Average Error: 0.2 → 0.1
Time: 20.1s
Precision: 64
\[\left(x \cdot x\right) \cdot \left(3 - x \cdot 2\right)\]
↓
\[\left(x \cdot x\right) \cdot 3 + \left(-2 \cdot {x}^{3}\right)\]
\left(x \cdot x\right) \cdot \left(3 - x \cdot 2\right)
↓
\left(x \cdot x\right) \cdot 3 + \left(-2 \cdot {x}^{3}\right)
double f(double x) {
        double r505689 = x;
        double r505690 = r505689 * r505689;
        double r505691 = 3.0;
        double r505692 = 2.0;
        double r505693 = r505689 * r505692;
        double r505694 = r505691 - r505693;
        double r505695 = r505690 * r505694;
        return r505695;
}
↓
double f(double x) {
        double r505696 = x;
        double r505697 = r505696 * r505696;
        double r505698 = 3.0;
        double r505699 = r505697 * r505698;
        double r505700 = 2.0;
        double r505701 = 3.0;
        double r505702 = pow(r505696, r505701);
        double r505703 = r505700 * r505702;
        double r505704 = -r505703;
        double r505705 = r505699 + r505704;
        return r505705;
}

Error

Bits error versus x

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Results

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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. Final simplification0.1

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

Reproduce

herbie shell --seed 2019322 
(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))))