Average Error: 0.2 → 0.2
Time: 2.9s
Precision: 64
\[\left(3 \cdot \left(2 - x \cdot 3\right)\right) \cdot x\]
↓
\[6 \cdot x - 9 \cdot {x}^{2}\]
\left(3 \cdot \left(2 - x \cdot 3\right)\right) \cdot x
↓
6 \cdot x - 9 \cdot {x}^{2}
double code(double x) {
	return ((3.0 * (2.0 - (x * 3.0))) * x);
}
↓
double code(double x) {
	return ((6.0 * x) - (9.0 * pow(x, 2.0)));
}

Error

Bits error versus x

Try it out

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. 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. Simplified0.3

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

  6. Taylor expanded around 0 0.2

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

  7. Final simplification0.2

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

Reproduce

herbie shell --seed 2020049 +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))