Average Error: 29.2 → 29.2
Time: 33.6s
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 r48099 = x;
        double r48100 = y;
        double r48101 = r48099 * r48100;
        double r48102 = z;
        double r48103 = r48101 + r48102;
        double r48104 = r48103 * r48100;
        double r48105 = 27464.7644705;
        double r48106 = r48104 + r48105;
        double r48107 = r48106 * r48100;
        double r48108 = 230661.510616;
        double r48109 = r48107 + r48108;
        double r48110 = r48109 * r48100;
        double r48111 = t;
        double r48112 = r48110 + r48111;
        double r48113 = a;
        double r48114 = r48100 + r48113;
        double r48115 = r48114 * r48100;
        double r48116 = b;
        double r48117 = r48115 + r48116;
        double r48118 = r48117 * r48100;
        double r48119 = c;
        double r48120 = r48118 + r48119;
        double r48121 = r48120 * r48100;
        double r48122 = i;
        double r48123 = r48121 + r48122;
        double r48124 = r48112 / r48123;
        return r48124;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r48125 = x;
        double r48126 = y;
        double r48127 = z;
        double r48128 = fma(r48125, r48126, r48127);
        double r48129 = 27464.7644705;
        double r48130 = fma(r48128, r48126, r48129);
        double r48131 = 230661.510616;
        double r48132 = fma(r48130, r48126, r48131);
        double r48133 = t;
        double r48134 = fma(r48132, r48126, r48133);
        double r48135 = a;
        double r48136 = r48126 + r48135;
        double r48137 = b;
        double r48138 = fma(r48136, r48126, r48137);
        double r48139 = c;
        double r48140 = fma(r48138, r48126, r48139);
        double r48141 = i;
        double r48142 = fma(r48140, r48126, r48141);
        double r48143 = r48134 / r48142;
        return r48143;
}

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)))