Average Error: 0.0 → 0.0
Time: 2.0s
Precision: binary64
Cost: 448
\[0 \leq x \land x \leq 2\]
\[x \cdot \left(x \cdot x\right) + x \cdot x\]
↓
\[x \cdot \left(x + x \cdot x\right)\]
x \cdot \left(x \cdot x\right) + x \cdot x
↓
x \cdot \left(x + x \cdot x\right)
(FPCore (x) :precision binary64 (+ (* x (* x x)) (* x x)))
↓
(FPCore (x) :precision binary64 (* x (+ x (* x x))))
double code(double x) {
	return (x * (x * x)) + (x * x);
}
↓
double code(double x) {
	return x * (x + (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
\[\left(\left(1 + x\right) \cdot x\right) \cdot x\]

Alternatives

Alternative 1
Error0.0
Cost448
\[\left(x \cdot x\right) \cdot \left(x + 1\right)\]
Alternative 2
Error1.4
Cost192
\[x \cdot x\]
Alternative 3
Error31.1
Cost64
\[0\]
Alternative 4
Error61.3
Cost64
\[1\]

Error

Derivation

  1. Initial program 0.0

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

  3. Applied distribute-lft-out_binary64_24160.0

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

  4. Simplified0.0

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

  5. Simplified0.0

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

  6. Final simplification0.0

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

Reproduce

herbie shell --seed 2021044 
(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)))