Average Error: 29.2 → 29.2
Time: 34.1s
Precision: 64
\[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644704999984242022037506103515625\right) \cdot y + 230661.5106160000141244381666183471679688\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\]
↓
\[\frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x, y, z\right), y, 27464.7644704999984242022037506103515625\right), y, 230661.5106160000141244381666183471679688\right), y, t\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(y + a, y, b\right), y, c\right), y, i\right)}\]
\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}
↓
\frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x, y, z\right), y, 27464.7644704999984242022037506103515625\right), y, 230661.5106160000141244381666183471679688\right), y, t\right)}{\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 r48106 = x;
        double r48107 = y;
        double r48108 = r48106 * r48107;
        double r48109 = z;
        double r48110 = r48108 + r48109;
        double r48111 = r48110 * r48107;
        double r48112 = 27464.7644705;
        double r48113 = r48111 + r48112;
        double r48114 = r48113 * r48107;
        double r48115 = 230661.510616;
        double r48116 = r48114 + r48115;
        double r48117 = r48116 * r48107;
        double r48118 = t;
        double r48119 = r48117 + r48118;
        double r48120 = a;
        double r48121 = r48107 + r48120;
        double r48122 = r48121 * r48107;
        double r48123 = b;
        double r48124 = r48122 + r48123;
        double r48125 = r48124 * r48107;
        double r48126 = c;
        double r48127 = r48125 + r48126;
        double r48128 = r48127 * r48107;
        double r48129 = i;
        double r48130 = r48128 + r48129;
        double r48131 = r48119 / r48130;
        return r48131;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r48132 = x;
        double r48133 = y;
        double r48134 = z;
        double r48135 = fma(r48132, r48133, r48134);
        double r48136 = 27464.7644705;
        double r48137 = fma(r48135, r48133, r48136);
        double r48138 = 230661.510616;
        double r48139 = fma(r48137, r48133, r48138);
        double r48140 = t;
        double r48141 = fma(r48139, r48133, r48140);
        double r48142 = a;
        double r48143 = r48133 + r48142;
        double r48144 = b;
        double r48145 = fma(r48143, r48133, r48144);
        double r48146 = c;
        double r48147 = fma(r48145, r48133, r48146);
        double r48148 = i;
        double r48149 = fma(r48147, r48133, r48148);
        double r48150 = r48141 / r48149;
        return r48150;
}

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

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

  3. Final simplification29.2

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

Reproduce

herbie shell --seed 2019326 +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)))