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

Average Error: 6.0 → 0.6

Time: 13.8s

Precision: 64

Math

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

↓

\[\begin{array}{l} \mathbf{if}\;y \cdot \left(z - t\right) \le -5.119477841408171396085043863595344733691 \cdot 10^{134} \lor \neg \left(y \cdot \left(z - t\right) \le 2.663318528556724753017733536745886284962 \cdot 10^{296}\right):\\ \;\;\;\;x - \frac{y}{a} \cdot \left(z - t\right)\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y \cdot \left(z - t\right)}{a}\\ \end{array}\]

C

double f(double x, double y, double z, double t, double a) {
        double r235771 = x;
        double r235772 = y;
        double r235773 = z;
        double r235774 = t;
        double r235775 = r235773 - r235774;
        double r235776 = r235772 * r235775;
        double r235777 = a;
        double r235778 = r235776 / r235777;
        double r235779 = r235771 - r235778;
        return r235779;
}

↓

double f(double x, double y, double z, double t, double a) {
        double r235780 = y;
        double r235781 = z;
        double r235782 = t;
        double r235783 = r235781 - r235782;
        double r235784 = r235780 * r235783;
        double r235785 = -5.119477841408171e+134;
        bool r235786 = r235784 <= r235785;
        double r235787 = 2.6633185285567248e+296;
        bool r235788 = r235784 <= r235787;
        double r235789 = !r235788;
        bool r235790 = r235786 || r235789;
        double r235791 = x;
        double r235792 = a;
        double r235793 = r235780 / r235792;
        double r235794 = r235793 * r235783;
        double r235795 = r235791 - r235794;
        double r235796 = r235784 / r235792;
        double r235797 = r235791 - r235796;
        double r235798 = r235790 ? r235795 : r235797;
        return r235798;
}

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	0.6

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

Derivation

1. Split input into 2 regimes

2. if (* y (- z t)) < -5.119477841408171e+134 or 2.6633185285567248e+296 < (* y (- z t))

   1. Initial program 28.8

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

   3. Applied associate-/l* 2.0

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

   5. Applied associate-/r/ 1.2

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

   if -5.119477841408171e+134 < (* y (- z t)) < 2.6633185285567248e+296

   1. Initial program 0.4

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

4. Final simplification 0.6

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot \left(z - t\right) \le -5.119477841408171396085043863595344733691 \cdot 10^{134} \lor \neg \left(y \cdot \left(z - t\right) \le 2.663318528556724753017733536745886284962 \cdot 10^{296}\right):\\ \;\;\;\;x - \frac{y}{a} \cdot \left(z - t\right)\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y \cdot \left(z - t\right)}{a}\\ \end{array}\]

Reproduce

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

  :herbie-target
  (if (< y -1.07612662163899753e-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)))