Average Error: 0.1 → 0.0
Time: 6.6s
Precision: binary64
\[\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c\]
↓
\[x \cdot y + \left(z \cdot \frac{t}{16} + \left(c - a \cdot \frac{b}{4}\right)\right)\]
\left(\left(x \cdot y + \frac{z \cdot t}{16}\right) - \frac{a \cdot b}{4}\right) + c
↓
x \cdot y + \left(z \cdot \frac{t}{16} + \left(c - a \cdot \frac{b}{4}\right)\right)
(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))))))
double code(double x, double y, double z, double t, double a, double b, double c) {
	return ((double) (((double) (((double) (((double) (x * y)) + (((double) (z * t)) / 16.0))) - (((double) (a * b)) / 4.0))) + c));
}
↓
double code(double x, double y, double z, double t, double a, double b, double c) {
	return ((double) (((double) (x * y)) + ((double) (((double) (z * (t / 16.0))) + ((double) (c - ((double) (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

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

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. Simplified0.0

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

  3. Final simplification0.0

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

Reproduce

herbie shell --seed 2020198 
(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))