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

Average Error: 3.4 → 1.6

Time: 10.7s

Precision: binary64

Math

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

↓

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

FPCore

(FPCore (x y z t)
 :precision binary64
 (+ (- x (/ y (* z 3.0))) (/ t (* (* z 3.0) y))))

↓

(FPCore (x y z t)
 :precision binary64
 (- x (- (/ (/ y z) 3.0) (/ (/ t (* z 3.0)) 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 / z) / 3.0) - ((t / (z * 3.0)) / y));
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Target

Original	3.4
Target	1.6
Herbie	1.6

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

Derivation

1. Initial program 3.4

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

3. Applied associate-/r*_binary64_15708 1.6

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

5. Applied associate-/r*_binary64_15708 1.6

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

7. Applied associate-+l-_binary64_15699 1.6

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

8. Final simplification 1.6

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

Reproduce

herbie shell --seed 2021076 
(FPCore (x y z t)
  :name "Diagrams.Solve.Polynomial:cubForm  from diagrams-solve-0.1, H"
  :precision binary64

  :herbie-target
  (+ (- x (/ y (* z 3.0))) (/ (/ t (* z 3.0)) y))

  (+ (- x (/ y (* z 3.0))) (/ t (* (* z 3.0) y))))