Average Error: 0.0 → 0.0
Time: 875.0ms
Precision: binary64
\[0.0 \le x \le 2\]
\[x + x \cdot x\]
↓
\[x \cdot \left(1 + x\right)\]
x + x \cdot x
↓
x \cdot \left(1 + x\right)
double code(double x) {
	return ((double) (x + ((double) (x * x))));
}
↓
double code(double x) {
	return ((double) (x * ((double) (1.0 + x))));
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original0.0
Target0.0
Herbie0.0
\[\left(1 + x\right) \cdot x\]

Derivation

  1. Initial program 0.0

    \[x + x \cdot x\]
  2. Using strategy rm

  3. Applied *-un-lft-identity0.0

    \[\leadsto \color{blue}{1 \cdot x} + x \cdot x\]

  4. Applied distribute-rgt-out0.0

    \[\leadsto \color{blue}{x \cdot \left(1 + x\right)}\]

  5. Final simplification0.0

    \[\leadsto x \cdot \left(1 + x\right)\]

Reproduce

herbie shell --seed 2020174 
(FPCore (x)
  :name "Expression 2, p15"
  :precision binary64
  :pre (<= 0.0 x 2.0)

  :herbie-target
  (* (+ 1.0 x) x)

  (+ x (* x x)))