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

Average Error: 6.6 → 0.9

Time: 14.9s

Precision: 64

• Falling back on racket egraph because egg-herbie package not installed

Math

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

↓

\[\begin{array}{l} \mathbf{if}\;x + \frac{y \cdot \left(z - x\right)}{t} = -\infty \lor \neg \left(x + \frac{y \cdot \left(z - x\right)}{t} \le 3.35127994072859967 \cdot 10^{271}\right):\\ \;\;\;\;\mathsf{fma}\left(\frac{y}{t}, z - x, x\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \left(z - x\right)}{t}\\ \end{array}\]

C

double f(double x, double y, double z, double t) {
        double r316805 = x;
        double r316806 = y;
        double r316807 = z;
        double r316808 = r316807 - r316805;
        double r316809 = r316806 * r316808;
        double r316810 = t;
        double r316811 = r316809 / r316810;
        double r316812 = r316805 + r316811;
        return r316812;
}

↓

double f(double x, double y, double z, double t) {
        double r316813 = x;
        double r316814 = y;
        double r316815 = z;
        double r316816 = r316815 - r316813;
        double r316817 = r316814 * r316816;
        double r316818 = t;
        double r316819 = r316817 / r316818;
        double r316820 = r316813 + r316819;
        double r316821 = -inf.0;
        bool r316822 = r316820 <= r316821;
        double r316823 = 3.3512799407285997e+271;
        bool r316824 = r316820 <= r316823;
        double r316825 = !r316824;
        bool r316826 = r316822 || r316825;
        double r316827 = r316814 / r316818;
        double r316828 = fma(r316827, r316816, r316813);
        double r316829 = r316826 ? r316828 : r316820;
        return r316829;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Target

Original	6.6
Target	2.1
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 3.3512799407285997e+271 < (+ x (/ (* y (- z x)) t))

   1. Initial program 45.4

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

   2. Simplified 1.6

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

   if -inf.0 < (+ x (/ (* y (- z x)) t)) < 3.3512799407285997e+271

   1. Initial program 0.8

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

4. Final simplification 0.9

   \[\leadsto \begin{array}{l} \mathbf{if}\;x + \frac{y \cdot \left(z - x\right)}{t} = -\infty \lor \neg \left(x + \frac{y \cdot \left(z - x\right)}{t} \le 3.35127994072859967 \cdot 10^{271}\right):\\ \;\;\;\;\mathsf{fma}\left(\frac{y}{t}, z - x, x\right)\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y \cdot \left(z - x\right)}{t}\\ \end{array}\]

Reproduce

herbie shell --seed 2020043 +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)))