Average Error: 28.2 → 28.2
Time: 37.8s
Precision: 64
\[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\]
↓
\[\frac{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, x, z\right), 27464.7644705\right), 230661.510616\right), t\right)}{\mathsf{fma}\left(\mathsf{fma}\left(y, \mathsf{fma}\left(y + a, y, b\right), c\right), y, i\right)}\]
\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\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(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, x, z\right), 27464.7644705\right), 230661.510616\right), t\right)}{\mathsf{fma}\left(\mathsf{fma}\left(y, \mathsf{fma}\left(y + a, y, b\right), c\right), y, i\right)}
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r2613375 = x;
        double r2613376 = y;
        double r2613377 = r2613375 * r2613376;
        double r2613378 = z;
        double r2613379 = r2613377 + r2613378;
        double r2613380 = r2613379 * r2613376;
        double r2613381 = 27464.7644705;
        double r2613382 = r2613380 + r2613381;
        double r2613383 = r2613382 * r2613376;
        double r2613384 = 230661.510616;
        double r2613385 = r2613383 + r2613384;
        double r2613386 = r2613385 * r2613376;
        double r2613387 = t;
        double r2613388 = r2613386 + r2613387;
        double r2613389 = a;
        double r2613390 = r2613376 + r2613389;
        double r2613391 = r2613390 * r2613376;
        double r2613392 = b;
        double r2613393 = r2613391 + r2613392;
        double r2613394 = r2613393 * r2613376;
        double r2613395 = c;
        double r2613396 = r2613394 + r2613395;
        double r2613397 = r2613396 * r2613376;
        double r2613398 = i;
        double r2613399 = r2613397 + r2613398;
        double r2613400 = r2613388 / r2613399;
        return r2613400;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r2613401 = y;
        double r2613402 = x;
        double r2613403 = z;
        double r2613404 = fma(r2613401, r2613402, r2613403);
        double r2613405 = 27464.7644705;
        double r2613406 = fma(r2613401, r2613404, r2613405);
        double r2613407 = 230661.510616;
        double r2613408 = fma(r2613401, r2613406, r2613407);
        double r2613409 = t;
        double r2613410 = fma(r2613401, r2613408, r2613409);
        double r2613411 = a;
        double r2613412 = r2613401 + r2613411;
        double r2613413 = b;
        double r2613414 = fma(r2613412, r2613401, r2613413);
        double r2613415 = c;
        double r2613416 = fma(r2613401, r2613414, r2613415);
        double r2613417 = i;
        double r2613418 = fma(r2613416, r2613401, r2613417);
        double r2613419 = r2613410 / r2613418;
        return r2613419;
}

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 28.2

    \[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\]

  2. Simplified28.2

    \[\leadsto \color{blue}{\frac{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, x, z\right), 27464.7644705\right), 230661.510616\right), t\right)}{\mathsf{fma}\left(\mathsf{fma}\left(y, \mathsf{fma}\left(y + a, y, b\right), c\right), y, i\right)}}\]

  3. Final simplification28.2

    \[\leadsto \frac{\mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, \mathsf{fma}\left(y, x, z\right), 27464.7644705\right), 230661.510616\right), t\right)}{\mathsf{fma}\left(\mathsf{fma}\left(y, \mathsf{fma}\left(y + a, y, b\right), c\right), y, i\right)}\]

Reproduce

herbie shell --seed 2019144 +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)))