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

Average Error: 6.5 → 0.9

Time: 2.8s

Precision: 64

Math

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

↓

\[\begin{array}{l} \mathbf{if}\;x + \frac{y \cdot \left(z - x\right)}{t} = -\infty \lor \neg \left(x + \frac{y \cdot \left(z - x\right)}{t} \le 1.3494005157116993 \cdot 10^{294}\right):\\ \;\;\;\;\mathsf{fma}\left(\frac{y}{t}, z - x, x\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \left(z - x\right)}{t}\\ \end{array}\]

C

double f(double x, double y, double z, double t) {
        double r311111 = x;
        double r311112 = y;
        double r311113 = z;
        double r311114 = r311113 - r311111;
        double r311115 = r311112 * r311114;
        double r311116 = t;
        double r311117 = r311115 / r311116;
        double r311118 = r311111 + r311117;
        return r311118;
}

↓

double f(double x, double y, double z, double t) {
        double r311119 = x;
        double r311120 = y;
        double r311121 = z;
        double r311122 = r311121 - r311119;
        double r311123 = r311120 * r311122;
        double r311124 = t;
        double r311125 = r311123 / r311124;
        double r311126 = r311119 + r311125;
        double r311127 = -inf.0;
        bool r311128 = r311126 <= r311127;
        double r311129 = 1.3494005157116993e+294;
        bool r311130 = r311126 <= r311129;
        double r311131 = !r311130;
        bool r311132 = r311128 || r311131;
        double r311133 = r311120 / r311124;
        double r311134 = fma(r311133, r311122, r311119);
        double r311135 = r311132 ? r311134 : r311126;
        return r311135;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Target

Original	6.5
Target	2.0
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 1.3494005157116993e+294 < (+ x (/ (* y (- z x)) t))

   1. Initial program 56.0

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

   2. Simplified 0.9

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

   if -inf.0 < (+ x (/ (* y (- z x)) t)) < 1.3494005157116993e+294

   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

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \frac{y \cdot \left(z - x\right)}{t} = -\infty \lor \neg \left(x + \frac{y \cdot \left(z - x\right)}{t} \le 1.3494005157116993 \cdot 10^{294}\right):\\ \;\;\;\;\mathsf{fma}\left(\frac{y}{t}, z - x, x\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \left(z - x\right)}{t}\\ \end{array}\]

Reproduce

herbie shell --seed 2020024 +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)))