Average Error: 0.2 → 0.2
Time: 4.0s
Precision: binary64
\[\left(x \cdot x\right) \cdot \left(3 - x \cdot 2\right)\]
↓
\[x \cdot \left(x \cdot 3 + \left(x \cdot x\right) \cdot -2\right)\]
\left(x \cdot x\right) \cdot \left(3 - x \cdot 2\right)
↓
x \cdot \left(x \cdot 3 + \left(x \cdot x\right) \cdot -2\right)
(FPCore (x) :precision binary64 (* (* x x) (- 3.0 (* x 2.0))))
↓
(FPCore (x) :precision binary64 (* x (+ (* x 3.0) (* (* x x) -2.0))))
double code(double x) {
	return (x * x) * (3.0 - (x * 2.0));
}
↓
double code(double x) {
	return x * ((x * 3.0) + ((x * 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
\[x \cdot \left(x \cdot \left(3 - x \cdot 2\right)\right)\]

Derivation

  1. Initial program 0.2

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

  2. Taylor expanded around 0 0.1

    \[\leadsto \color{blue}{3 \cdot {x}^{2} - 2 \cdot {x}^{3}}\]

  3. Simplified0.2

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

  5. Applied sub-neg_binary64_208720.2

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

  6. Applied distribute-rgt-in_binary64_208290.2

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

  7. Simplified0.2

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

  8. Final simplification0.2

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

Reproduce

herbie shell --seed 2021093 
(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))))