Average Error: 0.3 → 0.2
Time: 10.2s
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 r586029 = 3.0;
        double r586030 = 2.0;
        double r586031 = x;
        double r586032 = r586031 * r586029;
        double r586033 = r586030 - r586032;
        double r586034 = r586029 * r586033;
        double r586035 = r586034 * r586031;
        return r586035;
}
↓
double f(double x) {
        double r586036 = 6.0;
        double r586037 = x;
        double r586038 = r586036 * r586037;
        double r586039 = 9.0;
        double r586040 = 2.0;
        double r586041 = pow(r586037, r586040);
        double r586042 = r586039 * r586041;
        double r586043 = r586038 - r586042;
        return r586043;
}

Error

Bits error versus x

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Your Program's Arguments

Results

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Target

Original0.3
Target0.2
Herbie0.2
\[6 \cdot x - 9 \cdot \left(x \cdot x\right)\]

Derivation

  1. Initial program 0.3

    \[\left(3 \cdot \left(2 - x \cdot 3\right)\right) \cdot x\]

  2. Taylor expanded around 0 0.2

    \[\leadsto \color{blue}{\left(6 - 9 \cdot x\right)} \cdot x\]
  3. Using strategy rm

  4. Applied flip--0.3

    \[\leadsto \color{blue}{\frac{6 \cdot 6 - \left(9 \cdot x\right) \cdot \left(9 \cdot x\right)}{6 + 9 \cdot x}} \cdot x\]

  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 2020045 
(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))