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

Average Error: 2.3 → 2.3

Time: 3.1s

Precision: 64

Math

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

↓

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

C

double f(double x, double y, double z, double t) {
        double r431494 = x;
        double r431495 = y;
        double r431496 = r431494 / r431495;
        double r431497 = z;
        double r431498 = t;
        double r431499 = r431497 - r431498;
        double r431500 = r431496 * r431499;
        double r431501 = r431500 + r431498;
        return r431501;
}

↓

double f(double x, double y, double z, double t) {
        double r431502 = x;
        double r431503 = y;
        double r431504 = r431502 / r431503;
        double r431505 = z;
        double r431506 = t;
        double r431507 = r431505 - r431506;
        double r431508 = fma(r431504, r431507, r431506);
        return r431508;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Target

Original	2.3
Target	2.3
Herbie	2.3

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

Derivation

1. Initial program 2.3

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

2. Simplified 2.3

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

3. Final simplification 2.3

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

Reproduce

herbie shell --seed 2019356 +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))