Diagrams.Solve.Polynomial:cubForm from diagrams-solve-0.1, A

Average Error: 3.4 → 0.3

Time: 20.1s

Precision: 64

Math

\[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b\]

↓

\[\begin{array}{l} \mathbf{if}\;\left(y \cdot 9\right) \cdot z = -\infty:\\ \;\;\;\;\left(x \cdot 2 - y \cdot \left(9 \cdot \left(z \cdot t\right)\right)\right) + \left(a \cdot 27\right) \cdot b\\ \mathbf{elif}\;\left(y \cdot 9\right) \cdot z \le 2.262366288556408035237151108670047605634 \cdot 10^{267}:\\ \;\;\;\;\left(2 \cdot x + 27 \cdot \left(a \cdot b\right)\right) - 9 \cdot \left(t \cdot \left(z \cdot y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot 2 - y \cdot \left(9 \cdot \left(z \cdot t\right)\right)\right) + \left(a \cdot 27\right) \cdot b\\ \end{array}\]

C

double f(double x, double y, double z, double t, double a, double b) {
        double r261108335 = x;
        double r261108336 = 2.0;
        double r261108337 = r261108335 * r261108336;
        double r261108338 = y;
        double r261108339 = 9.0;
        double r261108340 = r261108338 * r261108339;
        double r261108341 = z;
        double r261108342 = r261108340 * r261108341;
        double r261108343 = t;
        double r261108344 = r261108342 * r261108343;
        double r261108345 = r261108337 - r261108344;
        double r261108346 = a;
        double r261108347 = 27.0;
        double r261108348 = r261108346 * r261108347;
        double r261108349 = b;
        double r261108350 = r261108348 * r261108349;
        double r261108351 = r261108345 + r261108350;
        return r261108351;
}

↓

double f(double x, double y, double z, double t, double a, double b) {
        double r261108352 = y;
        double r261108353 = 9.0;
        double r261108354 = r261108352 * r261108353;
        double r261108355 = z;
        double r261108356 = r261108354 * r261108355;
        double r261108357 = -inf.0;
        bool r261108358 = r261108356 <= r261108357;
        double r261108359 = x;
        double r261108360 = 2.0;
        double r261108361 = r261108359 * r261108360;
        double r261108362 = t;
        double r261108363 = r261108355 * r261108362;
        double r261108364 = r261108353 * r261108363;
        double r261108365 = r261108352 * r261108364;
        double r261108366 = r261108361 - r261108365;
        double r261108367 = a;
        double r261108368 = 27.0;
        double r261108369 = r261108367 * r261108368;
        double r261108370 = b;
        double r261108371 = r261108369 * r261108370;
        double r261108372 = r261108366 + r261108371;
        double r261108373 = 2.262366288556408e+267;
        bool r261108374 = r261108356 <= r261108373;
        double r261108375 = r261108360 * r261108359;
        double r261108376 = r261108367 * r261108370;
        double r261108377 = r261108368 * r261108376;
        double r261108378 = r261108375 + r261108377;
        double r261108379 = r261108355 * r261108352;
        double r261108380 = r261108362 * r261108379;
        double r261108381 = r261108353 * r261108380;
        double r261108382 = r261108378 - r261108381;
        double r261108383 = r261108374 ? r261108382 : r261108372;
        double r261108384 = r261108358 ? r261108372 : r261108383;
        return r261108384;
}

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

Target

Original	3.4
Target	2.4
Herbie	0.3

\[\begin{array}{l} \mathbf{if}\;y \lt 7.590524218811188954625810696587370427881 \cdot 10^{-161}:\\ \;\;\;\;\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + a \cdot \left(27 \cdot b\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot 2 - 9 \cdot \left(y \cdot \left(t \cdot z\right)\right)\right) + \left(a \cdot 27\right) \cdot b\\ \end{array}\]

Derivation

1. Split input into 2 regimes

2. if (* (* y 9.0) z) < -inf.0 or 2.262366288556408e+267 < (* (* y 9.0) z)

   1. Initial program 49.5

      \[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b\]
   2. Using strategy rm

   3. Applied associate-*l* 1.8

      \[\leadsto \left(x \cdot 2 - \color{blue}{\left(y \cdot 9\right) \cdot \left(z \cdot t\right)}\right) + \left(a \cdot 27\right) \cdot b\]
   4. Using strategy rm

   5. Applied associate-*l* 0.5

      \[\leadsto \left(x \cdot 2 - \color{blue}{y \cdot \left(9 \cdot \left(z \cdot t\right)\right)}\right) + \left(a \cdot 27\right) \cdot b\]

   if -inf.0 < (* (* y 9.0) z) < 2.262366288556408e+267

   1. Initial program 0.4

      \[\left(x \cdot 2 - \left(\left(y \cdot 9\right) \cdot z\right) \cdot t\right) + \left(a \cdot 27\right) \cdot b\]

   2. Taylor expanded around inf 0.3

      \[\leadsto \color{blue}{\left(2 \cdot x + 27 \cdot \left(a \cdot b\right)\right) - 9 \cdot \left(t \cdot \left(z \cdot y\right)\right)}\]
3. Recombined 2 regimes into one program.

4. Final simplification 0.3

   \[\leadsto \begin{array}{l} \mathbf{if}\;\left(y \cdot 9\right) \cdot z = -\infty:\\ \;\;\;\;\left(x \cdot 2 - y \cdot \left(9 \cdot \left(z \cdot t\right)\right)\right) + \left(a \cdot 27\right) \cdot b\\ \mathbf{elif}\;\left(y \cdot 9\right) \cdot z \le 2.262366288556408035237151108670047605634 \cdot 10^{267}:\\ \;\;\;\;\left(2 \cdot x + 27 \cdot \left(a \cdot b\right)\right) - 9 \cdot \left(t \cdot \left(z \cdot y\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\left(x \cdot 2 - y \cdot \left(9 \cdot \left(z \cdot t\right)\right)\right) + \left(a \cdot 27\right) \cdot b\\ \end{array}\]

Reproduce

herbie shell --seed 2019173 
(FPCore (x y z t a b)
  :name "Diagrams.Solve.Polynomial:cubForm  from diagrams-solve-0.1, A"

  :herbie-target
  (if (< y 7.590524218811189e-161) (+ (- (* x 2.0) (* (* (* y 9.0) z) t)) (* a (* 27.0 b))) (+ (- (* x 2.0) (* 9.0 (* y (* t z)))) (* (* a 27.0) b)))

  (+ (- (* x 2.0) (* (* (* y 9.0) z) t)) (* (* a 27.0) b)))