Average Error: 29.0 → 29.1
Time: 41.6s
Precision: 64
\[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644704999984242022037506103515625\right) \cdot y + 230661.5106160000141244381666183471679688\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\]
↓
\[\frac{1}{\mathsf{fma}\left(\mathsf{fma}\left(y, \mathsf{fma}\left(y, a + y, b\right), c\right), y, i\right)} \cdot \left(t + \left(y \cdot \left(y \cdot \left(z + x \cdot y\right) + 27464.7644704999984242022037506103515625\right) + 230661.5106160000141244381666183471679688\right) \cdot y\right)\]
\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{1}{\mathsf{fma}\left(\mathsf{fma}\left(y, \mathsf{fma}\left(y, a + y, b\right), c\right), y, i\right)} \cdot \left(t + \left(y \cdot \left(y \cdot \left(z + x \cdot y\right) + 27464.7644704999984242022037506103515625\right) + 230661.5106160000141244381666183471679688\right) \cdot y\right)
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r3390275 = x;
        double r3390276 = y;
        double r3390277 = r3390275 * r3390276;
        double r3390278 = z;
        double r3390279 = r3390277 + r3390278;
        double r3390280 = r3390279 * r3390276;
        double r3390281 = 27464.7644705;
        double r3390282 = r3390280 + r3390281;
        double r3390283 = r3390282 * r3390276;
        double r3390284 = 230661.510616;
        double r3390285 = r3390283 + r3390284;
        double r3390286 = r3390285 * r3390276;
        double r3390287 = t;
        double r3390288 = r3390286 + r3390287;
        double r3390289 = a;
        double r3390290 = r3390276 + r3390289;
        double r3390291 = r3390290 * r3390276;
        double r3390292 = b;
        double r3390293 = r3390291 + r3390292;
        double r3390294 = r3390293 * r3390276;
        double r3390295 = c;
        double r3390296 = r3390294 + r3390295;
        double r3390297 = r3390296 * r3390276;
        double r3390298 = i;
        double r3390299 = r3390297 + r3390298;
        double r3390300 = r3390288 / r3390299;
        return r3390300;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r3390301 = 1.0;
        double r3390302 = y;
        double r3390303 = a;
        double r3390304 = r3390303 + r3390302;
        double r3390305 = b;
        double r3390306 = fma(r3390302, r3390304, r3390305);
        double r3390307 = c;
        double r3390308 = fma(r3390302, r3390306, r3390307);
        double r3390309 = i;
        double r3390310 = fma(r3390308, r3390302, r3390309);
        double r3390311 = r3390301 / r3390310;
        double r3390312 = t;
        double r3390313 = z;
        double r3390314 = x;
        double r3390315 = r3390314 * r3390302;
        double r3390316 = r3390313 + r3390315;
        double r3390317 = r3390302 * r3390316;
        double r3390318 = 27464.7644705;
        double r3390319 = r3390317 + r3390318;
        double r3390320 = r3390302 * r3390319;
        double r3390321 = 230661.510616;
        double r3390322 = r3390320 + r3390321;
        double r3390323 = r3390322 * r3390302;
        double r3390324 = r3390312 + r3390323;
        double r3390325 = r3390311 * r3390324;
        return r3390325;
}

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 29.0

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

  3. Applied div-inv29.1

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

  4. Simplified29.1

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

  5. Final simplification29.1

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

Reproduce

herbie shell --seed 2019169 +o rules:numerics
(FPCore (x y z t a b c i)
  :name "Numeric.SpecFunctions:logGamma from math-functions-0.1.5.2"
  (/ (+ (* (+ (* (+ (* (+ (* x y) z) y) 27464.7644705) y) 230661.510616) y) t) (+ (* (+ (* (+ (* (+ y a) y) b) y) c) y) i)))