Average Error: 0.2 → 0.1
Time: 4.0s
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 r3668 = x;
        double r3669 = r3668 * r3668;
        double r3670 = 3.0;
        double r3671 = 2.0;
        double r3672 = r3668 * r3671;
        double r3673 = r3670 - r3672;
        double r3674 = r3669 * r3673;
        return r3674;
}
↓
double f(double x) {
        double r3675 = x;
        double r3676 = r3675 * r3675;
        double r3677 = 3.0;
        double r3678 = r3676 * r3677;
        double r3679 = 2.0;
        double r3680 = 3.0;
        double r3681 = pow(r3675, r3680);
        double r3682 = r3679 * r3681;
        double r3683 = -r3682;
        double r3684 = r3678 + r3683;
        return r3684;
}

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 2020025 +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))))