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

Average Error: 6.1 → 1.9

Time: 17.4s

Precision: 64

Math

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

↓

\[\begin{array}{l} \mathbf{if}\;t \le -5.465265749393871 \cdot 10^{-262}:\\ \;\;\;\;x + \frac{y}{\sqrt[3]{t} \cdot \sqrt[3]{t}} \cdot \frac{z - x}{\sqrt[3]{t}}\\ \mathbf{elif}\;t \le 1.9712458760545623 \cdot 10^{+50}:\\ \;\;\;\;\frac{y \cdot \left(z - x\right)}{t} + x\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\sqrt[3]{t} \cdot \sqrt[3]{t}} \cdot \frac{z - x}{\sqrt[3]{t}}\\ \end{array}\]

C

double f(double x, double y, double z, double t) {
        double r16628246 = x;
        double r16628247 = y;
        double r16628248 = z;
        double r16628249 = r16628248 - r16628246;
        double r16628250 = r16628247 * r16628249;
        double r16628251 = t;
        double r16628252 = r16628250 / r16628251;
        double r16628253 = r16628246 + r16628252;
        return r16628253;
}

↓

double f(double x, double y, double z, double t) {
        double r16628254 = t;
        double r16628255 = -5.465265749393871e-262;
        bool r16628256 = r16628254 <= r16628255;
        double r16628257 = x;
        double r16628258 = y;
        double r16628259 = cbrt(r16628254);
        double r16628260 = r16628259 * r16628259;
        double r16628261 = r16628258 / r16628260;
        double r16628262 = z;
        double r16628263 = r16628262 - r16628257;
        double r16628264 = r16628263 / r16628259;
        double r16628265 = r16628261 * r16628264;
        double r16628266 = r16628257 + r16628265;
        double r16628267 = 1.9712458760545623e+50;
        bool r16628268 = r16628254 <= r16628267;
        double r16628269 = r16628258 * r16628263;
        double r16628270 = r16628269 / r16628254;
        double r16628271 = r16628270 + r16628257;
        double r16628272 = r16628268 ? r16628271 : r16628266;
        double r16628273 = r16628256 ? r16628266 : r16628272;
        return r16628273;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Target

Original	6.1
Target	2.0
Herbie	1.9

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

Derivation

1. Split input into 2 regimes

2. if t < -5.465265749393871e-262 or 1.9712458760545623e+50 < t

   1. Initial program 7.4

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

   3. Applied add-cube-cbrt 7.8

      \[\leadsto x + \frac{y \cdot \left(z - x\right)}{\color{blue}{\left(\sqrt[3]{t} \cdot \sqrt[3]{t}\right) \cdot \sqrt[3]{t}}}\]

   4. Applied times-frac 1.8

      \[\leadsto x + \color{blue}{\frac{y}{\sqrt[3]{t} \cdot \sqrt[3]{t}} \cdot \frac{z - x}{\sqrt[3]{t}}}\]

   if -5.465265749393871e-262 < t < 1.9712458760545623e+50

   1. Initial program 2.1

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

4. Final simplification 1.9

   \[\leadsto \begin{array}{l} \mathbf{if}\;t \le -5.465265749393871 \cdot 10^{-262}:\\ \;\;\;\;x + \frac{y}{\sqrt[3]{t} \cdot \sqrt[3]{t}} \cdot \frac{z - x}{\sqrt[3]{t}}\\ \mathbf{elif}\;t \le 1.9712458760545623 \cdot 10^{+50}:\\ \;\;\;\;\frac{y \cdot \left(z - x\right)}{t} + x\\ \mathbf{else}:\\ \;\;\;\;x + \frac{y}{\sqrt[3]{t} \cdot \sqrt[3]{t}} \cdot \frac{z - x}{\sqrt[3]{t}}\\ \end{array}\]

Reproduce

herbie shell --seed 2019163 +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)))