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

Average Error: 6.2 → 0.6

Time: 5.3s

Precision: 64

Math

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

↓

\[\begin{array}{l} \mathbf{if}\;\frac{y \cdot \left(z - t\right)}{a} \le -4.7670371624464174 \cdot 10^{302} \lor \neg \left(\frac{y \cdot \left(z - t\right)}{a} \le 1.18372496395244078 \cdot 10^{304}\right):\\ \;\;\;\;x + y \cdot \frac{z - t}{a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \left(z - t\right)}{a}\\ \end{array}\]

C

double f(double x, double y, double z, double t, double a) {
        double r271802 = x;
        double r271803 = y;
        double r271804 = z;
        double r271805 = t;
        double r271806 = r271804 - r271805;
        double r271807 = r271803 * r271806;
        double r271808 = a;
        double r271809 = r271807 / r271808;
        double r271810 = r271802 + r271809;
        return r271810;
}

↓

double f(double x, double y, double z, double t, double a) {
        double r271811 = y;
        double r271812 = z;
        double r271813 = t;
        double r271814 = r271812 - r271813;
        double r271815 = r271811 * r271814;
        double r271816 = a;
        double r271817 = r271815 / r271816;
        double r271818 = -4.7670371624464174e+302;
        bool r271819 = r271817 <= r271818;
        double r271820 = 1.1837249639524408e+304;
        bool r271821 = r271817 <= r271820;
        double r271822 = !r271821;
        bool r271823 = r271819 || r271822;
        double r271824 = x;
        double r271825 = r271814 / r271816;
        double r271826 = r271811 * r271825;
        double r271827 = r271824 + r271826;
        double r271828 = r271824 + r271817;
        double r271829 = r271823 ? r271827 : r271828;
        return r271829;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Bits error versus a

Target

Original	6.2
Target	0.7
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)) a) < -4.7670371624464174e+302 or 1.1837249639524408e+304 < (/ (* y (- z t)) a)

   1. Initial program 60.5

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

   3. Applied *-un-lft-identity 60.5

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

   4. Applied times-frac 2.1

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

   5. Simplified 2.1

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

   if -4.7670371624464174e+302 < (/ (* y (- z t)) a) < 1.1837249639524408e+304

   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

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{y \cdot \left(z - t\right)}{a} \le -4.7670371624464174 \cdot 10^{302} \lor \neg \left(\frac{y \cdot \left(z - t\right)}{a} \le 1.18372496395244078 \cdot 10^{304}\right):\\ \;\;\;\;x + y \cdot \frac{z - t}{a}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \left(z - t\right)}{a}\\ \end{array}\]

Reproduce

herbie shell --seed 2020003 
(FPCore (x y z t a)
  :name "Optimisation.CirclePacking:place from circle-packing-0.1.0.4, E"
  :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)))