Average Error: 0.0 → 0.0
Time: 4.1s
Precision: binary64
Cost: 13056
\[x \cdot e^{y \cdot y}\]
↓
\[x \cdot {\left(e^{y}\right)}^{y}\]
x \cdot e^{y \cdot y}
↓
x \cdot {\left(e^{y}\right)}^{y}
(FPCore (x y) :precision binary64 (* x (exp (* y y))))
↓
(FPCore (x y) :precision binary64 (* x (pow (exp y) y)))
double code(double x, double y) {
	return x * exp(y * y);
}
↓
double code(double x, double y) {
	return x * pow(exp(y), 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

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

Alternatives

Alternative 1
Error0.0
Cost6720
\[x \cdot e^{y \cdot y}\]
Alternative 2
Error0.6
Cost448
\[x + x \cdot \left(y \cdot y\right)\]
Alternative 3
Error1.0
Cost64
\[x\]
Alternative 4
Error60.6
Cost385
\[\begin{array}{l} \mathbf{if}\;x \leq 1.61212272646465 \cdot 10^{-310}:\\ \;\;\;\;-1\\ \mathbf{else}:\\ \;\;\;\;1\\ \end{array}\]
Alternative 5
Error61.6
Cost64
\[0\]
Alternative 6
Error61.8
Cost64
\[1\]

Error

Derivation

  1. Initial program 0.0

    \[x \cdot e^{y \cdot y}\]
  2. Using strategy rm

  3. Applied add-log-exp_binary64_229640.0

    \[\leadsto x \cdot e^{\color{blue}{\log \left(e^{y}\right)} \cdot y}\]

  4. Applied exp-to-pow_binary64_229870.0

    \[\leadsto x \cdot \color{blue}{{\left(e^{y}\right)}^{y}}\]

  5. Simplified0.0

    \[\leadsto \color{blue}{x \cdot {\left(e^{y}\right)}^{y}}\]

  6. Final simplification0.0

    \[\leadsto x \cdot {\left(e^{y}\right)}^{y}\]

Reproduce

herbie shell --seed 2021044 
(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))))