Average Error: 5.3 → 5.3
Time: 3.9s
Precision: binary64
\[x \cdot \left(1 + y \cdot y\right)\]
↓
\[x + x \cdot {y}^{2}\]
x \cdot \left(1 + y \cdot y\right)
↓
x + x \cdot {y}^{2}
(FPCore (x y) :precision binary64 (* x (+ 1.0 (* y y))))
↓
(FPCore (x y) :precision binary64 (+ x (* x (pow y 2.0))))
double code(double x, double y) {
	return x * (1.0 + (y * y));
}
↓
double code(double x, double y) {
	return x + (x * pow(y, 2.0));
}

Error

Bits error versus x

Bits error versus y

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original5.3
Target0.1
Herbie5.3
\[x + \left(x \cdot y\right) \cdot y\]

Derivation

  1. Initial program 5.3

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

  2. Taylor expanded around 0 5.3

    \[\leadsto \color{blue}{x \cdot {y}^{2} + x}\]

  3. Final simplification5.3

    \[\leadsto x + x \cdot {y}^{2}\]

Reproduce

herbie shell --seed 2021043 
(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))))