Average Error: 29.2 → 29.3
Time: 9.4s
Precision: 64
\[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644704999984242022037506103515625\right) \cdot y + 230661.5106160000141244381666183471679688\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\]
↓
\[\left(\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644704999984242022037506103515625\right) \cdot y + 230661.5106160000141244381666183471679688\right) \cdot y + t\right) \cdot \frac{1}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(y + a, y, b\right), y, c\right), y, i\right) \cdot 1}\]
\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}
↓
\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) \cdot 1}
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r66072 = x;
        double r66073 = y;
        double r66074 = r66072 * r66073;
        double r66075 = z;
        double r66076 = r66074 + r66075;
        double r66077 = r66076 * r66073;
        double r66078 = 27464.7644705;
        double r66079 = r66077 + r66078;
        double r66080 = r66079 * r66073;
        double r66081 = 230661.510616;
        double r66082 = r66080 + r66081;
        double r66083 = r66082 * r66073;
        double r66084 = t;
        double r66085 = r66083 + r66084;
        double r66086 = a;
        double r66087 = r66073 + r66086;
        double r66088 = r66087 * r66073;
        double r66089 = b;
        double r66090 = r66088 + r66089;
        double r66091 = r66090 * r66073;
        double r66092 = c;
        double r66093 = r66091 + r66092;
        double r66094 = r66093 * r66073;
        double r66095 = i;
        double r66096 = r66094 + r66095;
        double r66097 = r66085 / r66096;
        return r66097;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r66098 = x;
        double r66099 = y;
        double r66100 = r66098 * r66099;
        double r66101 = z;
        double r66102 = r66100 + r66101;
        double r66103 = r66102 * r66099;
        double r66104 = 27464.7644705;
        double r66105 = r66103 + r66104;
        double r66106 = r66105 * r66099;
        double r66107 = 230661.510616;
        double r66108 = r66106 + r66107;
        double r66109 = r66108 * r66099;
        double r66110 = t;
        double r66111 = r66109 + r66110;
        double r66112 = 1.0;
        double r66113 = a;
        double r66114 = r66099 + r66113;
        double r66115 = b;
        double r66116 = fma(r66114, r66099, r66115);
        double r66117 = c;
        double r66118 = fma(r66116, r66099, r66117);
        double r66119 = i;
        double r66120 = fma(r66118, r66099, r66119);
        double r66121 = r66120 * r66112;
        double r66122 = r66112 / r66121;
        double r66123 = r66111 * r66122;
        return r66123;
}

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. Using strategy rm

  3. Applied div-inv29.3

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

  4. Simplified29.3

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

  5. Final simplification29.3

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

Reproduce

herbie shell --seed 2019352 +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) 27464.7644705) y) 230661.510616) y) t) (+ (* (+ (* (+ (* (+ y a) y) b) y) c) y) i)))