Numeric.SpecFunctions:logGamma from math-functions-0.1.5.2

Average Error: 29.4 → 28.6

Time: 17.5s

Precision: 64

• Falling back on racket egraph because egg-herbie package not installed

Math

\[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.764470499998\right) \cdot y + 230661.510616000014\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\]

↓

\[\begin{array}{l} \mathbf{if}\;\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.764470499998\right) \cdot y + 230661.510616000014\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \le 2.1539959223483919 \cdot 10^{306}:\\ \;\;\;\;\frac{\left(\left(\sqrt[3]{\left(\left(x \cdot y + z\right) \cdot y + 27464.764470499998\right) \cdot y} \cdot \sqrt[3]{\left(\left(x \cdot y + z\right) \cdot y + 27464.764470499998\right) \cdot y}\right) \cdot \sqrt[3]{\left(\left(x \cdot y + z\right) \cdot y + 27464.764470499998\right) \cdot y} + 230661.510616000014\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\\ \mathbf{else}:\\ \;\;\;\;0\\ \end{array}\]

C

double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r77304 = x;
        double r77305 = y;
        double r77306 = r77304 * r77305;
        double r77307 = z;
        double r77308 = r77306 + r77307;
        double r77309 = r77308 * r77305;
        double r77310 = 27464.7644705;
        double r77311 = r77309 + r77310;
        double r77312 = r77311 * r77305;
        double r77313 = 230661.510616;
        double r77314 = r77312 + r77313;
        double r77315 = r77314 * r77305;
        double r77316 = t;
        double r77317 = r77315 + r77316;
        double r77318 = a;
        double r77319 = r77305 + r77318;
        double r77320 = r77319 * r77305;
        double r77321 = b;
        double r77322 = r77320 + r77321;
        double r77323 = r77322 * r77305;
        double r77324 = c;
        double r77325 = r77323 + r77324;
        double r77326 = r77325 * r77305;
        double r77327 = i;
        double r77328 = r77326 + r77327;
        double r77329 = r77317 / r77328;
        return r77329;
}

↓

double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r77330 = x;
        double r77331 = y;
        double r77332 = r77330 * r77331;
        double r77333 = z;
        double r77334 = r77332 + r77333;
        double r77335 = r77334 * r77331;
        double r77336 = 27464.7644705;
        double r77337 = r77335 + r77336;
        double r77338 = r77337 * r77331;
        double r77339 = 230661.510616;
        double r77340 = r77338 + r77339;
        double r77341 = r77340 * r77331;
        double r77342 = t;
        double r77343 = r77341 + r77342;
        double r77344 = a;
        double r77345 = r77331 + r77344;
        double r77346 = r77345 * r77331;
        double r77347 = b;
        double r77348 = r77346 + r77347;
        double r77349 = r77348 * r77331;
        double r77350 = c;
        double r77351 = r77349 + r77350;
        double r77352 = r77351 * r77331;
        double r77353 = i;
        double r77354 = r77352 + r77353;
        double r77355 = r77343 / r77354;
        double r77356 = 2.153995922348392e+306;
        bool r77357 = r77355 <= r77356;
        double r77358 = cbrt(r77338);
        double r77359 = r77358 * r77358;
        double r77360 = r77359 * r77358;
        double r77361 = r77360 + r77339;
        double r77362 = r77361 * r77331;
        double r77363 = r77362 + r77342;
        double r77364 = r77363 / r77354;
        double r77365 = 0.0;
        double r77366 = r77357 ? r77364 : r77365;
        return r77366;
}

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)) < 2.153995922348392e+306

   1. Initial program 5.8

      \[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.764470499998\right) \cdot y + 230661.510616000014\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\]
   2. Using strategy rm

   3. Applied add-cube-cbrt 6.0

      \[\leadsto \frac{\left(\color{blue}{\left(\sqrt[3]{\left(\left(x \cdot y + z\right) \cdot y + 27464.764470499998\right) \cdot y} \cdot \sqrt[3]{\left(\left(x \cdot y + z\right) \cdot y + 27464.764470499998\right) \cdot y}\right) \cdot \sqrt[3]{\left(\left(x \cdot y + z\right) \cdot y + 27464.764470499998\right) \cdot y}} + 230661.510616000014\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\]

   if 2.153995922348392e+306 < (/ (+ (* (+ (* (+ (* (+ (* x y) z) y) 27464.7644705) y) 230661.510616) y) t) (+ (* (+ (* (+ (* (+ y a) y) b) y) c) y) i))

   1. Initial program 64.0

      \[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.764470499998\right) \cdot y + 230661.510616000014\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\]

   2. Taylor expanded around 0 61.8

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

4. Final simplification 28.6

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.764470499998\right) \cdot y + 230661.510616000014\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i} \le 2.1539959223483919 \cdot 10^{306}:\\ \;\;\;\;\frac{\left(\left(\sqrt[3]{\left(\left(x \cdot y + z\right) \cdot y + 27464.764470499998\right) \cdot y} \cdot \sqrt[3]{\left(\left(x \cdot y + z\right) \cdot y + 27464.764470499998\right) \cdot y}\right) \cdot \sqrt[3]{\left(\left(x \cdot y + z\right) \cdot y + 27464.764470499998\right) \cdot y} + 230661.510616000014\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\\ \mathbf{else}:\\ \;\;\;\;0\\ \end{array}\]

Reproduce

herbie shell --seed 2020042 
(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)))