Average Error: 0.2 → 0.1
Time: 12.5s
Precision: 64
\[\left(x \cdot x\right) \cdot \left(3 - x \cdot 2\right)\]
↓
\[\left(x \cdot 3\right) \cdot x + \left(-2 \cdot {x}^{3}\right)\]
\left(x \cdot x\right) \cdot \left(3 - x \cdot 2\right)
↓
\left(x \cdot 3\right) \cdot x + \left(-2 \cdot {x}^{3}\right)
double f(double x) {
        double r471792 = x;
        double r471793 = r471792 * r471792;
        double r471794 = 3.0;
        double r471795 = 2.0;
        double r471796 = r471792 * r471795;
        double r471797 = r471794 - r471796;
        double r471798 = r471793 * r471797;
        return r471798;
}
↓
double f(double x) {
        double r471799 = x;
        double r471800 = 3.0;
        double r471801 = r471799 * r471800;
        double r471802 = r471801 * r471799;
        double r471803 = 2.0;
        double r471804 = 3.0;
        double r471805 = pow(r471799, r471804);
        double r471806 = r471803 * r471805;
        double r471807 = -r471806;
        double r471808 = r471802 + r471807;
        return r471808;
}

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. Simplified0.2

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

  6. Simplified0.1

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

  7. Final simplification0.1

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

Reproduce

herbie shell --seed 2019326 +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))))