Average Error: 0.1 → 0.1
Time: 16.1s
Precision: 64
\[3 \cdot \left(\left(\left(x \cdot 3\right) \cdot x - x \cdot 4\right) + 1\right)\]
↓
\[3 + x \cdot \left(9 \cdot x - 12\right)\]
3 \cdot \left(\left(\left(x \cdot 3\right) \cdot x - x \cdot 4\right) + 1\right)
↓
3 + x \cdot \left(9 \cdot x - 12\right)
double f(double x) {
        double r563619 = 3.0;
        double r563620 = x;
        double r563621 = r563620 * r563619;
        double r563622 = r563621 * r563620;
        double r563623 = 4.0;
        double r563624 = r563620 * r563623;
        double r563625 = r563622 - r563624;
        double r563626 = 1.0;
        double r563627 = r563625 + r563626;
        double r563628 = r563619 * r563627;
        return r563628;
}
↓
double f(double x) {
        double r563629 = 3.0;
        double r563630 = x;
        double r563631 = 9.0;
        double r563632 = r563631 * r563630;
        double r563633 = 12.0;
        double r563634 = r563632 - r563633;
        double r563635 = r563630 * r563634;
        double r563636 = r563629 + r563635;
        return r563636;
}

Error

Bits error versus x

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Results

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Target

Original0.1
Target0.1
Herbie0.1
\[3 + \left(\left(9 \cdot x\right) \cdot x - 12 \cdot x\right)\]

Derivation

  1. Initial program 0.1

    \[3 \cdot \left(\left(\left(x \cdot 3\right) \cdot x - x \cdot 4\right) + 1\right)\]

  2. Taylor expanded around 0 0.1

    \[\leadsto \color{blue}{\left(9 \cdot {x}^{2} + 3\right) - 12 \cdot x}\]

  3. Simplified0.1

    \[\leadsto \color{blue}{3 + x \cdot \left(9 \cdot x - 12\right)}\]

  4. Final simplification0.1

    \[\leadsto 3 + x \cdot \left(9 \cdot x - 12\right)\]

Reproduce

herbie shell --seed 2019306 
(FPCore (x)
  :name "Diagrams.Tangent:$catParam from diagrams-lib-1.3.0.3, D"
  :precision binary64

  :herbie-target
  (+ 3 (- (* (* 9 x) x) (* 12 x)))

  (* 3 (+ (- (* (* x 3) x) (* x 4)) 1)))