Diagrams.Solve.Polynomial:quartForm from diagrams-solve-0.1, B

Average Error: 0.0 → 0.1

Time: 1.7s

Precision: 64

Math

\[\left(\frac{1}{8} \cdot x - \frac{y \cdot z}{2}\right) + t\]

↓

\[\left(\frac{1}{8} \cdot x - \frac{y}{\frac{2}{z}}\right) + t\]

C

double code(double x, double y, double z, double t) {
	return ((double) (((double) (((double) (((double) (1.0 / 8.0)) * x)) - ((double) (((double) (y * z)) / 2.0)))) + t));
}

↓

double code(double x, double y, double z, double t) {
	return ((double) (((double) (((double) (((double) (1.0 / 8.0)) * x)) - ((double) (y / ((double) (2.0 / z)))))) + t));
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Target

Original	0.0
Target	0.0
Herbie	0.1

\[\left(\frac{x}{8} + t\right) - \frac{z}{2} \cdot y\]

Derivation

1. Initial program 0.0

   \[\left(\frac{1}{8} \cdot x - \frac{y \cdot z}{2}\right) + t\]
2. Using strategy rm

3. Applied associate-/l* 0.1

   \[\leadsto \left(\frac{1}{8} \cdot x - \color{blue}{\frac{y}{\frac{2}{z}}}\right) + t\]

4. Final simplification 0.1

   \[\leadsto \left(\frac{1}{8} \cdot x - \frac{y}{\frac{2}{z}}\right) + t\]

Reproduce

herbie shell --seed 2020124 
(FPCore (x y z t)
  :name "Diagrams.Solve.Polynomial:quartForm  from diagrams-solve-0.1, B"
  :precision binary64

  :herbie-target
  (- (+ (/ x 8.0) t) (* (/ z 2.0) y))

  (+ (- (* (/ 1.0 8.0) x) (/ (* y z) 2.0)) t))