Average Error: 0.0 → 0.0
Time: 1.2s
Precision: binary64
\[0.0 \le x \le 2\]
\[x \cdot \left(x \cdot x\right) + x \cdot x\]
↓
\[{x}^{2} \cdot \left(x + 1\right)\]
x \cdot \left(x \cdot x\right) + x \cdot x
↓
{x}^{2} \cdot \left(x + 1\right)
double code(double x) {
	return ((double) (((double) (x * ((double) (x * x)))) + ((double) (x * x))));
}
↓
double code(double x) {
	return ((double) (((double) pow(x, 2.0)) * ((double) (x + 1.0))));
}

Error

Bits error versus x

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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. Simplified0.0

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

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

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

  5. Applied distribute-rgt-out0.0

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

  6. Applied associate-*r*0.0

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

  7. Simplified0.0

    \[\leadsto \color{blue}{{x}^{2}} \cdot \left(x + 1\right)\]

  8. Final simplification0.0

    \[\leadsto {x}^{2} \cdot \left(x + 1\right)\]

Reproduce

herbie shell --seed 2020147 
(FPCore (x)
  :name "Expression 3, p15"
  :precision binary64
  :pre (<= 0.0 x 2.0)

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

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