Diagrams.Solve.Polynomial:cubForm from diagrams-solve-0.1, H

Average Error: 3.5 → 1.7

Time: 2.1s

Precision: 64

Math

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

↓

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

C

double code(double x, double y, double z, double t) {
	return ((x - (y / (z * 3.0))) + (t / ((z * 3.0) * y)));
}

↓

double code(double x, double y, double z, double t) {
	return ((x - ((y / 3.0) / z)) + ((t / z) * (1.0 / (3.0 * y))));
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Target

Original	3.5
Target	1.7
Herbie	1.7

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

Derivation

1. Initial program 3.5

   \[\left(x - \frac{y}{z \cdot 3}\right) + \frac{t}{\left(z \cdot 3\right) \cdot y}\]
2. Using strategy rm

3. Applied associate-*l* 3.5

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

4. Applied associate-/r* 1.7

   \[\leadsto \left(x - \frac{y}{z \cdot 3}\right) + \color{blue}{\frac{\frac{t}{z}}{3 \cdot y}}\]
5. Using strategy rm

6. Applied *-commutative 1.7

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

7. Applied associate-/r* 1.7

   \[\leadsto \left(x - \color{blue}{\frac{\frac{y}{3}}{z}}\right) + \frac{\frac{t}{z}}{3 \cdot y}\]
8. Using strategy rm

9. Applied div-inv 1.7

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

10. Final simplification 1.7

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

Reproduce

herbie shell --seed 2020078 
(FPCore (x y z t)
  :name "Diagrams.Solve.Polynomial:cubForm  from diagrams-solve-0.1, H"
  :precision binary64

  :herbie-target
  (+ (- x (/ y (* z 3))) (/ (/ t (* z 3)) y))

  (+ (- x (/ y (* z 3))) (/ t (* (* z 3) y))))