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

Average Error: 0.1 → 0.1

Time: 6.8s

Precision: binary64

Math

\[\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c\]

↓

\[x \cdot y + \left(\frac{z \cdot t}{16} + \left(c - \frac{a \cdot b}{4}\right)\right)\]

FPCore

(FPCore (x y z t a b c)
 :precision binary64
 (+ (- (+ (* x y) (/ (* z t) 16.0)) (/ (* a b) 4.0)) c))

↓

(FPCore (x y z t a b c)
 :precision binary64
 (+ (* x y) (+ (/ (* z t) 16.0) (- c (/ (* a b) 4.0)))))

C

double code(double x, double y, double z, double t, double a, double b, double c) {
	return (((x * y) + ((z * t) / 16.0)) - ((a * b) / 4.0)) + c;
}

↓

double code(double x, double y, double z, double t, double a, double b, double c) {
	return (x * y) + (((z * t) / 16.0) + (c - ((a * b) / 4.0)));
}

Error

Bits error versus x

Bits error versus y

Bits error versus z

Bits error versus t

Bits error versus a

Bits error versus b

Bits error versus c

Derivation

1. Initial program 0.1

   \[\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c\]
2. Using strategy rm

3. Applied associate--l+_binary64_7176 0.1

   \[\leadsto \color{blue}{\left(x \cdot y + \left(\frac{z \cdot t}{16} - \frac{a \cdot b}{4}\right)\right)} + c\]

4. Applied associate-+l+_binary64_7172 0.1

   \[\leadsto \color{blue}{x \cdot y + \left(\left(\frac{z \cdot t}{16} - \frac{a \cdot b}{4}\right) + c\right)}\]

5. Simplified 0.1

   \[\leadsto x \cdot y + \color{blue}{\left(\frac{z \cdot t}{16} + \left(c - \frac{a \cdot b}{4}\right)\right)}\]

6. Final simplification 0.1

   \[\leadsto x \cdot y + \left(\frac{z \cdot t}{16} + \left(c - \frac{a \cdot b}{4}\right)\right)\]

Reproduce

herbie shell --seed 2020356 
(FPCore (x y z t a b c)
  :name "Diagrams.Solve.Polynomial:quartForm  from diagrams-solve-0.1, C"
  :precision binary64
  (+ (- (+ (* x y) (/ (* z t) 16.0)) (/ (* a b) 4.0)) c))