Average Error: 28.1 → 28.1
Time: 34.1s
Precision: 64
\[\frac{\left(\left(\left(x \cdot y + z\right) \cdot y + 27464.7644705\right) \cdot y + 230661.510616\right) \cdot y + t}{\left(\left(\left(y + a\right) \cdot y + b\right) \cdot y + c\right) \cdot y + i}\]
↓
\[\frac{1}{\mathsf{fma}\left(\left(\mathsf{fma}\left(y, \left(\mathsf{fma}\left(\left(y + a\right), y, b\right)\right), c\right)\right), y, i\right)} \cdot \mathsf{fma}\left(y, \left(\mathsf{fma}\left(y, \left(\mathsf{fma}\left(y, \left(\mathsf{fma}\left(y, x, z\right)\right), 27464.7644705\right)\right), 230661.510616\right)\right), t\right)\]
\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{1}{\mathsf{fma}\left(\left(\mathsf{fma}\left(y, \left(\mathsf{fma}\left(\left(y + a\right), y, b\right)\right), c\right)\right), y, i\right)} \cdot \mathsf{fma}\left(y, \left(\mathsf{fma}\left(y, \left(\mathsf{fma}\left(y, \left(\mathsf{fma}\left(y, x, z\right)\right), 27464.7644705\right)\right), 230661.510616\right)\right), t\right)
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r2469395 = x;
        double r2469396 = y;
        double r2469397 = r2469395 * r2469396;
        double r2469398 = z;
        double r2469399 = r2469397 + r2469398;
        double r2469400 = r2469399 * r2469396;
        double r2469401 = 27464.7644705;
        double r2469402 = r2469400 + r2469401;
        double r2469403 = r2469402 * r2469396;
        double r2469404 = 230661.510616;
        double r2469405 = r2469403 + r2469404;
        double r2469406 = r2469405 * r2469396;
        double r2469407 = t;
        double r2469408 = r2469406 + r2469407;
        double r2469409 = a;
        double r2469410 = r2469396 + r2469409;
        double r2469411 = r2469410 * r2469396;
        double r2469412 = b;
        double r2469413 = r2469411 + r2469412;
        double r2469414 = r2469413 * r2469396;
        double r2469415 = c;
        double r2469416 = r2469414 + r2469415;
        double r2469417 = r2469416 * r2469396;
        double r2469418 = i;
        double r2469419 = r2469417 + r2469418;
        double r2469420 = r2469408 / r2469419;
        return r2469420;
}
↓
double f(double x, double y, double z, double t, double a, double b, double c, double i) {
        double r2469421 = 1.0;
        double r2469422 = y;
        double r2469423 = a;
        double r2469424 = r2469422 + r2469423;
        double r2469425 = b;
        double r2469426 = fma(r2469424, r2469422, r2469425);
        double r2469427 = c;
        double r2469428 = fma(r2469422, r2469426, r2469427);
        double r2469429 = i;
        double r2469430 = fma(r2469428, r2469422, r2469429);
        double r2469431 = r2469421 / r2469430;
        double r2469432 = x;
        double r2469433 = z;
        double r2469434 = fma(r2469422, r2469432, r2469433);
        double r2469435 = 27464.7644705;
        double r2469436 = fma(r2469422, r2469434, r2469435);
        double r2469437 = 230661.510616;
        double r2469438 = fma(r2469422, r2469436, r2469437);
        double r2469439 = t;
        double r2469440 = fma(r2469422, r2469438, r2469439);
        double r2469441 = r2469431 * r2469440;
        return r2469441;
}

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 28.1

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

  2. Simplified28.1

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

  4. Applied div-inv28.1

    \[\leadsto \color{blue}{\mathsf{fma}\left(y, \left(\mathsf{fma}\left(y, \left(\mathsf{fma}\left(y, \left(\mathsf{fma}\left(y, x, z\right)\right), 27464.7644705\right)\right), 230661.510616\right)\right), t\right) \cdot \frac{1}{\mathsf{fma}\left(\left(\mathsf{fma}\left(y, \left(\mathsf{fma}\left(\left(y + a\right), y, b\right)\right), c\right)\right), y, i\right)}}\]

  5. Final simplification28.1

    \[\leadsto \frac{1}{\mathsf{fma}\left(\left(\mathsf{fma}\left(y, \left(\mathsf{fma}\left(\left(y + a\right), y, b\right)\right), c\right)\right), y, i\right)} \cdot \mathsf{fma}\left(y, \left(\mathsf{fma}\left(y, \left(\mathsf{fma}\left(y, \left(\mathsf{fma}\left(y, x, z\right)\right), 27464.7644705\right)\right), 230661.510616\right)\right), t\right)\]

Reproduce

herbie shell --seed 2019133 +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)))