Average Error: 0.2 → 0.2
Time: 8.2s
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 r438362 = 3.0;
        double r438363 = 2.0;
        double r438364 = x;
        double r438365 = r438364 * r438362;
        double r438366 = r438363 - r438365;
        double r438367 = r438362 * r438366;
        double r438368 = r438367 * r438364;
        return r438368;
}
↓
double f(double x) {
        double r438369 = x;
        double r438370 = 6.0;
        double r438371 = 9.0;
        double r438372 = r438369 * r438371;
        double r438373 = r438370 - r438372;
        double r438374 = r438369 * r438373;
        return r438374;
}

Error

Bits error versus x

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Your Program's Arguments

Results

Enter valid numbers for all inputs

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. Taylor expanded around 0 0.2

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

  3. Simplified0.2

    \[\leadsto \color{blue}{x \cdot \left(6 - x \cdot 9\right)}\]

  4. Final simplification0.2

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

Reproduce

herbie shell --seed 2019208 +o rules:numerics
(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))