Average Error: 0.1 → 0.1
Time: 15.8s
Precision: 64
\[3 \cdot \left(\left(\left(x \cdot 3\right) \cdot x - x \cdot 4\right) + 1\right)\]
↓
\[3 + \left(9 \cdot x - 12\right) \cdot x\]
3 \cdot \left(\left(\left(x \cdot 3\right) \cdot x - x \cdot 4\right) + 1\right)
↓
3 + \left(9 \cdot x - 12\right) \cdot x
double f(double x) {
        double r31465663 = 3.0;
        double r31465664 = x;
        double r31465665 = r31465664 * r31465663;
        double r31465666 = r31465665 * r31465664;
        double r31465667 = 4.0;
        double r31465668 = r31465664 * r31465667;
        double r31465669 = r31465666 - r31465668;
        double r31465670 = 1.0;
        double r31465671 = r31465669 + r31465670;
        double r31465672 = r31465663 * r31465671;
        return r31465672;
}
↓
double f(double x) {
        double r31465673 = 3.0;
        double r31465674 = 9.0;
        double r31465675 = x;
        double r31465676 = r31465674 * r31465675;
        double r31465677 = 12.0;
        double r31465678 = r31465676 - r31465677;
        double r31465679 = r31465678 * r31465675;
        double r31465680 = r31465673 + r31465679;
        return r31465680;
}

Error

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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

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

Reproduce

herbie shell --seed 2019172 
(FPCore (x)
  :name "Diagrams.Tangent:$catParam from diagrams-lib-1.3.0.3, D"

  :herbie-target
  (+ 3.0 (- (* (* 9.0 x) x) (* 12.0 x)))

  (* 3.0 (+ (- (* (* x 3.0) x) (* x 4.0)) 1.0)))