Average Error: 0.0 → 0.0
Time: 1.8s
Precision: 64
\[0.0 \le x \le 2\]
\[x \cdot \left(x \cdot x\right) + x \cdot x\]
↓
\[\frac{\left(x \cdot x - 1\right) \cdot \left(x \cdot x\right)}{x - 1}\]
x \cdot \left(x \cdot x\right) + x \cdot x
↓
\frac{\left(x \cdot x - 1\right) \cdot \left(x \cdot x\right)}{x - 1}
double code(double x) {
	return ((x * (x * x)) + (x * x));
}
↓
double code(double x) {
	return ((((x * x) - 1.0) * (x * x)) / (x - 1.0));
}

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

Derivation

  1. Initial program 0.0

    \[x \cdot \left(x \cdot x\right) + x \cdot x\]
  2. Using strategy rm

  3. Applied distribute-lft1-in0.0

    \[\leadsto \color{blue}{\left(x + 1\right) \cdot \left(x \cdot x\right)}\]
  4. Using strategy rm

  5. Applied flip-+0.0

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

  6. Applied associate-*l/0.0

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

  7. Simplified0.0

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

  8. Final simplification0.0

    \[\leadsto \frac{\left(x \cdot x - 1\right) \cdot \left(x \cdot x\right)}{x - 1}\]

Reproduce

herbie shell --seed 2020078 
(FPCore (x)
  :name "Expression 3, p15"
  :precision binary64
  :pre (<= 0.0 x 2)

  :herbie-target
  (* (* (+ 1 x) x) x)

  (+ (* x (* x x)) (* x x)))