Average Error: 0.2 → 0.1
Time: 21.9s
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 r587896 = x;
        double r587897 = r587896 * r587896;
        double r587898 = 3.0;
        double r587899 = 2.0;
        double r587900 = r587896 * r587899;
        double r587901 = r587898 - r587900;
        double r587902 = r587897 * r587901;
        return r587902;
}
↓
double f(double x) {
        double r587903 = x;
        double r587904 = 3.0;
        double r587905 = r587903 * r587904;
        double r587906 = r587905 * r587903;
        double r587907 = 2.0;
        double r587908 = 3.0;
        double r587909 = pow(r587903, r587908);
        double r587910 = r587907 * r587909;
        double r587911 = -r587910;
        double r587912 = r587906 + r587911;
        return r587912;
}

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 2019303 +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))))