Average Error: 28.7 → 28.7
Time: 27.7s
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 r64097 = x;
        double r64098 = y;
        double r64099 = r64097 * r64098;
        double r64100 = z;
        double r64101 = r64099 + r64100;
        double r64102 = r64101 * r64098;
        double r64103 = 27464.7644705;
        double r64104 = r64102 + r64103;
        double r64105 = r64104 * r64098;
        double r64106 = 230661.510616;
        double r64107 = r64105 + r64106;
        double r64108 = r64107 * r64098;
        double r64109 = t;
        double r64110 = r64108 + r64109;
        double r64111 = a;
        double r64112 = r64098 + r64111;
        double r64113 = r64112 * r64098;
        double r64114 = b;
        double r64115 = r64113 + r64114;
        double r64116 = r64115 * r64098;
        double r64117 = c;
        double r64118 = r64116 + r64117;
        double r64119 = r64118 * r64098;
        double r64120 = i;
        double r64121 = r64119 + r64120;
        double r64122 = r64110 / r64121;
        return r64122;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r64123 = x;
        double r64124 = y;
        double r64125 = z;
        double r64126 = fma(r64123, r64124, r64125);
        double r64127 = 27464.7644705;
        double r64128 = fma(r64126, r64124, r64127);
        double r64129 = 230661.510616;
        double r64130 = fma(r64128, r64124, r64129);
        double r64131 = t;
        double r64132 = fma(r64130, r64124, r64131);
        double r64133 = a;
        double r64134 = r64124 + r64133;
        double r64135 = b;
        double r64136 = fma(r64134, r64124, r64135);
        double r64137 = c;
        double r64138 = fma(r64136, r64124, r64137);
        double r64139 = i;
        double r64140 = fma(r64138, r64124, r64139);
        double r64141 = r64132 / r64140;
        return r64141;
}

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 28.7

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

  2. Simplified28.7

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

  3. Final simplification28.7

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

Reproduce

herbie shell --seed 2019208 +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) 27464.764470499998) y) 230661.510616000014) y) t) (+ (* (+ (* (+ (* (+ y a) y) b) y) c) y) i)))