Average Error: 5.0 → 0.1
Time: 1.8s
Precision: binary64
\[x \cdot \left(1 + y \cdot y\right)\]
↓
\[x \cdot 1 + y \cdot \left(x \cdot y\right)\]
x \cdot \left(1 + y \cdot y\right)
↓
x \cdot 1 + y \cdot \left(x \cdot y\right)
(FPCore (x y) :precision binary64 (* x (+ 1.0 (* y y))))
↓
(FPCore (x y) :precision binary64 (+ (* x 1.0) (* y (* x y))))
double code(double x, double y) {
	return ((double) (x * ((double) (1.0 + ((double) (y * y))))));
}
↓
double code(double x, double y) {
	return ((double) (((double) (x * 1.0)) + ((double) (y * ((double) (x * y))))));
}

Error

Bits error versus x

Bits error versus y

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original5.0
Target0.1
Herbie0.1
\[x + \left(x \cdot y\right) \cdot y\]

Derivation

  1. Initial program Error: 5.0 bits

    \[x \cdot \left(1 + y \cdot y\right)\]
  2. Using strategy rm

  3. Applied distribute-lft-inError: 5.0 bits

    \[\leadsto \color{blue}{x \cdot 1 + x \cdot \left(y \cdot y\right)}\]
  4. Using strategy rm

  5. Applied associate-*r*Error: 0.1 bits

    \[\leadsto x \cdot 1 + \color{blue}{\left(x \cdot y\right) \cdot y}\]

  6. Final simplificationError: 0.1 bits

    \[\leadsto x \cdot 1 + y \cdot \left(x \cdot y\right)\]

Reproduce

herbie shell --seed 2020204 
(FPCore (x y)
  :name "Numeric.Integration.TanhSinh:everywhere from integration-0.2.1"
  :precision binary64

  :herbie-target
  (+ x (* (* x y) y))

  (* x (+ 1.0 (* y y))))