Average Error: 0.2 → 0.1
Time: 14.4s
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 r570648 = x;
        double r570649 = r570648 * r570648;
        double r570650 = 3.0;
        double r570651 = 2.0;
        double r570652 = r570648 * r570651;
        double r570653 = r570650 - r570652;
        double r570654 = r570649 * r570653;
        return r570654;
}
↓
double f(double x) {
        double r570655 = x;
        double r570656 = r570655 * r570655;
        double r570657 = 3.0;
        double r570658 = r570656 * r570657;
        double r570659 = 2.0;
        double r570660 = 3.0;
        double r570661 = pow(r570655, r570660);
        double r570662 = r570659 * r570661;
        double r570663 = -r570662;
        double r570664 = r570658 + r570663;
        return r570664;
}

Error

Bits error versus x

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Your Program's Arguments

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 2019323 
(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))))