Average Error: 0.2 → 0.1
Time: 14.7s
Precision: 64
\[\left(x \cdot x\right) \cdot \left(3 - x \cdot 2\right)\]
↓
\[x \cdot \left(x \cdot 3\right) + \left(-2 \cdot {x}^{3}\right)\]
\left(x \cdot x\right) \cdot \left(3 - x \cdot 2\right)
↓
x \cdot \left(x \cdot 3\right) + \left(-2 \cdot {x}^{3}\right)
double f(double x) {
        double r1245609 = x;
        double r1245610 = r1245609 * r1245609;
        double r1245611 = 3.0;
        double r1245612 = 2.0;
        double r1245613 = r1245609 * r1245612;
        double r1245614 = r1245611 - r1245613;
        double r1245615 = r1245610 * r1245614;
        return r1245615;
}
↓
double f(double x) {
        double r1245616 = x;
        double r1245617 = 3.0;
        double r1245618 = r1245616 * r1245617;
        double r1245619 = r1245616 * r1245618;
        double r1245620 = 2.0;
        double r1245621 = 3.0;
        double r1245622 = pow(r1245616, r1245621);
        double r1245623 = r1245620 * r1245622;
        double r1245624 = -r1245623;
        double r1245625 = r1245619 + r1245624;
        return r1245625;
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original0.2
Target0.2
Herbie0.1
\[x \cdot \left(x \cdot \left(3 - x \cdot 2\right)\right)\]

Derivation

  1. Initial program 0.2

    \[\left(x \cdot x\right) \cdot \left(3 - x \cdot 2\right)\]
  2. Using strategy rm

  3. Applied sub-neg0.2

    \[\leadsto \left(x \cdot x\right) \cdot \color{blue}{\left(3 + \left(-x \cdot 2\right)\right)}\]

  4. Applied distribute-lft-in0.2

    \[\leadsto \color{blue}{\left(x \cdot x\right) \cdot 3 + \left(x \cdot x\right) \cdot \left(-x \cdot 2\right)}\]

  5. Simplified0.1

    \[\leadsto \left(x \cdot x\right) \cdot 3 + \color{blue}{\left(-2 \cdot {x}^{3}\right)}\]
  6. Using strategy rm

  7. Applied associate-*l*0.1

    \[\leadsto \color{blue}{x \cdot \left(x \cdot 3\right)} + \left(-2 \cdot {x}^{3}\right)\]

  8. Final simplification0.1

    \[\leadsto x \cdot \left(x \cdot 3\right) + \left(-2 \cdot {x}^{3}\right)\]

Reproduce

herbie shell --seed 2019303 
(FPCore (x)
  :name "Data.Spline.Key:interpolateKeys from smoothie-0.4.0.2"
  :precision binary64

  :herbie-target
  (* x (* x (- 3 (* x 2))))

  (* (* x x) (- 3 (* x 2))))