Numeric.SpecFunctions:logGamma from math-functions-0.1.5.2

Average Error: 29.1 → 28.3

Time: 32.1s

Precision: 64

Math

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

↓

\[\begin{array}{l} \mathbf{if}\;\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644704999984242022037506103515625\right) \cdot y + 230661.5106160000141244381666183471679688\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \le 3.62450759398618954484228470238219178564 \cdot 10^{294}:\\ \;\;\;\;\left(\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644704999984242022037506103515625\right) \cdot y + 230661.5106160000141244381666183471679688\right) \cdot y + t\right) \cdot \frac{1}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\\ \mathbf{else}:\\ \;\;\;\;0\\ \end{array}\]

C

double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r67190 = x;
        double r67191 = y;
        double r67192 = r67190 * r67191;
        double r67193 = z;
        double r67194 = r67192 + r67193;
        double r67195 = r67194 * r67191;
        double r67196 = 27464.7644705;
        double r67197 = r67195 + r67196;
        double r67198 = r67197 * r67191;
        double r67199 = 230661.510616;
        double r67200 = r67198 + r67199;
        double r67201 = r67200 * r67191;
        double r67202 = t;
        double r67203 = r67201 + r67202;
        double r67204 = a;
        double r67205 = r67191 + r67204;
        double r67206 = r67205 * r67191;
        double r67207 = b;
        double r67208 = r67206 + r67207;
        double r67209 = r67208 * r67191;
        double r67210 = c;
        double r67211 = r67209 + r67210;
        double r67212 = r67211 * r67191;
        double r67213 = i;
        double r67214 = r67212 + r67213;
        double r67215 = r67203 / r67214;
        return r67215;
}

↓

double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r67216 = x;
        double r67217 = y;
        double r67218 = r67216 * r67217;
        double r67219 = z;
        double r67220 = r67218 + r67219;
        double r67221 = r67220 * r67217;
        double r67222 = 27464.7644705;
        double r67223 = r67221 + r67222;
        double r67224 = r67223 * r67217;
        double r67225 = 230661.510616;
        double r67226 = r67224 + r67225;
        double r67227 = r67226 * r67217;
        double r67228 = t;
        double r67229 = r67227 + r67228;
        double r67230 = a;
        double r67231 = r67217 + r67230;
        double r67232 = r67231 * r67217;
        double r67233 = b;
        double r67234 = r67232 + r67233;
        double r67235 = r67234 * r67217;
        double r67236 = c;
        double r67237 = r67235 + r67236;
        double r67238 = r67237 * r67217;
        double r67239 = i;
        double r67240 = r67238 + r67239;
        double r67241 = r67229 / r67240;
        double r67242 = 3.6245075939861895e+294;
        bool r67243 = r67241 <= r67242;
        double r67244 = 1.0;
        double r67245 = r67244 / r67240;
        double r67246 = r67229 * r67245;
        double r67247 = 0.0;
        double r67248 = r67243 ? r67246 : r67247;
        return r67248;
}

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. Split input into 2 regimes

2. if (/ (+ (* (+ (* (+ (* (+ (* x y) z) y) 27464.7644705) y) 230661.510616) y) t) (+ (* (+ (* (+ (* (+ y a) y) b) y) c) y) i)) < 3.6245075939861895e+294

   1. Initial program 5.1

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

   3. Applied div-inv 5.2

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

   if 3.6245075939861895e+294 < (/ (+ (* (+ (* (+ (* (+ (* x y) z) y) 27464.7644705) y) 230661.510616) y) t) (+ (* (+ (* (+ (* (+ y a) y) b) y) c) y) i))

   1. Initial program 63.8

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

   2. Taylor expanded around 0 61.7

      \[\leadsto \color{blue}{0}\]
3. Recombined 2 regimes into one program.

4. Final simplification 28.3

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644704999984242022037506103515625\right) \cdot y + 230661.5106160000141244381666183471679688\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \le 3.62450759398618954484228470238219178564 \cdot 10^{294}:\\ \;\;\;\;\left(\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644704999984242022037506103515625\right) \cdot y + 230661.5106160000141244381666183471679688\right) \cdot y + t\right) \cdot \frac{1}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\\ \mathbf{else}:\\ \;\;\;\;0\\ \end{array}\]

Reproduce

herbie shell --seed 2019347 
(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)))