Average Error: 0.2 → 0.2
Time: 2.5s
Precision: 64
\[\left(3 \cdot \left(2 - x \cdot 3\right)\right) \cdot x\]
↓
\[6 \cdot x - 9 \cdot {x}^{2}\]
\left(3 \cdot \left(2 - x \cdot 3\right)\right) \cdot x
↓
6 \cdot x - 9 \cdot {x}^{2}
double f(double x) {
        double r709799 = 3.0;
        double r709800 = 2.0;
        double r709801 = x;
        double r709802 = r709801 * r709799;
        double r709803 = r709800 - r709802;
        double r709804 = r709799 * r709803;
        double r709805 = r709804 * r709801;
        return r709805;
}
↓
double f(double x) {
        double r709806 = 6.0;
        double r709807 = x;
        double r709808 = r709806 * r709807;
        double r709809 = 9.0;
        double r709810 = 2.0;
        double r709811 = pow(r709807, r709810);
        double r709812 = r709809 * r709811;
        double r709813 = r709808 - r709812;
        return r709813;
}

Error

Bits error versus x

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Results

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Target

Original0.2
Target0.2
Herbie0.2
\[6 \cdot x - 9 \cdot \left(x \cdot x\right)\]

Derivation

  1. Initial program 0.2

    \[\left(3 \cdot \left(2 - x \cdot 3\right)\right) \cdot x\]
  2. Using strategy rm

  3. Applied flip--0.3

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

  4. Applied associate-*r/0.3

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

  5. Taylor expanded around 0 0.2

    \[\leadsto \color{blue}{6 \cdot x - 9 \cdot {x}^{2}}\]

  6. Final simplification0.2

    \[\leadsto 6 \cdot x - 9 \cdot {x}^{2}\]

Reproduce

herbie shell --seed 2020003 
(FPCore (x)
  :name "Diagrams.Tangent:$catParam from diagrams-lib-1.3.0.3, E"
  :precision binary64

  :herbie-target
  (- (* 6 x) (* 9 (* x x)))

  (* (* 3 (- 2 (* x 3))) x))