Average Error: 0.2 → 0.1
Time: 14.3s
Precision: 64
\[\left(x \cdot x\right) \cdot \left(3 - x \cdot 2\right)\]
↓
\[x \cdot \left(x \cdot 3\right) + \left(-2\right) \cdot {x}^{3}\]
\left(x \cdot x\right) \cdot \left(3 - x \cdot 2\right)
↓
x \cdot \left(x \cdot 3\right) + \left(-2\right) \cdot {x}^{3}
double f(double x) {
        double r642101 = x;
        double r642102 = r642101 * r642101;
        double r642103 = 3.0;
        double r642104 = 2.0;
        double r642105 = r642101 * r642104;
        double r642106 = r642103 - r642105;
        double r642107 = r642102 * r642106;
        return r642107;
}
↓
double f(double x) {
        double r642108 = x;
        double r642109 = 3.0;
        double r642110 = r642108 * r642109;
        double r642111 = r642108 * r642110;
        double r642112 = 2.0;
        double r642113 = -r642112;
        double r642114 = 3.0;
        double r642115 = pow(r642108, r642114);
        double r642116 = r642113 * r642115;
        double r642117 = r642111 + r642116;
        return r642117;
}

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. Simplified0.2

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

  6. Simplified0.1

    \[\leadsto 3 \cdot \left(x \cdot x\right) + \color{blue}{\left(-2\right) \cdot {x}^{3}}\]
  7. Using strategy rm

  8. Applied *-un-lft-identity0.1

    \[\leadsto \color{blue}{\left(1 \cdot 3\right)} \cdot \left(x \cdot x\right) + \left(-2\right) \cdot {x}^{3}\]

  9. Applied associate-*l*0.1

    \[\leadsto \color{blue}{1 \cdot \left(3 \cdot \left(x \cdot x\right)\right)} + \left(-2\right) \cdot {x}^{3}\]

  10. Simplified0.1

    \[\leadsto 1 \cdot \color{blue}{\left(x \cdot \left(x \cdot 3\right)\right)} + \left(-2\right) \cdot {x}^{3}\]

  11. Final simplification0.1

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

Reproduce

herbie shell --seed 2019198 
(FPCore (x)
  :name "Data.Spline.Key:interpolateKeys from smoothie-0.4.0.2"

  :herbie-target
  (* x (* x (- 3.0 (* x 2.0))))

  (* (* x x) (- 3.0 (* x 2.0))))