Average Error: 0.2 → 0.2
Time: 1.7s
Precision: binary64
\[\left(x \cdot x\right) \cdot \left(3 - x \cdot 2\right)\]
↓
\[x \cdot \frac{x \cdot \left(3 \cdot 3 - x \cdot \left(x \cdot \left(2 \cdot 2\right)\right)\right)}{3 + x \cdot 2}\]
\left(x \cdot x\right) \cdot \left(3 - x \cdot 2\right)
↓
x \cdot \frac{x \cdot \left(3 \cdot 3 - x \cdot \left(x \cdot \left(2 \cdot 2\right)\right)\right)}{3 + x \cdot 2}
double code(double x) {
	return ((double) (((double) (x * x)) * ((double) (3.0 - ((double) (x * 2.0))))));
}
↓
double code(double x) {
	return ((double) (x * ((double) (((double) (x * ((double) (((double) (3.0 * 3.0)) - ((double) (x * ((double) (x * ((double) (2.0 * 2.0)))))))))) / ((double) (3.0 + ((double) (x * 2.0))))))));
}

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
\[x \cdot \left(x \cdot \left(3 - x \cdot 2\right)\right)\]

Derivation

  1. Initial program 0.2

    \[\left(x \cdot x\right) \cdot \left(3 - x \cdot 2\right)\]

  2. Simplified0.2

    \[\leadsto \color{blue}{x \cdot \left(x \cdot \left(3 - x \cdot 2\right)\right)}\]
  3. Using strategy rm

  4. Applied flip--0.2

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

  5. Applied associate-*r/0.2

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

  6. Simplified0.2

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

  7. Final simplification0.2

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

Reproduce

herbie shell --seed 2020184 
(FPCore (x)
  :name "Data.Spline.Key:interpolateKeys from smoothie-0.4.0.2"
  :precision binary64

  :herbie-target
  (* x (* x (- 3.0 (* x 2.0))))

  (* (* x x) (- 3.0 (* x 2.0))))