Average Error: 0.0 → 0.4
Time: 4.3s
Precision: binary64
\[x \cdot e^{y \cdot y}\]
↓
\[x \cdot {y}^{2} + \left(0.5 \cdot \left(x \cdot {y}^{4}\right) + \left(x + 0.16666666666666666 \cdot \left(x \cdot {y}^{6}\right)\right)\right)\]
x \cdot e^{y \cdot y}
↓
x \cdot {y}^{2} + \left(0.5 \cdot \left(x \cdot {y}^{4}\right) + \left(x + 0.16666666666666666 \cdot \left(x \cdot {y}^{6}\right)\right)\right)
(FPCore (x y) :precision binary64 (* x (exp (* y y))))
↓
(FPCore (x y)
 :precision binary64
 (+
  (* x (pow y 2.0))
  (+
   (* 0.5 (* x (pow y 4.0)))
   (+ x (* 0.16666666666666666 (* x (pow y 6.0)))))))
double code(double x, double y) {
	return x * exp(y * y);
}
↓
double code(double x, double y) {
	return (x * pow(y, 2.0)) + ((0.5 * (x * pow(y, 4.0))) + (x + (0.16666666666666666 * (x * pow(y, 6.0)))));
}

Error

Bits error versus x

Bits error versus y

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original0.0
Target0.0
Herbie0.4
\[x \cdot {\left(e^{y}\right)}^{y}\]

Derivation

  1. Initial program 0.0

    \[x \cdot e^{y \cdot y}\]

  2. Taylor expanded around 0 0.4

    \[\leadsto \color{blue}{x \cdot {y}^{2} + \left(0.5 \cdot \left(x \cdot {y}^{4}\right) + \left(x + 0.16666666666666666 \cdot \left(x \cdot {y}^{6}\right)\right)\right)}\]

  3. Final simplification0.4

    \[\leadsto x \cdot {y}^{2} + \left(0.5 \cdot \left(x \cdot {y}^{4}\right) + \left(x + 0.16666666666666666 \cdot \left(x \cdot {y}^{6}\right)\right)\right)\]

Reproduce

herbie shell --seed 2021060 
(FPCore (x y)
  :name "Data.Number.Erf:$dmerfcx from erf-2.0.0.0"
  :precision binary64

  :herbie-target
  (* x (pow (exp y) y))

  (* x (exp (* y y))))