Average Error: 29.2 → 29.2
Time: 26.6s
Precision: 64
\[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644704999984242022037506103515625\right) \cdot y + 230661.5106160000141244381666183471679688\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\]
↓
\[\frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x, y, z\right), y, 27464.7644704999984242022037506103515625\right), y, 230661.5106160000141244381666183471679688\right), y, t\right)}{\mathsf{fma}\left(\mathsf{fma}\left(y \cdot y, a, y \cdot \left(y \cdot y + b\right)\right) + c, y, i\right)}\]
\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{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x, y, z\right), y, 27464.7644704999984242022037506103515625\right), y, 230661.5106160000141244381666183471679688\right), y, t\right)}{\mathsf{fma}\left(\mathsf{fma}\left(y \cdot y, a, y \cdot \left(y \cdot y + b\right)\right) + c, y, i\right)}
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r3282341 = x;
        double r3282342 = y;
        double r3282343 = r3282341 * r3282342;
        double r3282344 = z;
        double r3282345 = r3282343 + r3282344;
        double r3282346 = r3282345 * r3282342;
        double r3282347 = 27464.7644705;
        double r3282348 = r3282346 + r3282347;
        double r3282349 = r3282348 * r3282342;
        double r3282350 = 230661.510616;
        double r3282351 = r3282349 + r3282350;
        double r3282352 = r3282351 * r3282342;
        double r3282353 = t;
        double r3282354 = r3282352 + r3282353;
        double r3282355 = a;
        double r3282356 = r3282342 + r3282355;
        double r3282357 = r3282356 * r3282342;
        double r3282358 = b;
        double r3282359 = r3282357 + r3282358;
        double r3282360 = r3282359 * r3282342;
        double r3282361 = c;
        double r3282362 = r3282360 + r3282361;
        double r3282363 = r3282362 * r3282342;
        double r3282364 = i;
        double r3282365 = r3282363 + r3282364;
        double r3282366 = r3282354 / r3282365;
        return r3282366;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r3282367 = x;
        double r3282368 = y;
        double r3282369 = z;
        double r3282370 = fma(r3282367, r3282368, r3282369);
        double r3282371 = 27464.7644705;
        double r3282372 = fma(r3282370, r3282368, r3282371);
        double r3282373 = 230661.510616;
        double r3282374 = fma(r3282372, r3282368, r3282373);
        double r3282375 = t;
        double r3282376 = fma(r3282374, r3282368, r3282375);
        double r3282377 = r3282368 * r3282368;
        double r3282378 = a;
        double r3282379 = b;
        double r3282380 = r3282377 + r3282379;
        double r3282381 = r3282368 * r3282380;
        double r3282382 = fma(r3282377, r3282378, r3282381);
        double r3282383 = c;
        double r3282384 = r3282382 + r3282383;
        double r3282385 = i;
        double r3282386 = fma(r3282384, r3282368, r3282385);
        double r3282387 = r3282376 / r3282386;
        return r3282387;
}

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 29.2

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

  2. Simplified29.2

    \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x, y, z\right), y, 27464.7644704999984242022037506103515625\right), y, 230661.5106160000141244381666183471679688\right), y, t\right)}{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(y + a, y, b\right), y, c\right), y, i\right)}}\]
  3. Using strategy rm

  4. Applied fma-udef29.2

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

  5. Taylor expanded around inf 29.3

    \[\leadsto \frac{\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(\mathsf{fma}\left(x, y, z\right), y, 27464.7644704999984242022037506103515625\right), y, 230661.5106160000141244381666183471679688\right), y, t\right)}{\mathsf{fma}\left(\color{blue}{\left(a \cdot {y}^{2} + \left({y}^{3} + y \cdot b\right)\right)} + c, y, i\right)}\]

  6. Simplified29.2

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

  7. Final simplification29.2

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

Reproduce

herbie shell --seed 2019174 +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)))