Average Error: 0.2 → 0.1
Time: 10.3s
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 r840533 = x;
        double r840534 = r840533 * r840533;
        double r840535 = 3.0;
        double r840536 = 2.0;
        double r840537 = r840533 * r840536;
        double r840538 = r840535 - r840537;
        double r840539 = r840534 * r840538;
        return r840539;
}
↓
double f(double x) {
        double r840540 = x;
        double r840541 = r840540 * r840540;
        double r840542 = 3.0;
        double r840543 = r840541 * r840542;
        double r840544 = 2.0;
        double r840545 = 3.0;
        double r840546 = pow(r840540, r840545);
        double r840547 = r840544 * r840546;
        double r840548 = -r840547;
        double r840549 = r840543 + r840548;
        return r840549;
}

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))))