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

Average Error: 1.9 → 0.9

Time: 26.1s

Precision: 64

Math

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

↓

\[\begin{array}{l} \mathbf{if}\;\frac{x}{y} \le -7.840712946502026926766947963049170150444 \cdot 10^{-238} \lor \neg \left(\frac{x}{y} \le -0.0\right) \land \frac{x}{y} \le 9.273878276426671796812652531873498118302 \cdot 10^{124}:\\ \;\;\;\;\frac{x}{y} \cdot \left(z - t\right) + t\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{z - t}{y} + t\\ \end{array}\]

C

double f(double x, double y, double z, double t) {
        double r401404 = x;
        double r401405 = y;
        double r401406 = r401404 / r401405;
        double r401407 = z;
        double r401408 = t;
        double r401409 = r401407 - r401408;
        double r401410 = r401406 * r401409;
        double r401411 = r401410 + r401408;
        return r401411;
}

↓

double f(double x, double y, double z, double t) {
        double r401412 = x;
        double r401413 = y;
        double r401414 = r401412 / r401413;
        double r401415 = -7.840712946502027e-238;
        bool r401416 = r401414 <= r401415;
        double r401417 = -0.0;
        bool r401418 = r401414 <= r401417;
        double r401419 = !r401418;
        double r401420 = 9.273878276426672e+124;
        bool r401421 = r401414 <= r401420;
        bool r401422 = r401419 && r401421;
        bool r401423 = r401416 || r401422;
        double r401424 = z;
        double r401425 = t;
        double r401426 = r401424 - r401425;
        double r401427 = r401414 * r401426;
        double r401428 = r401427 + r401425;
        double r401429 = r401426 / r401413;
        double r401430 = r401412 * r401429;
        double r401431 = r401430 + r401425;
        double r401432 = r401423 ? r401428 : r401431;
        return r401432;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Target

Original	1.9
Target	2.0
Herbie	0.9

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

Derivation

1. Split input into 2 regimes

2. if (/ x y) < -7.840712946502027e-238 or -0.0 < (/ x y) < 9.273878276426672e+124

   1. Initial program 1.3

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

   if -7.840712946502027e-238 < (/ x y) < -0.0 or 9.273878276426672e+124 < (/ x y)

   1. Initial program 4.3

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

   3. Applied div-inv 4.4

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

   4. Applied associate-*l* 1.3

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

   5. Simplified 1.3

      \[\leadsto x \cdot \color{blue}{\frac{z - t}{y}} + t\]
3. Recombined 2 regimes into one program.

4. Final simplification 0.9

   \[\leadsto \begin{array}{l} \mathbf{if}\;\frac{x}{y} \le -7.840712946502026926766947963049170150444 \cdot 10^{-238} \lor \neg \left(\frac{x}{y} \le -0.0\right) \land \frac{x}{y} \le 9.273878276426671796812652531873498118302 \cdot 10^{124}:\\ \;\;\;\;\frac{x}{y} \cdot \left(z - t\right) + t\\ \mathbf{else}:\\ \;\;\;\;x \cdot \frac{z - t}{y} + t\\ \end{array}\]

Reproduce

herbie shell --seed 2019306 +o rules:numerics
(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))