Average Error: 0.2 → 0.2
Time: 14.8s
Precision: 64
\[\left(3 \cdot \left(2 - x \cdot 3\right)\right) \cdot x\]
↓
\[\left(6 - x \cdot 9\right) \cdot x\]
\left(3 \cdot \left(2 - x \cdot 3\right)\right) \cdot x
↓
\left(6 - x \cdot 9\right) \cdot x
double f(double x) {
        double r37148766 = 3.0;
        double r37148767 = 2.0;
        double r37148768 = x;
        double r37148769 = r37148768 * r37148766;
        double r37148770 = r37148767 - r37148769;
        double r37148771 = r37148766 * r37148770;
        double r37148772 = r37148771 * r37148768;
        return r37148772;
}
↓
double f(double x) {
        double r37148773 = 6.0;
        double r37148774 = x;
        double r37148775 = 9.0;
        double r37148776 = r37148774 * r37148775;
        double r37148777 = r37148773 - r37148776;
        double r37148778 = r37148777 * r37148774;
        return r37148778;
}

Error

Bits error versus x

Try it out

Your Program's Arguments

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. Taylor expanded around 0 0.2

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

  3. Final simplification0.2

    \[\leadsto \left(6 - x \cdot 9\right) \cdot x\]

Reproduce

herbie shell --seed 2019171 
(FPCore (x)
  :name "Diagrams.Tangent:$catParam from diagrams-lib-1.3.0.3, E"

  :herbie-target
  (- (* 6.0 x) (* 9.0 (* x x)))

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