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

Average Error: 6.0 → 0.5

Time: 12.6s

Precision: 64

Math

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

↓

\[\begin{array}{l} \mathbf{if}\;y \cdot \left(z - t\right) \le -5.434306758875114331318867771849536485386 \cdot 10^{152} \lor \neg \left(y \cdot \left(z - t\right) \le 2.663318528556724753017733536745886284962 \cdot 10^{296}\right):\\ \;\;\;\;x + \frac{y}{a} \cdot \left(z - t\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{1}{\frac{a}{y \cdot \left(z - t\right)}}\\ \end{array}\]

C

double f(double x, double y, double z, double t, double a) {
        double r280977 = x;
        double r280978 = y;
        double r280979 = z;
        double r280980 = t;
        double r280981 = r280979 - r280980;
        double r280982 = r280978 * r280981;
        double r280983 = a;
        double r280984 = r280982 / r280983;
        double r280985 = r280977 + r280984;
        return r280985;
}

↓

double f(double x, double y, double z, double t, double a) {
        double r280986 = y;
        double r280987 = z;
        double r280988 = t;
        double r280989 = r280987 - r280988;
        double r280990 = r280986 * r280989;
        double r280991 = -5.434306758875114e+152;
        bool r280992 = r280990 <= r280991;
        double r280993 = 2.6633185285567248e+296;
        bool r280994 = r280990 <= r280993;
        double r280995 = !r280994;
        bool r280996 = r280992 || r280995;
        double r280997 = x;
        double r280998 = a;
        double r280999 = r280986 / r280998;
        double r281000 = r280999 * r280989;
        double r281001 = r280997 + r281000;
        double r281002 = 1.0;
        double r281003 = r280998 / r280990;
        double r281004 = r281002 / r281003;
        double r281005 = r280997 + r281004;
        double r281006 = r280996 ? r281001 : r281005;
        return r281006;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Bits error versus a

Target

Original	6.0
Target	0.7
Herbie	0.5

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

Derivation

1. Split input into 2 regimes

2. if (* y (- z t)) < -5.434306758875114e+152 or 2.6633185285567248e+296 < (* y (- z t))

   1. Initial program 31.0

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

   3. Applied associate-/l* 1.8

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

   5. Applied associate-/r/ 0.9

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

   if -5.434306758875114e+152 < (* y (- z t)) < 2.6633185285567248e+296

   1. Initial program 0.4

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

   3. Applied clear-num 0.4

      \[\leadsto x + \color{blue}{\frac{1}{\frac{a}{y \cdot \left(z - t\right)}}}\]
3. Recombined 2 regimes into one program.

4. Final simplification 0.5

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot \left(z - t\right) \le -5.434306758875114331318867771849536485386 \cdot 10^{152} \lor \neg \left(y \cdot \left(z - t\right) \le 2.663318528556724753017733536745886284962 \cdot 10^{296}\right):\\ \;\;\;\;x + \frac{y}{a} \cdot \left(z - t\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{1}{\frac{a}{y \cdot \left(z - t\right)}}\\ \end{array}\]

Reproduce

herbie shell --seed 2019304 
(FPCore (x y z t a)
  :name "Optimisation.CirclePacking:place from circle-packing-0.1.0.4, E"
  :precision binary64

  :herbie-target
  (if (< y -1.07612662163899753e-10) (+ x (/ 1 (/ (/ a (- z t)) y))) (if (< y 2.8944268627920891e-49) (+ x (/ (* y (- z t)) a)) (+ x (/ y (/ a (- z t))))))

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