Average Error: 0.2 → 0.1
Time: 2.3s
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 r913591 = x;
        double r913592 = r913591 * r913591;
        double r913593 = 3.0;
        double r913594 = 2.0;
        double r913595 = r913591 * r913594;
        double r913596 = r913593 - r913595;
        double r913597 = r913592 * r913596;
        return r913597;
}
↓
double f(double x) {
        double r913598 = x;
        double r913599 = 3.0;
        double r913600 = r913598 * r913599;
        double r913601 = r913598 * r913600;
        double r913602 = 2.0;
        double r913603 = 3.0;
        double r913604 = pow(r913598, r913603);
        double r913605 = r913602 * r913604;
        double r913606 = -r913605;
        double r913607 = r913601 + r913606;
        return r913607;
}

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 2020065 +o rules:numerics
(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))))