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

Average Error: 5.7 → 0.6

Time: 15.6s

Precision: 64

Math

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

↓

\[\begin{array}{l} \mathbf{if}\;y \cdot \left(z - t\right) \le -6.4435085564630181 \cdot 10^{176} \lor \neg \left(y \cdot \left(z - t\right) \le 3.04984407197611456 \cdot 10^{197}\right):\\ \;\;\;\;x + y \cdot \frac{z - t}{a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \left(z - t\right)}{a}\\ \end{array}\]

C

double f(double x, double y, double z, double t, double a) {
        double r225863 = x;
        double r225864 = y;
        double r225865 = z;
        double r225866 = t;
        double r225867 = r225865 - r225866;
        double r225868 = r225864 * r225867;
        double r225869 = a;
        double r225870 = r225868 / r225869;
        double r225871 = r225863 + r225870;
        return r225871;
}

↓

double f(double x, double y, double z, double t, double a) {
        double r225872 = y;
        double r225873 = z;
        double r225874 = t;
        double r225875 = r225873 - r225874;
        double r225876 = r225872 * r225875;
        double r225877 = -6.443508556463018e+176;
        bool r225878 = r225876 <= r225877;
        double r225879 = 3.0498440719761146e+197;
        bool r225880 = r225876 <= r225879;
        double r225881 = !r225880;
        bool r225882 = r225878 || r225881;
        double r225883 = x;
        double r225884 = a;
        double r225885 = r225875 / r225884;
        double r225886 = r225872 * r225885;
        double r225887 = r225883 + r225886;
        double r225888 = r225876 / r225884;
        double r225889 = r225883 + r225888;
        double r225890 = r225882 ? r225887 : r225889;
        return r225890;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Bits error versus a

Target

Original	5.7
Target	0.6
Herbie	0.6

\[\begin{array}{l} \mathbf{if}\;y \lt -1.07612662163899753 \cdot 10^{-10}:\\ \;\;\;\;x + \frac{1}{\frac{\frac{a}{z - t}}{y}}\\ \mathbf{elif}\;y \lt 2.8944268627920891 \cdot 10^{-49}:\\ \;\;\;\;x + \frac{y \cdot \left(z - t\right)}{a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\frac{a}{z - t}}\\ \end{array}\]

Derivation

1. Split input into 2 regimes

2. if (* y (- z t)) < -6.443508556463018e+176 or 3.0498440719761146e+197 < (* y (- z t))

   1. Initial program 25.3

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

   3. Applied *-un-lft-identity 25.3

      \[\leadsto x + \frac{y \cdot \left(z - t\right)}{\color{blue}{1 \cdot a}}\]

   4. Applied times-frac 1.4

      \[\leadsto x + \color{blue}{\frac{y}{1} \cdot \frac{z - t}{a}}\]

   5. Simplified 1.4

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

   if -6.443508556463018e+176 < (* y (- z t)) < 3.0498440719761146e+197

   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

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \cdot \left(z - t\right) \le -6.4435085564630181 \cdot 10^{176} \lor \neg \left(y \cdot \left(z - t\right) \le 3.04984407197611456 \cdot 10^{197}\right):\\ \;\;\;\;x + y \cdot \frac{z - t}{a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \left(z - t\right)}{a}\\ \end{array}\]

Reproduce

herbie shell --seed 2019198 
(FPCore (x y z t a)
  :name "Optimisation.CirclePacking:place from circle-packing-0.1.0.4, E"

  :herbie-target
  (if (< y -1.0761266216389975e-10) (+ x (/ 1.0 (/ (/ a (- z t)) y))) (if (< y 2.894426862792089e-49) (+ x (/ (* y (- z t)) a)) (+ x (/ y (/ a (- z t))))))

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