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

Average Error: 6.8 → 0.9

Time: 15.4s

Precision: 64

Math

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

↓

\[\begin{array}{l} \mathbf{if}\;x + \frac{y \cdot \left(z - x\right)}{t} = -\infty \lor \neg \left(x + \frac{y \cdot \left(z - x\right)}{t} \le 6.01396636564187938 \cdot 10^{302}\right):\\ \;\;\;\;x + \frac{y}{\frac{t}{z - x}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \left(z - x\right)}{t}\\ \end{array}\]

C

double f(double x, double y, double z, double t) {
        double r248723 = x;
        double r248724 = y;
        double r248725 = z;
        double r248726 = r248725 - r248723;
        double r248727 = r248724 * r248726;
        double r248728 = t;
        double r248729 = r248727 / r248728;
        double r248730 = r248723 + r248729;
        return r248730;
}

↓

double f(double x, double y, double z, double t) {
        double r248731 = x;
        double r248732 = y;
        double r248733 = z;
        double r248734 = r248733 - r248731;
        double r248735 = r248732 * r248734;
        double r248736 = t;
        double r248737 = r248735 / r248736;
        double r248738 = r248731 + r248737;
        double r248739 = -inf.0;
        bool r248740 = r248738 <= r248739;
        double r248741 = 6.013966365641879e+302;
        bool r248742 = r248738 <= r248741;
        double r248743 = !r248742;
        bool r248744 = r248740 || r248743;
        double r248745 = r248736 / r248734;
        double r248746 = r248732 / r248745;
        double r248747 = r248731 + r248746;
        double r248748 = r248744 ? r248747 : r248738;
        return r248748;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Target

Original	6.8
Target	2.2
Herbie	0.9

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

Derivation

1. Split input into 2 regimes

2. if (+ x (/ (* y (- z x)) t)) < -inf.0 or 6.013966365641879e+302 < (+ x (/ (* y (- z x)) t))

   1. Initial program 60.8

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

   3. Applied associate-/l* 1.0

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

   if -inf.0 < (+ x (/ (* y (- z x)) t)) < 6.013966365641879e+302

   1. Initial program 0.9

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

4. Final simplification 0.9

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \frac{y \cdot \left(z - x\right)}{t} = -\infty \lor \neg \left(x + \frac{y \cdot \left(z - x\right)}{t} \le 6.01396636564187938 \cdot 10^{302}\right):\\ \;\;\;\;x + \frac{y}{\frac{t}{z - x}}\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \left(z - x\right)}{t}\\ \end{array}\]

Reproduce

herbie shell --seed 2019198 +o rules:numerics
(FPCore (x y z t)
  :name "Optimisation.CirclePacking:place from circle-packing-0.1.0.4, D"

  :herbie-target
  (- x (+ (* x (/ y t)) (* (- z) (/ y t))))

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