = r2265023 + r2265036;
        double r2265038 = r2265037 * r2265023;
        double r2265039 = b;
        double r2265040 = r2265038 + r2265039;
        double r2265041 = r2265040 * r2265023;
        double r2265042 = c;
        double r2265043 = r2265041 + r2265042;
        double r2265044 = r2265043 * r2265023;
        double r2265045 = i;
        double r2265046 = r2265044 + r2265045;
        double r2265047 = r2265035 / r2265046;
        return r2265047;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r2265048 = 1.0;
        double r2265049 = y;
        double r2265050 = a;
        double r2265051 = r2265049 + r2265050;
        double r2265052 = b;
        double r2265053 = fma(r2265051, r2265049, r2265052);
        double r2265054 = c;
        double r2265055 = fma(r2265049, r2265053, r2265054);
        double r2265056 = i;
        double r2265057 = fma(r2265055, r2265049, r2265056);
        double r2265058 = r2265048 / r2265057;
        double r2265059 = x;
        double r2265060 = z;
        double r2265061 = fma(r2265049, r2265059, r2265060);
        double r2265062 = 27464.7644705;
        double r2265063 = fma(r2265049, r2265061, r2265062);
        double r2265064 = 230661.510616;
        double r2265065 = fma(r2265049, r2265063, r2265064);
        double r2265066 = t;
        double r2265067 = fma(r2265049, r2265065, r2265066);
        double r2265068 = r2265058 * r2265067;
        return r2265068;
}

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)))