Average Error: 0.2 → 0.1
Time: 17.5s
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 r509706 = x;
        double r509707 = r509706 * r509706;
        double r509708 = 3.0;
        double r509709 = 2.0;
        double r509710 = r509706 * r509709;
        double r509711 = r509708 - r509710;
        double r509712 = r509707 * r509711;
        return r509712;
}
↓
double f(double x) {
        double r509713 = x;
        double r509714 = 3.0;
        double r509715 = r509713 * r509714;
        double r509716 = r509715 * r509713;
        double r509717 = 2.0;
        double r509718 = 3.0;
        double r509719 = pow(r509713, r509718);
        double r509720 = r509717 * r509719;
        double r509721 = -r509720;
        double r509722 = r509716 + r509721;
        return r509722;
}

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 2019323 +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))))