Average Error: 0.0 → 0.0
Time: 1.1s
Precision: 64
\[0.0 \le x \le 2\]
\[x \cdot \left(x \cdot x\right) + x \cdot x\]
↓
\[\left(x \cdot x + x\right) \cdot x\]
x \cdot \left(x \cdot x\right) + x \cdot x
↓
\left(x \cdot x + x\right) \cdot x
double f(double x) {
        double r121257 = x;
        double r121258 = r121257 * r121257;
        double r121259 = r121257 * r121258;
        double r121260 = r121259 + r121258;
        return r121260;
}
↓
double f(double x) {
        double r121261 = x;
        double r121262 = r121261 * r121261;
        double r121263 = r121262 + r121261;
        double r121264 = r121263 * r121261;
        return r121264;
}

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. Simplified0.0

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

  4. Applied *-commutative0.0

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

  5. Final simplification0.0

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

Reproduce

herbie shell --seed 2020046 
(FPCore (x)
  :name "Expression 3, p15"
  :precision binary64
  :pre (<= 0.0 x 2)

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

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