Average Error: 0.0 → 0.0
Time: 1.4s
Precision: binary64
\[0 \leq x \land x \leq 2\]
\[x \cdot \left(x \cdot x\right) + x \cdot x\]
↓
\[\left(x + 1\right) \cdot \left(x \cdot x\right)\]
x \cdot \left(x \cdot x\right) + x \cdot x
↓
\left(x + 1\right) \cdot \left(x \cdot x\right)
(FPCore (x) :precision binary64 (+ (* x (* x x)) (* x x)))
↓
(FPCore (x) :precision binary64 (* (+ x 1.0) (* x x)))
double code(double x) {
	return ((double) (((double) (x * ((double) (x * x)))) + ((double) (x * x))));
}
↓
double code(double x) {
	return ((double) (((double) (x + 1.0)) * ((double) (x * 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
\[\left(\left(1 + x\right) \cdot x\right) \cdot x\]

Derivation

  1. Initial program Error: 0.0 bits

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

  2. SimplifiedError: 0.0 bits

    \[\leadsto \color{blue}{x \cdot x + {x}^{3}}\]
  3. Using strategy rm

  4. Applied cube-multError: 0.0 bits

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

  5. Applied distribute-rgt1-inError: 0.0 bits

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

  6. Final simplificationError: 0.0 bits

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

Reproduce

herbie shell --seed 2020203 
(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)))