Average Error: 0.2 → 0.1
Time: 19.2s
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 r721618 = x;
        double r721619 = r721618 * r721618;
        double r721620 = 3.0;
        double r721621 = 2.0;
        double r721622 = r721618 * r721621;
        double r721623 = r721620 - r721622;
        double r721624 = r721619 * r721623;
        return r721624;
}
↓
double f(double x) {
        double r721625 = x;
        double r721626 = 3.0;
        double r721627 = r721625 * r721626;
        double r721628 = r721627 * r721625;
        double r721629 = 2.0;
        double r721630 = 3.0;
        double r721631 = pow(r721625, r721630);
        double r721632 = r721629 * r721631;
        double r721633 = -r721632;
        double r721634 = r721628 + r721633;
        return r721634;
}

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 2019304 +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))))