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

Average Error: 2.1 → 2.1

Time: 5.6s

Precision: binary64

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

Math

\[\frac{x - y}{z - y} \cdot t\]

↓

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

C

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

↓

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

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Target

Original	2.1
Target	2.1
Herbie	2.1

\[\frac{t}{\frac{z - y}{x - y}}\]

Derivation

1. Initial program 2.1

   \[\frac{x - y}{z - y} \cdot t\]
2. Using strategy rm

3. Applied div-sub 2.1

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

4. Final simplification 2.1

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

Reproduce

herbie shell --seed 2020182 
(FPCore (x y z t)
  :name "Numeric.Signal.Multichannel:$cput from hsignal-0.2.7.1"
  :precision binary64

  :herbie-target
  (/ t (/ (- z y) (- x y)))

  (* (/ (- x y) (- z y)) t))