Average Error: 0.2 → 0.1
Time: 2.0s
Precision: 64
\[\left(x \cdot x\right) \cdot \left(3 - x \cdot 2\right)\]
↓
\[\left(x \cdot x\right) \cdot 3 - 2 \cdot {x}^{3}\]
\left(x \cdot x\right) \cdot \left(3 - x \cdot 2\right)
↓
\left(x \cdot x\right) \cdot 3 - 2 \cdot {x}^{3}
double code(double x) {
	return ((double) (((double) (x * x)) * ((double) (3.0 - ((double) (x * 2.0))))));
}
↓
double code(double x) {
	return ((double) (((double) (((double) (x * x)) * 3.0)) - ((double) (2.0 * ((double) pow(x, 3.0))))));
}

Error

Bits error versus x

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Your Program's Arguments

Results

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Target

Original0.2
Target0.2
Herbie0.1
\[x \cdot \left(x \cdot \left(3 - x \cdot 2\right)\right)\]

Derivation

  1. Initial program 0.2

    \[\left(x \cdot x\right) \cdot \left(3 - x \cdot 2\right)\]
  2. Using strategy rm

  3. Applied sub-neg0.2

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

  4. Applied distribute-lft-in0.2

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

  5. Simplified0.1

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

  7. Applied unsub-neg0.1

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

  8. Final simplification0.1

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

Reproduce

herbie shell --seed 2020128 
(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))))