Numeric.SpecFunctions:logGamma from math-functions-0.1.5.2

Average Error: 29.1 → 29.2

Time: 23.2s

Precision: 64

Math

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

↓

\[\frac{\left(\left(\sqrt[3]{\left(x \cdot y + z\right) \cdot y + 27464.7644704999984242022037506103515625} \cdot \sqrt[3]{\left(x \cdot y + z\right) \cdot y + 27464.7644704999984242022037506103515625}\right) \cdot \left(\sqrt[3]{\left(x \cdot y + z\right) \cdot y + 27464.7644704999984242022037506103515625} \cdot y\right) + 230661.5106160000141244381666183471679688\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\]

C

double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r55107 = x;
        double r55108 = y;
        double r55109 = r55107 * r55108;
        double r55110 = z;
        double r55111 = r55109 + r55110;
        double r55112 = r55111 * r55108;
        double r55113 = 27464.7644705;
        double r55114 = r55112 + r55113;
        double r55115 = r55114 * r55108;
        double r55116 = 230661.510616;
        double r55117 = r55115 + r55116;
        double r55118 = r55117 * r55108;
        double r55119 = t;
        double r55120 = r55118 + r55119;
        double r55121 = a;
        double r55122 = r55108 + r55121;
        double r55123 = r55122 * r55108;
        double r55124 = b;
        double r55125 = r55123 + r55124;
        double r55126 = r55125 * r55108;
        double r55127 = c;
        double r55128 = r55126 + r55127;
        double r55129 = r55128 * r55108;
        double r55130 = i;
        double r55131 = r55129 + r55130;
        double r55132 = r55120 / r55131;
        return r55132;
}

↓

double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r55133 = x;
        double r55134 = y;
        double r55135 = r55133 * r55134;
        double r55136 = z;
        double r55137 = r55135 + r55136;
        double r55138 = r55137 * r55134;
        double r55139 = 27464.7644705;
        double r55140 = r55138 + r55139;
        double r55141 = cbrt(r55140);
        double r55142 = r55141 * r55141;
        double r55143 = r55141 * r55134;
        double r55144 = r55142 * r55143;
        double r55145 = 230661.510616;
        double r55146 = r55144 + r55145;
        double r55147 = r55146 * r55134;
        double r55148 = t;
        double r55149 = r55147 + r55148;
        double r55150 = a;
        double r55151 = r55134 + r55150;
        double r55152 = r55151 * r55134;
        double r55153 = b;
        double r55154 = r55152 + r55153;
        double r55155 = r55154 * r55134;
        double r55156 = c;
        double r55157 = r55155 + r55156;
        double r55158 = r55157 * r55134;
        double r55159 = i;
        double r55160 = r55158 + r55159;
        double r55161 = r55149 / r55160;
        return r55161;
}

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 29.1

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

3. Applied add-cube-cbrt 29.2

   \[\leadsto \frac{\left(\color{blue}{\left(\left(\sqrt[3]{\left(x \cdot y + z\right) \cdot y + 27464.7644704999984242022037506103515625} \cdot \sqrt[3]{\left(x \cdot y + z\right) \cdot y + 27464.7644704999984242022037506103515625}\right) \cdot \sqrt[3]{\left(x \cdot y + z\right) \cdot y + 27464.7644704999984242022037506103515625}\right)} \cdot y + 230661.5106160000141244381666183471679688\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\]

4. Applied associate-*l* 29.2

   \[\leadsto \frac{\left(\color{blue}{\left(\sqrt[3]{\left(x \cdot y + z\right) \cdot y + 27464.7644704999984242022037506103515625} \cdot \sqrt[3]{\left(x \cdot y + z\right) \cdot y + 27464.7644704999984242022037506103515625}\right) \cdot \left(\sqrt[3]{\left(x \cdot y + z\right) \cdot y + 27464.7644704999984242022037506103515625} \cdot y\right)} + 230661.5106160000141244381666183471679688\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\]

5. Final simplification 29.2

   \[\leadsto \frac{\left(\left(\sqrt[3]{\left(x \cdot y + z\right) \cdot y + 27464.7644704999984242022037506103515625} \cdot \sqrt[3]{\left(x \cdot y + z\right) \cdot y + 27464.7644704999984242022037506103515625}\right) \cdot \left(\sqrt[3]{\left(x \cdot y + z\right) \cdot y + 27464.7644704999984242022037506103515625} \cdot y\right) + 230661.5106160000141244381666183471679688\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\]

Reproduce

herbie shell --seed 2019294 
(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)))