Optimisation.CirclePacking:place from circle-packing-0.1.0.4, F

Average Error: 6.1 → 0.4

Time: 14.2s

Precision: 64

Math

\[x - \frac{y \cdot \left(z - t\right)}{a}\]

↓

\[\begin{array}{l} \mathbf{if}\;y \cdot \left(z - t\right) = -\infty \lor \neg \left(y \cdot \left(z - t\right) \le 2.358413248954256348213035766917854469977 \cdot 10^{175}\right):\\ \;\;\;\;x - \frac{y}{a} \cdot \left(z - t\right)\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y \cdot \left(z - t\right)}{a}\\ \end{array}\]

C

double f(double x, double y, double z, double t, double a) {
        double r203404 = x;
        double r203405 = y;
        double r203406 = z;
        double r203407 = t;
        double r203408 = r203406 - r203407;
        double r203409 = r203405 * r203408;
        double r203410 = a;
        double r203411 = r203409 / r203410;
        double r203412 = r203404 - r203411;
        return r203412;
}

↓

double f(double x, double y, double z, double t, double a) {
        double r203413 = y;
        double r203414 = z;
        double r203415 = t;
        double r203416 = r203414 - r203415;
        double r203417 = r203413 * r203416;
        double r203418 = -inf.0;
        bool r203419 = r203417 <= r203418;
        double r203420 = 2.3584132489542563e+175;
        bool r203421 = r203417 <= r203420;
        double r203422 = !r203421;
        bool r203423 = r203419 || r203422;
        double r203424 = x;
        double r203425 = a;
        double r203426 = r203413 / r203425;
        double r203427 = r203426 * r203416;
        double r203428 = r203424 - r203427;
        double r203429 = r203417 / r203425;
        double r203430 = r203424 - r203429;
        double r203431 = r203423 ? r203428 : r203430;
        return r203431;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Bits error versus a

Target

Original	6.1
Target	0.6
Herbie	0.4

\[\begin{array}{l} \mathbf{if}\;y \lt -1.07612662163899753216593153715602325729 \cdot 10^{-10}:\\ \;\;\;\;x - \frac{1}{\frac{\frac{a}{z - t}}{y}}\\ \mathbf{elif}\;y \lt 2.894426862792089097262541964056085749132 \cdot 10^{-49}:\\ \;\;\;\;x - \frac{y \cdot \left(z - t\right)}{a}\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y}{\frac{a}{z - t}}\\ \end{array}\]

Derivation

1. Split input into 2 regimes

2. if (* y (- z t)) < -inf.0 or 2.3584132489542563e+175 < (* y (- z t))

   1. Initial program 35.2

      \[x - \frac{y \cdot \left(z - t\right)}{a}\]
   2. Using strategy rm

   3. Applied associate-/l* 1.2

      \[\leadsto x - \color{blue}{\frac{y}{\frac{a}{z - t}}}\]
   4. Using strategy rm

   5. Applied associate-/r/ 0.6

      \[\leadsto x - \color{blue}{\frac{y}{a} \cdot \left(z - t\right)}\]

   if -inf.0 < (* y (- z t)) < 2.3584132489542563e+175

   1. Initial program 0.3

      \[x - \frac{y \cdot \left(z - t\right)}{a}\]
3. Recombined 2 regimes into one program.

4. Final simplification 0.4

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot \left(z - t\right) = -\infty \lor \neg \left(y \cdot \left(z - t\right) \le 2.358413248954256348213035766917854469977 \cdot 10^{175}\right):\\ \;\;\;\;x - \frac{y}{a} \cdot \left(z - t\right)\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y \cdot \left(z - t\right)}{a}\\ \end{array}\]

Reproduce

herbie shell --seed 2019326 
(FPCore (x y z t a)
  :name "Optimisation.CirclePacking:place from circle-packing-0.1.0.4, F"
  :precision binary64

  :herbie-target
  (if (< y -1.0761266216389975e-10) (- x (/ 1 (/ (/ a (- z t)) y))) (if (< y 2.894426862792089e-49) (- x (/ (* y (- z t)) a)) (- x (/ y (/ a (- z t))))))

  (- x (/ (* y (- z t)) a)))