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

Average Error: 2.2 → 2.2

Time: 4.2s

Precision: 64

Math

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

↓

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

C

double f(double x, double y, double z, double t) {
        double r518298 = x;
        double r518299 = y;
        double r518300 = r518298 / r518299;
        double r518301 = z;
        double r518302 = t;
        double r518303 = r518301 - r518302;
        double r518304 = r518300 * r518303;
        double r518305 = r518304 + r518302;
        return r518305;
}

↓

double f(double x, double y, double z, double t) {
        double r518306 = x;
        double r518307 = y;
        double r518308 = r518306 / r518307;
        double r518309 = z;
        double r518310 = t;
        double r518311 = r518309 - r518310;
        double r518312 = r518308 * r518311;
        double r518313 = r518312 + r518310;
        return r518313;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Target

Original	2.2
Target	2.4
Herbie	2.2

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

Derivation

1. Initial program 2.2

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

2. Final simplification 2.2

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

Reproduce

herbie shell --seed 2019353 +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 2.759456554562692e-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))