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

Average Error: 1.9 → 2.2

Time: 23.1s

Precision: binary64

Math

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

↓

\[\begin{array}{l} \mathbf{if}\;y \le -1.8415800691353711 \cdot 10^{-151}:\\ \;\;\;\;x \cdot \frac{z - t}{y} + t\\ \mathbf{elif}\;y \le 3.5907182236266797 \cdot 10^{-229}:\\ \;\;\;\;\frac{1}{\sqrt[3]{y} \cdot \sqrt[3]{y}} \cdot \left(\frac{x}{\sqrt[3]{y}} \cdot \left(z - t\right)\right) + t\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} \cdot \left(z - t\right) + t\\ \end{array}\]

C

double code(double x, double y, double z, double t) {
	return ((double) (((double) (((double) (x / y)) * ((double) (z - t)))) + t));
}

↓

double code(double x, double y, double z, double t) {
	double VAR;
	if ((y <= -1.841580069135371e-151)) {
		VAR = ((double) (((double) (x * ((double) (((double) (z - t)) / y)))) + t));
	} else {
		double VAR_1;
		if ((y <= 3.59071822362668e-229)) {
			VAR_1 = ((double) (((double) (((double) (1.0 / ((double) (((double) cbrt(y)) * ((double) cbrt(y)))))) * ((double) (((double) (x / ((double) cbrt(y)))) * ((double) (z - t)))))) + t));
		} else {
			VAR_1 = ((double) (((double) (((double) (x / y)) * ((double) (z - t)))) + t));
		}
		VAR = VAR_1;
	}
	return VAR;
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Target

Original	1.9
Target	2.2
Herbie	2.2

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

Derivation

1. Split input into 3 regimes

2. if y < -1.8415800691353711e-151

   1. Initial program 1.6

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

   3. Applied div-inv 1.6

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

   4. Applied associate-*l* 3.1

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

   5. Simplified 3.0

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

   if -1.8415800691353711e-151 < y < 3.5907182236266797e-229

   1. Initial program 5.9

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

   3. Applied add-cube-cbrt 6.8

      \[\leadsto \frac{x}{\color{blue}{\left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right) \cdot \sqrt[3]{y}}} \cdot \left(z - t\right) + t\]

   4. Applied *-un-lft-identity 6.8

      \[\leadsto \frac{\color{blue}{1 \cdot x}}{\left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right) \cdot \sqrt[3]{y}} \cdot \left(z - t\right) + t\]

   5. Applied times-frac 6.8

      \[\leadsto \color{blue}{\left(\frac{1}{\sqrt[3]{y} \cdot \sqrt[3]{y}} \cdot \frac{x}{\sqrt[3]{y}}\right)} \cdot \left(z - t\right) + t\]

   6. Applied associate-*l* 3.1

      \[\leadsto \color{blue}{\frac{1}{\sqrt[3]{y} \cdot \sqrt[3]{y}} \cdot \left(\frac{x}{\sqrt[3]{y}} \cdot \left(z - t\right)\right)} + t\]

   if 3.5907182236266797e-229 < y

   1. Initial program 1.3

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

4. Final simplification 2.2

   \[\leadsto \begin{array}{l} \mathbf{if}\;y \le -1.8415800691353711 \cdot 10^{-151}:\\ \;\;\;\;x \cdot \frac{z - t}{y} + t\\ \mathbf{elif}\;y \le 3.5907182236266797 \cdot 10^{-229}:\\ \;\;\;\;\frac{1}{\sqrt[3]{y} \cdot \sqrt[3]{y}} \cdot \left(\frac{x}{\sqrt[3]{y}} \cdot \left(z - t\right)\right) + t\\ \mathbf{else}:\\ \;\;\;\;\frac{x}{y} \cdot \left(z - t\right) + t\\ \end{array}\]

Reproduce

herbie shell --seed 2020163 
(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))