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

Average Error: 6.2 → 0.8

Time: 3.1s

Precision: 64

Math

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

↓

\[\begin{array}{l} \mathbf{if}\;x + \frac{y \cdot \left(z - x\right)}{t} = -\infty \lor \neg \left(x + \frac{y \cdot \left(z - x\right)}{t} \le 2.41460299605345588497500145653142679709 \cdot 10^{297}\right):\\ \;\;\;\;\mathsf{fma}\left(\frac{y}{t}, z - x, x\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \left(z - x\right)}{t}\\ \end{array}\]

C

double f(double x, double y, double z, double t) {
        double r394086 = x;
        double r394087 = y;
        double r394088 = z;
        double r394089 = r394088 - r394086;
        double r394090 = r394087 * r394089;
        double r394091 = t;
        double r394092 = r394090 / r394091;
        double r394093 = r394086 + r394092;
        return r394093;
}

↓

double f(double x, double y, double z, double t) {
        double r394094 = x;
        double r394095 = y;
        double r394096 = z;
        double r394097 = r394096 - r394094;
        double r394098 = r394095 * r394097;
        double r394099 = t;
        double r394100 = r394098 / r394099;
        double r394101 = r394094 + r394100;
        double r394102 = -inf.0;
        bool r394103 = r394101 <= r394102;
        double r394104 = 2.414602996053456e+297;
        bool r394105 = r394101 <= r394104;
        double r394106 = !r394105;
        bool r394107 = r394103 || r394106;
        double r394108 = r394095 / r394099;
        double r394109 = fma(r394108, r394097, r394094);
        double r394110 = r394107 ? r394109 : r394101;
        return r394110;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Target

Original	6.2
Target	2.2
Herbie	0.8

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

Derivation

1. Split input into 2 regimes

2. if (+ x (/ (* y (- z x)) t)) < -inf.0 or 2.414602996053456e+297 < (+ x (/ (* y (- z x)) t))

   1. Initial program 55.7

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

   2. Simplified 0.7

      \[\leadsto \color{blue}{\mathsf{fma}\left(\frac{y}{t}, z - x, x\right)}\]

   if -inf.0 < (+ x (/ (* y (- z x)) t)) < 2.414602996053456e+297

   1. Initial program 0.8

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

4. Final simplification 0.8

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \frac{y \cdot \left(z - x\right)}{t} = -\infty \lor \neg \left(x + \frac{y \cdot \left(z - x\right)}{t} \le 2.41460299605345588497500145653142679709 \cdot 10^{297}\right):\\ \;\;\;\;\mathsf{fma}\left(\frac{y}{t}, z - x, x\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \left(z - x\right)}{t}\\ \end{array}\]

Reproduce

herbie shell --seed 2019362 +o rules:numerics
(FPCore (x y z t)
  :name "Optimisation.CirclePacking:place from circle-packing-0.1.0.4, D"
  :precision binary64

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

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