Average Error: 0.2 → 0.2
Time: 10.7s
Precision: 64
\[\left(3 \cdot \left(2 - x \cdot 3\right)\right) \cdot x\]
↓
\[x \cdot \left(6 - x \cdot 9\right)\]
\left(3 \cdot \left(2 - x \cdot 3\right)\right) \cdot x
↓
x \cdot \left(6 - x \cdot 9\right)
double f(double x) {
        double r484423 = 3.0;
        double r484424 = 2.0;
        double r484425 = x;
        double r484426 = r484425 * r484423;
        double r484427 = r484424 - r484426;
        double r484428 = r484423 * r484427;
        double r484429 = r484428 * r484425;
        return r484429;
}
↓
double f(double x) {
        double r484430 = x;
        double r484431 = 6.0;
        double r484432 = 9.0;
        double r484433 = r484430 * r484432;
        double r484434 = r484431 - r484433;
        double r484435 = r484430 * r484434;
        return r484435;
}

Error

Bits error versus x

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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. Using strategy rm

  3. Applied flip--0.3

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

  4. Applied associate-*r/0.3

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

  5. Taylor expanded around 0 0.2

    \[\leadsto \color{blue}{6 \cdot x - 9 \cdot {x}^{2}}\]

  6. Final simplification0.2

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

Reproduce

herbie shell --seed 2019291 
(FPCore (x)
  :name "Diagrams.Tangent:$catParam from diagrams-lib-1.3.0.3, E"
  :precision binary64

  :herbie-target
  (- (* 6 x) (* 9 (* x x)))

  (* (* 3 (- 2 (* x 3))) x))