Average Error: 0.2 → 0.1
Time: 2.8s
Precision: 64
\[\left(x \cdot x\right) \cdot \left(3 - x \cdot 2\right)\]
↓
\[x \cdot \left(x \cdot 3\right) + \left(-2 \cdot {x}^{3}\right)\]
\left(x \cdot x\right) \cdot \left(3 - x \cdot 2\right)
↓
x \cdot \left(x \cdot 3\right) + \left(-2 \cdot {x}^{3}\right)
double f(double x) {
        double r740456 = x;
        double r740457 = r740456 * r740456;
        double r740458 = 3.0;
        double r740459 = 2.0;
        double r740460 = r740456 * r740459;
        double r740461 = r740458 - r740460;
        double r740462 = r740457 * r740461;
        return r740462;
}
↓
double f(double x) {
        double r740463 = x;
        double r740464 = 3.0;
        double r740465 = r740463 * r740464;
        double r740466 = r740463 * r740465;
        double r740467 = 2.0;
        double r740468 = 3.0;
        double r740469 = pow(r740463, r740468);
        double r740470 = r740467 * r740469;
        double r740471 = -r740470;
        double r740472 = r740466 + r740471;
        return r740472;
}

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. Simplified0.1

    \[\leadsto \left(x \cdot x\right) \cdot 3 + \color{blue}{\left(-2 \cdot {x}^{3}\right)}\]
  6. Using strategy rm

  7. Applied associate-*l*0.1

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

  8. Final simplification0.1

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

Reproduce

herbie shell --seed 2020047 
(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))))