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

Average Error: 6.4 → 0.8

Time: 2.6s

Precision: 64

Math

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

↓

\[\begin{array}{l} \mathbf{if}\;x + \frac{y \cdot \left(z - x\right)}{t} = -\infty \lor \neg \left(x + \frac{y \cdot \left(z - x\right)}{t} \le 1.390199870564766 \cdot 10^{300}\right):\\ \;\;\;\;\mathsf{fma}\left(\frac{y}{t}, z - x, x\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \left(z - x\right)}{t}\\ \end{array}\]

C

double f(double x, double y, double z, double t) {
        double r315495 = x;
        double r315496 = y;
        double r315497 = z;
        double r315498 = r315497 - r315495;
        double r315499 = r315496 * r315498;
        double r315500 = t;
        double r315501 = r315499 / r315500;
        double r315502 = r315495 + r315501;
        return r315502;
}

↓

double f(double x, double y, double z, double t) {
        double r315503 = x;
        double r315504 = y;
        double r315505 = z;
        double r315506 = r315505 - r315503;
        double r315507 = r315504 * r315506;
        double r315508 = t;
        double r315509 = r315507 / r315508;
        double r315510 = r315503 + r315509;
        double r315511 = -inf.0;
        bool r315512 = r315510 <= r315511;
        double r315513 = 1.3901998705647658e+300;
        bool r315514 = r315510 <= r315513;
        double r315515 = !r315514;
        bool r315516 = r315512 || r315515;
        double r315517 = r315504 / r315508;
        double r315518 = fma(r315517, r315506, r315503);
        double r315519 = r315516 ? r315518 : r315510;
        return r315519;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Target

Original	6.4
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 1.3901998705647658e+300 < (+ x (/ (* y (- z x)) t))

   1. Initial program 59.7

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

   2. Simplified 0.8

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

   if -inf.0 < (+ x (/ (* y (- z x)) t)) < 1.3901998705647658e+300

   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

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \frac{y \cdot \left(z - x\right)}{t} = -\infty \lor \neg \left(x + \frac{y \cdot \left(z - x\right)}{t} \le 1.390199870564766 \cdot 10^{300}\right):\\ \;\;\;\;\mathsf{fma}\left(\frac{y}{t}, z - x, x\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \left(z - x\right)}{t}\\ \end{array}\]

Reproduce

herbie shell --seed 2020033 +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)))