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

Average Error: 6.1 → 1.5

Time: 12.0s

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 r290078 = x;
        double r290079 = y;
        double r290080 = z;
        double r290081 = t;
        double r290082 = r290080 - r290081;
        double r290083 = r290079 * r290082;
        double r290084 = a;
        double r290085 = r290083 / r290084;
        double r290086 = r290078 - r290085;
        return r290086;
}

↓

double f(double x, double y, double z, double t, double a) {
        double r290087 = y;
        double r290088 = z;
        double r290089 = t;
        double r290090 = r290088 - r290089;
        double r290091 = r290087 * r290090;
        double r290092 = a;
        double r290093 = r290091 / r290092;
        double r290094 = -5.5621956809643025e+178;
        bool r290095 = r290093 <= r290094;
        double r290096 = 1.3317847127302016e-49;
        bool r290097 = r290093 <= r290096;
        double r290098 = !r290097;
        bool r290099 = r290095 || r290098;
        double r290100 = x;
        double r290101 = r290087 / r290092;
        double r290102 = r290090 * r290101;
        double r290103 = -r290102;
        double r290104 = r290100 + r290103;
        double r290105 = r290100 - r290093;
        double r290106 = r290099 ? r290104 : r290105;
        return r290106;
}

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)))