Average Error: 0.0 → 0.0

Time: 3.8s

Precision: binary64

Cost: 25856

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

↓

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

(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)

Try it out

In
Out

Enter valid numbers for all inputs

Target

Original	0.0
Target	0.0
Herbie	0.0

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

Derivation

Initial program 0.0
\[x \cdot e^{y \cdot y} \]
Applied egg-rr0.0
\[\leadsto x \cdot \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left({\left(e^{y}\right)}^{y}\right)\right)} \]
Final simplification0.0
\[\leadsto x \cdot \mathsf{expm1}\left(\mathsf{log1p}\left({\left(e^{y}\right)}^{y}\right)\right) \]

Alternatives

Alternative 1
Error	0.0
Cost	13056

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

Alternative 2
Error	0.0
Cost	6720

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

Alternative 3
Error	0.6
Cost	448

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

Alternative 4
Error	0.6
Cost	448

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

Alternative 5
Error	1.0
Cost	64

\[x \]

Reproduce

herbie shell --seed 2022356 
(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))))