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

Average Error: 2.1 → 2.1

Time: 18.1s

Precision: 64

• Falling back on racket egraph because egg-herbie package not installed

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 r545638 = x;
        double r545639 = y;
        double r545640 = r545638 / r545639;
        double r545641 = z;
        double r545642 = t;
        double r545643 = r545641 - r545642;
        double r545644 = r545640 * r545643;
        double r545645 = r545644 + r545642;
        return r545645;
}

↓

double f(double x, double y, double z, double t) {
        double r545646 = x;
        double r545647 = y;
        double r545648 = r545646 / r545647;
        double r545649 = z;
        double r545650 = t;
        double r545651 = r545649 - r545650;
        double r545652 = r545648 * r545651;
        double r545653 = r545652 + r545650;
        return r545653;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Target

Original	2.1
Target	2.2
Herbie	2.1

\[\begin{array}{l} \mathbf{if}\;z \lt 2.7594565545626922 \cdot 10^{-282}:\\ \;\;\;\;\frac{x}{y} \cdot \left(z - t\right) + t\\ \mathbf{elif}\;z \lt 2.326994450874436 \cdot 10^{-110}:\\ \;\;\;\;x \cdot \frac{z - t}{y} + t\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} \cdot \left(z - t\right) + t\\ \end{array}\]

Derivation

1. Initial program 2.1

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

2. Final simplification 2.1

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

Reproduce

herbie shell --seed 2020045 
(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))