Numeric.Signal.Multichannel:$cget from hsignal-0.2.7.1

Average Error: 2.1 → 1.5

Time: 15.4s

Precision: 64

Math

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

↓

\[\begin{array}{l} \mathbf{if}\;y \le -42978108798448336633856:\\ \;\;\;\;x \cdot \frac{z - t}{y} + t\\ \mathbf{elif}\;y \le 1.813938713754940024500643274185129154443 \cdot 10^{-40}:\\ \;\;\;\;\frac{x \cdot \left(z - t\right)}{y} + t\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} \cdot \left(z - t\right) + t\\ \end{array}\]

C

double f(double x, double y, double z, double t) {
        double r293127 = x;
        double r293128 = y;
        double r293129 = r293127 / r293128;
        double r293130 = z;
        double r293131 = t;
        double r293132 = r293130 - r293131;
        double r293133 = r293129 * r293132;
        double r293134 = r293133 + r293131;
        return r293134;
}

↓

double f(double x, double y, double z, double t) {
        double r293135 = y;
        double r293136 = -4.297810879844834e+22;
        bool r293137 = r293135 <= r293136;
        double r293138 = x;
        double r293139 = z;
        double r293140 = t;
        double r293141 = r293139 - r293140;
        double r293142 = r293141 / r293135;
        double r293143 = r293138 * r293142;
        double r293144 = r293143 + r293140;
        double r293145 = 1.81393871375494e-40;
        bool r293146 = r293135 <= r293145;
        double r293147 = r293138 * r293141;
        double r293148 = r293147 / r293135;
        double r293149 = r293148 + r293140;
        double r293150 = r293138 / r293135;
        double r293151 = r293150 * r293141;
        double r293152 = r293151 + r293140;
        double r293153 = r293146 ? r293149 : r293152;
        double r293154 = r293137 ? r293144 : r293153;
        return r293154;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Target

Original	2.1
Target	2.3
Herbie	1.5

\[\begin{array}{l} \mathbf{if}\;z \lt 2.759456554562692182563154937894909044548 \cdot 10^{-282}:\\ \;\;\;\;\frac{x}{y} \cdot \left(z - t\right) + t\\ \mathbf{elif}\;z \lt 2.32699445087443595687739933019129648094 \cdot 10^{-110}:\\ \;\;\;\;x \cdot \frac{z - t}{y} + t\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} \cdot \left(z - t\right) + t\\ \end{array}\]

Derivation

1. Split input into 3 regimes

2. if y < -4.297810879844834e+22

   1. Initial program 1.3

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

   3. Applied div-inv 1.3

      \[\leadsto \color{blue}{\left(x \cdot \frac{1}{y}\right)} \cdot \left(z - t\right) + t\]

   4. Applied associate-*l* 1.4

      \[\leadsto \color{blue}{x \cdot \left(\frac{1}{y} \cdot \left(z - t\right)\right)} + t\]

   5. Simplified 1.3

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

   if -4.297810879844834e+22 < y < 1.81393871375494e-40

   1. Initial program 3.5

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

   3. Applied associate-*l/ 1.9

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

   if 1.81393871375494e-40 < y

   1. Initial program 1.2

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

4. Final simplification 1.5

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \le -42978108798448336633856:\\ \;\;\;\;x \cdot \frac{z - t}{y} + t\\ \mathbf{elif}\;y \le 1.813938713754940024500643274185129154443 \cdot 10^{-40}:\\ \;\;\;\;\frac{x \cdot \left(z - t\right)}{y} + t\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} \cdot \left(z - t\right) + t\\ \end{array}\]

Reproduce

herbie shell --seed 2019305 
(FPCore (x y z t)
  :name "Numeric.Signal.Multichannel:$cget from hsignal-0.2.7.1"
  :precision binary64

  :herbie-target
  (if (< z 2.7594565545626922e-282) (+ (* (/ x y) (- z t)) t) (if (< z 2.326994450874436e-110) (+ (* x (/ (- z t) y)) t) (+ (* (/ x y) (- z t)) t)))

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