Average Error: 0.2 → 0.1
Time: 2.3s
Precision: binary64
\[\left(x \cdot x\right) \cdot \left(3 - x \cdot 2\right)\]
↓
\[x \cdot \left(x \cdot 3\right) + 2 \cdot {\left(-x\right)}^{3}\]
\left(x \cdot x\right) \cdot \left(3 - x \cdot 2\right)
↓
x \cdot \left(x \cdot 3\right) + 2 \cdot {\left(-x\right)}^{3}
double code(double x) {
	return ((double) (((double) (x * x)) * ((double) (3.0 - ((double) (x * 2.0))))));
}
↓
double code(double x) {
	return ((double) (((double) (x * ((double) (x * 3.0)))) + ((double) (2.0 * ((double) pow(((double) -(x)), 3.0))))));
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

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

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. Simplified0.2

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

  6. Simplified0.1

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

  7. Final simplification0.1

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

Reproduce

herbie shell --seed 2020196 
(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))))