Average Error: 28.9 → 29.1
Time: 10.2s
Precision: 64
\[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644704999984242022037506103515625\right) \cdot y + 230661.5106160000141244381666183471679688\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\]
↓
\[\frac{1}{\frac{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644704999984242022037506103515625\right) \cdot y + 230661.5106160000141244381666183471679688\right) \cdot y + t}}\]
\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{1}{\frac{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644704999984242022037506103515625\right) \cdot y + 230661.5106160000141244381666183471679688\right) \cdot y + t}}
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r66093 = x;
        double r66094 = y;
        double r66095 = r66093 * r66094;
        double r66096 = z;
        double r66097 = r66095 + r66096;
        double r66098 = r66097 * r66094;
        double r66099 = 27464.7644705;
        double r66100 = r66098 + r66099;
        double r66101 = r66100 * r66094;
        double r66102 = 230661.510616;
        double r66103 = r66101 + r66102;
        double r66104 = r66103 * r66094;
        double r66105 = t;
        double r66106 = r66104 + r66105;
        double r66107 = a;
        double r66108 = r66094 + r66107;
        double r66109 = r66108 * r66094;
        double r66110 = b;
        double r66111 = r66109 + r66110;
        double r66112 = r66111 * r66094;
        double r66113 = c;
        double r66114 = r66112 + r66113;
        double r66115 = r66114 * r66094;
        double r66116 = i;
        double r66117 = r66115 + r66116;
        double r66118 = r66106 / r66117;
        return r66118;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r66119 = 1.0;
        double r66120 = y;
        double r66121 = a;
        double r66122 = r66120 + r66121;
        double r66123 = r66122 * r66120;
        double r66124 = b;
        double r66125 = r66123 + r66124;
        double r66126 = r66125 * r66120;
        double r66127 = c;
        double r66128 = r66126 + r66127;
        double r66129 = r66128 * r66120;
        double r66130 = i;
        double r66131 = r66129 + r66130;
        double r66132 = x;
        double r66133 = r66132 * r66120;
        double r66134 = z;
        double r66135 = r66133 + r66134;
        double r66136 = r66135 * r66120;
        double r66137 = 27464.7644705;
        double r66138 = r66136 + r66137;
        double r66139 = r66138 * r66120;
        double r66140 = 230661.510616;
        double r66141 = r66139 + r66140;
        double r66142 = r66141 * r66120;
        double r66143 = t;
        double r66144 = r66142 + r66143;
        double r66145 = r66131 / r66144;
        double r66146 = r66119 / r66145;
        return r66146;
}

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

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 28.9

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

  3. Applied clear-num29.1

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

  4. Final simplification29.1

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

Reproduce

herbie shell --seed 2019346 +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)))