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

Average Error: 0.1 → 0.1

Time: 4.2s

Precision: 64

Math

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

↓

\[\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - 0.25 \cdot \left(a \cdot b\right)\right) + c\]

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)) - (0.25 * (a * b))) + c);
}

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 clear-num 0.1

   \[\leadsto \left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \color{blue}{\frac{1}{\frac{4}{a \cdot b}}}\right) + c\]

4. Taylor expanded around 0 0.1

   \[\leadsto \left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \color{blue}{0.25 \cdot \left(a \cdot b\right)}\right) + c\]

5. Final simplification 0.1

   \[\leadsto \left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - 0.25 \cdot \left(a \cdot b\right)\right) + c\]

Reproduce

herbie shell --seed 2020057 
(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)) (/ (* a b) 4)) c))