Average Error: 29.2 → 29.2
Time: 23.5s
Precision: 64
\[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644704999984242022037506103515625\right) \cdot y + 230661.5106160000141244381666183471679688\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\]
↓
\[\frac{\mathsf{fma}\left(\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, x, z\right), 27464.7644704999984242022037506103515625\right), 230661.5106160000141244381666183471679688\right), y, t\right)}{\mathsf{fma}\left(\mathsf{fma}\left(y \cdot y, y + a, b \cdot y\right) + c, y, i\right)}\]
\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}
↓
\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 \cdot y, y + a, b \cdot y\right) + c, y, i\right)}
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r3475036 = x;
        double r3475037 = y;
        double r3475038 = r3475036 * r3475037;
        double r3475039 = z;
        double r3475040 = r3475038 + r3475039;
        double r3475041 = r3475040 * r3475037;
        double r3475042 = 27464.7644705;
        double r3475043 = r3475041 + r3475042;
        double r3475044 = r3475043 * r3475037;
        double r3475045 = 230661.510616;
        double r3475046 = r3475044 + r3475045;
        double r3475047 = r3475046 * r3475037;
        double r3475048 = t;
        double r3475049 = r3475047 + r3475048;
        double r3475050 = a;
        double r3475051 = r3475037 + r3475050;
        double r3475052 = r3475051 * r3475037;
        double r3475053 = b;
        double r3475054 = r3475052 + r3475053;
        double r3475055 = r3475054 * r3475037;
        double r3475056 = c;
        double r3475057 = r3475055 + r3475056;
        double r3475058 = r3475057 * r3475037;
        double r3475059 = i;
        double r3475060 = r3475058 + r3475059;
        double r3475061 = r3475049 / r3475060;
        return r3475061;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r3475062 = y;
        double r3475063 = x;
        double r3475064 = z;
        double r3475065 = fma(r3475062, r3475063, r3475064);
        double r3475066 = 27464.7644705;
        double r3475067 = fma(r3475062, r3475065, r3475066);
        double r3475068 = 230661.510616;
        double r3475069 = fma(r3475062, r3475067, r3475068);
        double r3475070 = t;
        double r3475071 = fma(r3475069, r3475062, r3475070);
        double r3475072 = r3475062 * r3475062;
        double r3475073 = a;
        double r3475074 = r3475062 + r3475073;
        double r3475075 = b;
        double r3475076 = r3475075 * r3475062;
        double r3475077 = fma(r3475072, r3475074, r3475076);
        double r3475078 = c;
        double r3475079 = r3475077 + r3475078;
        double r3475080 = i;
        double r3475081 = fma(r3475079, r3475062, r3475080);
        double r3475082 = r3475071 / r3475081;
        return r3475082;
}

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 29.2

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

  2. Simplified29.2

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

  4. Applied fma-udef29.2

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

  5. Taylor expanded around inf 29.3

    \[\leadsto \frac{\mathsf{fma}\left(\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, x, z\right), 27464.7644704999984242022037506103515625\right), 230661.5106160000141244381666183471679688\right), y, t\right)}{\mathsf{fma}\left(\color{blue}{\left(a \cdot {y}^{2} + \left({y}^{3} + y \cdot b\right)\right)} + c, y, i\right)}\]

  6. Simplified29.2

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

  7. Final simplification29.2

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

Reproduce

herbie shell --seed 2019174 +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)))