Average Error: 0.2 → 0.1
Time: 9.6s
Precision: 64
\[3 \cdot \left(\left(\left(x \cdot 3\right) \cdot x - x \cdot 4\right) + 1\right)\]
↓
\[3 + x \cdot \left(x \cdot 9 - 12\right)\]
3 \cdot \left(\left(\left(x \cdot 3\right) \cdot x - x \cdot 4\right) + 1\right)
↓
3 + x \cdot \left(x \cdot 9 - 12\right)
double f(double x) {
        double r596712 = 3.0;
        double r596713 = x;
        double r596714 = r596713 * r596712;
        double r596715 = r596714 * r596713;
        double r596716 = 4.0;
        double r596717 = r596713 * r596716;
        double r596718 = r596715 - r596717;
        double r596719 = 1.0;
        double r596720 = r596718 + r596719;
        double r596721 = r596712 * r596720;
        return r596721;
}
↓
double f(double x) {
        double r596722 = 3.0;
        double r596723 = x;
        double r596724 = 9.0;
        double r596725 = r596723 * r596724;
        double r596726 = 12.0;
        double r596727 = r596725 - r596726;
        double r596728 = r596723 * r596727;
        double r596729 = r596722 + r596728;
        return r596729;
}

Error

Bits error versus x

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Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original0.2
Target0.1
Herbie0.1
\[3 + \left(\left(9 \cdot x\right) \cdot x - 12 \cdot x\right)\]

Derivation

  1. Initial program 0.2

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

  2. Simplified0.1

    \[\leadsto \color{blue}{3 \cdot \left(1 + x \cdot \left(x \cdot 3 - 4\right)\right)}\]

  3. Taylor expanded around 0 0.1

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

  4. Simplified0.1

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

  5. Final simplification0.1

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

Reproduce

herbie shell --seed 2019235 
(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)))