Average Error: 0.2 → 0.1
Time: 10.6s
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 r1018980 = x;
        double r1018981 = r1018980 * r1018980;
        double r1018982 = 3.0;
        double r1018983 = 2.0;
        double r1018984 = r1018980 * r1018983;
        double r1018985 = r1018982 - r1018984;
        double r1018986 = r1018981 * r1018985;
        return r1018986;
}
↓
double f(double x) {
        double r1018987 = x;
        double r1018988 = r1018987 * r1018987;
        double r1018989 = 3.0;
        double r1018990 = r1018988 * r1018989;
        double r1018991 = 2.0;
        double r1018992 = 3.0;
        double r1018993 = pow(r1018987, r1018992);
        double r1018994 = r1018991 * r1018993;
        double r1018995 = -r1018994;
        double r1018996 = r1018990 + r1018995;
        return r1018996;
}

Error

Bits error versus x

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Results

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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 
(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))))