Average Error: 0.0 → 0.0
Time: 1.7s
Precision: binary64
Cost: 6720
\[x \cdot e^{y \cdot y}\]
↓
\[x \cdot e^{y \cdot y}\]
x \cdot e^{y \cdot y}
↓
x \cdot e^{y \cdot y}
(FPCore (x y) :precision binary64 (* x (exp (* y y))))
↓
(FPCore (x y) :precision binary64 (* x (exp (* y y))))
double code(double x, double y) {
	return x * exp(y * y);
}
↓
double code(double x, double y) {
	return x * 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
Cost26176
\[\sqrt{e^{y \cdot y}} \cdot \left(x \cdot \sqrt{e^{y \cdot y}}\right)\]
Alternative 2
Error0.4
Cost20352
\[\sqrt{e^{y \cdot y}} \cdot \left(x \cdot \left(y \cdot \frac{y}{2} + \left(1 + {y}^{4} \cdot 0.125\right)\right)\right)\]
Alternative 3
Error0.5
Cost448
\[x + x \cdot \left(y \cdot y\right)\]
Alternative 4
Error0.8
Cost64
\[x\]
Alternative 5
Error61.7
Cost64
\[1\]
Alternative 6
Error61.5
Cost64
\[0\]
Alternative 7
Error61.8
Cost64
\[-1\]

Error

Derivation

  1. Initial program 0.0

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

  2. Simplified0.0

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

  3. Final simplification0.0

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

Reproduce

herbie shell --seed 2021042 
(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))))