Average Error: 0.2 → 0.1
Time: 2.0s
Precision: binary64
\[\left(x \cdot x\right) \cdot \left(3 - x \cdot 2\right)\]
↓
\[x \cdot \left(x \cdot 3\right) - 2 \cdot {x}^{3}\]
\left(x \cdot x\right) \cdot \left(3 - x \cdot 2\right)
↓
x \cdot \left(x \cdot 3\right) - 2 \cdot {x}^{3}
(FPCore (x) :precision binary64 (* (* x x) (- 3.0 (* x 2.0))))
↓
(FPCore (x) :precision binary64 (- (* x (* x 3.0)) (* 2.0 (pow x 3.0))))
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(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 Error: 0.2 bits

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

  2. SimplifiedError: 0.2 bits

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

  4. Applied sub-negError: 0.2 bits

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

  5. Applied distribute-lft-inError: 0.2 bits

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

  6. Applied distribute-lft-inError: 0.2 bits

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

  7. SimplifiedError: 0.1 bits

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

  8. Final simplificationError: 0.1 bits

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

Reproduce

herbie shell --seed 2020204 
(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))))