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

Average Error: 6.0 → 0.8

Time: 15.2s

Precision: 64

Math

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

↓

\[\begin{array}{l} \mathbf{if}\;\frac{y \cdot \left(z - t\right)}{a} \le -8.963886535039347471937028690168546917254 \cdot 10^{299} \lor \neg \left(\frac{y \cdot \left(z - t\right)}{a} \le 1.947585218067920906632704854880810808419 \cdot 10^{229}\right):\\ \;\;\;\;x - \frac{y}{a} \cdot \left(z - t\right)\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y \cdot \left(z - t\right)}{a}\\ \end{array}\]

C

double f(double x, double y, double z, double t, double a) {
        double r219834 = x;
        double r219835 = y;
        double r219836 = z;
        double r219837 = t;
        double r219838 = r219836 - r219837;
        double r219839 = r219835 * r219838;
        double r219840 = a;
        double r219841 = r219839 / r219840;
        double r219842 = r219834 - r219841;
        return r219842;
}

↓

double f(double x, double y, double z, double t, double a) {
        double r219843 = y;
        double r219844 = z;
        double r219845 = t;
        double r219846 = r219844 - r219845;
        double r219847 = r219843 * r219846;
        double r219848 = a;
        double r219849 = r219847 / r219848;
        double r219850 = -8.963886535039347e+299;
        bool r219851 = r219849 <= r219850;
        double r219852 = 1.947585218067921e+229;
        bool r219853 = r219849 <= r219852;
        double r219854 = !r219853;
        bool r219855 = r219851 || r219854;
        double r219856 = x;
        double r219857 = r219843 / r219848;
        double r219858 = r219857 * r219846;
        double r219859 = r219856 - r219858;
        double r219860 = r219856 - r219849;
        double r219861 = r219855 ? r219859 : r219860;
        return r219861;
}

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	0.8

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

Derivation

1. Split input into 2 regimes

2. if (/ (* y (- z t)) a) < -8.963886535039347e+299 or 1.947585218067921e+229 < (/ (* y (- z t)) a)

   1. Initial program 41.8

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

   3. Applied associate-/l* 9.0

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

   5. Applied associate-/r/ 3.6

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

   if -8.963886535039347e+299 < (/ (* y (- z t)) a) < 1.947585218067921e+229

   1. Initial program 0.4

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

4. Final simplification 0.8

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y \cdot \left(z - t\right)}{a} \le -8.963886535039347471937028690168546917254 \cdot 10^{299} \lor \neg \left(\frac{y \cdot \left(z - t\right)}{a} \le 1.947585218067920906632704854880810808419 \cdot 10^{229}\right):\\ \;\;\;\;x - \frac{y}{a} \cdot \left(z - t\right)\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y \cdot \left(z - t\right)}{a}\\ \end{array}\]

Reproduce

herbie shell --seed 2019325 
(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)))