Average Error: 0.0 → 0.0
Time: 2.2s
Precision: binary64
\[x \cdot e^{y \cdot y} \]
↓
\[x \cdot \mathsf{expm1}\left(\mathsf{log1p}\left({\left(e^{y}\right)}^{y}\right)\right) \]
(FPCore (x y) :precision binary64 (* x (exp (* y y))))
↓
(FPCore (x y) :precision binary64 (* x (expm1 (log1p (pow (exp y) y)))))
double code(double x, double y) {
	return x * exp((y * y));
}
↓
double code(double x, double y) {
	return x * expm1(log1p(pow(exp(y), y)));
}

public static double code(double x, double y) {
	return x * Math.exp((y * y));
}
↓
public static double code(double x, double y) {
	return x * Math.expm1(Math.log1p(Math.pow(Math.exp(y), y)));
}

def code(x, y):
	return x * math.exp((y * y))
↓
def code(x, y):
	return x * math.expm1(math.log1p(math.pow(math.exp(y), y)))

function code(x, y)
	return Float64(x * exp(Float64(y * y)))
end
↓
function code(x, y)
	return Float64(x * expm1(log1p((exp(y) ^ y))))
end

code[x_, y_] := N[(x * N[Exp[N[(y * y), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]
↓
code[x_, y_] := N[(x * N[(Exp[N[Log[1 + N[Power[N[Exp[y], $MachinePrecision], y], $MachinePrecision]], $MachinePrecision]] - 1), $MachinePrecision]), $MachinePrecision]

x \cdot e^{y \cdot y}
↓
x \cdot \mathsf{expm1}\left(\mathsf{log1p}\left({\left(e^{y}\right)}^{y}\right)\right)

Error

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Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

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

Derivation

  1. Initial program 0.0

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

  2. Simplified0.0

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

  3. Applied egg-rr0.0

    \[\leadsto x \cdot \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left({\left(e^{y}\right)}^{y}\right)\right)} \]

  4. Final simplification0.0

    \[\leadsto x \cdot \mathsf{expm1}\left(\mathsf{log1p}\left({\left(e^{y}\right)}^{y}\right)\right) \]

Reproduce

herbie shell --seed 2022210 
(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))))