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

Average Error: 2.1 → 2.1

Time: 4.1s

Precision: 64

Math

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

↓

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

C

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

↓

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

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 clear-num 2.3

   \[\leadsto \color{blue}{\frac{1}{\frac{z - y}{x - y}}} \cdot t\]
4. Using strategy rm

5. Applied *-un-lft-identity 2.3

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

6. Applied *-un-lft-identity 2.3

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

7. Applied times-frac 2.3

   \[\leadsto \frac{1}{\color{blue}{\frac{1}{1} \cdot \frac{z - y}{x - y}}} \cdot t\]

8. Applied *-un-lft-identity 2.3

   \[\leadsto \frac{\color{blue}{1 \cdot 1}}{\frac{1}{1} \cdot \frac{z - y}{x - y}} \cdot t\]

9. Applied times-frac 2.3

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

10. Applied associate-*l* 2.3

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

11. Simplified 2.1

    \[\leadsto \frac{1}{\frac{1}{1}} \cdot \color{blue}{\frac{t}{\frac{z - y}{x - y}}}\]

12. Final simplification 2.1

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

Reproduce

herbie shell --seed 2020049 +o rules:numerics
(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))