Average Error: 0.2 → 0.1
Time: 12.8s
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 r870457 = x;
        double r870458 = r870457 * r870457;
        double r870459 = 3.0;
        double r870460 = 2.0;
        double r870461 = r870457 * r870460;
        double r870462 = r870459 - r870461;
        double r870463 = r870458 * r870462;
        return r870463;
}
↓
double f(double x) {
        double r870464 = x;
        double r870465 = 3.0;
        double r870466 = r870464 * r870465;
        double r870467 = r870466 * r870464;
        double r870468 = 2.0;
        double r870469 = 3.0;
        double r870470 = pow(r870464, r870469);
        double r870471 = r870468 * r870470;
        double r870472 = -r870471;
        double r870473 = r870467 + r870472;
        return r870473;
}

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 2019350 +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))))