Average Error: 0.0 → 0.0
Time: 2.4s
Precision: binary64
\[\left(\left(\left(x \cdot a + x \cdot b\right) + x \cdot c\right) + x \cdot d\right) + x \cdot e\]
↓
\[x \cdot \left(\left(\left(a + b\right) + c\right) + \left(d + e\right)\right)\]
\left(\left(\left(x \cdot a + x \cdot b\right) + x \cdot c\right) + x \cdot d\right) + x \cdot e
↓
x \cdot \left(\left(\left(a + b\right) + c\right) + \left(d + e\right)\right)
double code(double x, double a, double b, double c, double d, double e) {
	return ((double) (((double) (((double) (((double) (((double) (x * a)) + ((double) (x * b)))) + ((double) (x * c)))) + ((double) (x * d)))) + ((double) (x * e))));
}
↓
double code(double x, double a, double b, double c, double d, double e) {
	return ((double) (x * ((double) (((double) (((double) (a + b)) + c)) + ((double) (d + e))))));
}

Error

Bits error versus x

Bits error versus a

Bits error versus b

Bits error versus c

Bits error versus d

Bits error versus e

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.0

    \[\left(\left(\left(x \cdot a + x \cdot b\right) + x \cdot c\right) + x \cdot d\right) + x \cdot e\]

  2. Simplified0.0

    \[\leadsto \color{blue}{x \cdot \left(\left(\left(a + b\right) + c\right) + \left(d + e\right)\right)}\]

  3. Final simplification0.0

    \[\leadsto x \cdot \left(\left(\left(a + b\right) + c\right) + \left(d + e\right)\right)\]

Reproduce

herbie shell --seed 2020153 
(FPCore (x a b c d e)
  :name "(+ (+ (+ (+ (* x a) (* x b)) (* x c)) (* x d)) (* x e))"
  :precision binary64
  (+ (+ (+ (+ (* x a) (* x b)) (* x c)) (* x d)) (* x e)))