Average Error: 0.1 → 0.1
Time: 9.8s
Precision: 64
\[3 \cdot \left(\left(\left(x \cdot 3\right) \cdot x - x \cdot 4\right) + 1\right)\]
↓
\[3 + \left(x \cdot \left(x \cdot 9\right) + \left(-12\right) \cdot x\right)\]
3 \cdot \left(\left(\left(x \cdot 3\right) \cdot x - x \cdot 4\right) + 1\right)
↓
3 + \left(x \cdot \left(x \cdot 9\right) + \left(-12\right) \cdot x\right)
double f(double x) {
        double r708740 = 3.0;
        double r708741 = x;
        double r708742 = r708741 * r708740;
        double r708743 = r708742 * r708741;
        double r708744 = 4.0;
        double r708745 = r708741 * r708744;
        double r708746 = r708743 - r708745;
        double r708747 = 1.0;
        double r708748 = r708746 + r708747;
        double r708749 = r708740 * r708748;
        return r708749;
}
↓
double f(double x) {
        double r708750 = 3.0;
        double r708751 = x;
        double r708752 = 9.0;
        double r708753 = r708751 * r708752;
        double r708754 = r708751 * r708753;
        double r708755 = 12.0;
        double r708756 = -r708755;
        double r708757 = r708756 * r708751;
        double r708758 = r708754 + r708757;
        double r708759 = r708750 + r708758;
        return r708759;
}

Error

Bits error versus x

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Your Program's Arguments

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. 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. Using strategy rm

  6. Applied sub-neg0.1

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

  7. Applied distribute-lft-in0.1

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

  8. Simplified0.1

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

  9. Final simplification0.1

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

Reproduce

herbie shell --seed 2019350 
(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)))