Average Error: 0.0 → 0.0
Time: 1.4s
Precision: 64
\[0.0 \le x \le 2\]
\[x \cdot \left(x \cdot x\right) + x \cdot x\]
↓
\[{x}^{3} + {x}^{2}\]
x \cdot \left(x \cdot x\right) + x \cdot x
↓
{x}^{3} + {x}^{2}
double f(double x) {
        double r102613 = x;
        double r102614 = r102613 * r102613;
        double r102615 = r102613 * r102614;
        double r102616 = r102615 + r102614;
        return r102616;
}
↓
double f(double x) {
        double r102617 = x;
        double r102618 = 3.0;
        double r102619 = pow(r102617, r102618);
        double r102620 = 2.0;
        double r102621 = pow(r102617, r102620);
        double r102622 = r102619 + r102621;
        return r102622;
}

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 distribute-lft-in0.0

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

  5. Simplified0.0

    \[\leadsto \color{blue}{{x}^{3}} + x \cdot x\]

  6. Simplified0.0

    \[\leadsto {x}^{3} + \color{blue}{{x}^{2}}\]

  7. Final simplification0.0

    \[\leadsto {x}^{3} + {x}^{2}\]

Reproduce

herbie shell --seed 2020064 
(FPCore (x)
  :name "Expression 3, p15"
  :precision binary64
  :pre (<= 0.0 x 2)

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

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