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

Average Error: 6.1 → 1.5

Time: 10.8s

Precision: 64

Math

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

↓

\[\begin{array}{l} \mathbf{if}\;\frac{y \cdot \left(z - t\right)}{a} \le -5.562195680964302490149328614550000366002 \cdot 10^{178} \lor \neg \left(\frac{y \cdot \left(z - t\right)}{a} \le 1.33178471273020163591162836894697555885 \cdot 10^{-49}\right):\\ \;\;\;\;x + \left(-\left(z - t\right) \cdot \frac{y}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y \cdot \left(z - t\right)}{a}\\ \end{array}\]

C

double f(double x, double y, double z, double t, double a) {
        double r888132 = x;
        double r888133 = y;
        double r888134 = z;
        double r888135 = t;
        double r888136 = r888134 - r888135;
        double r888137 = r888133 * r888136;
        double r888138 = a;
        double r888139 = r888137 / r888138;
        double r888140 = r888132 - r888139;
        return r888140;
}

↓

double f(double x, double y, double z, double t, double a) {
        double r888141 = y;
        double r888142 = z;
        double r888143 = t;
        double r888144 = r888142 - r888143;
        double r888145 = r888141 * r888144;
        double r888146 = a;
        double r888147 = r888145 / r888146;
        double r888148 = -5.5621956809643025e+178;
        bool r888149 = r888147 <= r888148;
        double r888150 = 1.3317847127302016e-49;
        bool r888151 = r888147 <= r888150;
        double r888152 = !r888151;
        bool r888153 = r888149 || r888152;
        double r888154 = x;
        double r888155 = r888141 / r888146;
        double r888156 = r888144 * r888155;
        double r888157 = -r888156;
        double r888158 = r888154 + r888157;
        double r888159 = r888154 - r888147;
        double r888160 = r888153 ? r888158 : r888159;
        return r888160;
}

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	0.7
Herbie	1.5

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

Derivation

1. Split input into 2 regimes

2. if (/ (* y (- z t)) a) < -5.5621956809643025e+178 or 1.3317847127302016e-49 < (/ (* y (- z t)) a)

   1. Initial program 13.8

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

   3. Applied clear-num 13.8

      \[\leadsto x - \color{blue}{\frac{1}{\frac{a}{y \cdot \left(z - t\right)}}}\]
   4. Using strategy rm

   5. Applied sub-neg 13.8

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

   6. Simplified 2.7

      \[\leadsto x + \color{blue}{\left(-\frac{z - t}{\frac{a}{y}}\right)}\]
   7. Using strategy rm

   8. Applied div-inv 3.1

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

   9. Simplified 3.0

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

   if -5.5621956809643025e+178 < (/ (* y (- z t)) a) < 1.3317847127302016e-49

   1. Initial program 0.4

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

4. Final simplification 1.5

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y \cdot \left(z - t\right)}{a} \le -5.562195680964302490149328614550000366002 \cdot 10^{178} \lor \neg \left(\frac{y \cdot \left(z - t\right)}{a} \le 1.33178471273020163591162836894697555885 \cdot 10^{-49}\right):\\ \;\;\;\;x + \left(-\left(z - t\right) \cdot \frac{y}{a}\right)\\ \mathbf{else}:\\ \;\;\;\;x - \frac{y \cdot \left(z - t\right)}{a}\\ \end{array}\]

Reproduce

herbie shell --seed 2019303 
(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)))