Average Error: 0.2 → 0.1
Time: 12.0s
Precision: 64
\[\left(x \cdot x\right) \cdot \left(3 - x \cdot 2\right)\]
↓
\[\left(x \cdot x\right) \cdot 3 + \left(-2 \cdot {x}^{3}\right)\]
\left(x \cdot x\right) \cdot \left(3 - x \cdot 2\right)
↓
\left(x \cdot x\right) \cdot 3 + \left(-2 \cdot {x}^{3}\right)
double f(double x) {
        double r869774 = x;
        double r869775 = r869774 * r869774;
        double r869776 = 3.0;
        double r869777 = 2.0;
        double r869778 = r869774 * r869777;
        double r869779 = r869776 - r869778;
        double r869780 = r869775 * r869779;
        return r869780;
}
↓
double f(double x) {
        double r869781 = x;
        double r869782 = r869781 * r869781;
        double r869783 = 3.0;
        double r869784 = r869782 * r869783;
        double r869785 = 2.0;
        double r869786 = 3.0;
        double r869787 = pow(r869781, r869786);
        double r869788 = r869785 * r869787;
        double r869789 = -r869788;
        double r869790 = r869784 + r869789;
        return r869790;
}

Error

Bits error versus x

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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. Final simplification0.1

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

Reproduce

herbie shell --seed 2020042 +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))))