Average Error: 0.0 → 0.0
Time: 2.3s
Precision: binary64
\[x \cdot e^{y \cdot y} \]
↓
\[x \cdot \left({\left(\sqrt{e^{y}}\right)}^{y} \cdot \sqrt[3]{{\left({\left(e^{y}\right)}^{1.5}\right)}^{y}}\right) \]
(FPCore (x y) :precision binary64 (* x (exp (* y y))))
↓
(FPCore (x y)
 :precision binary64
 (* x (* (pow (sqrt (exp y)) y) (cbrt (pow (pow (exp y) 1.5) y)))))
double code(double x, double y) {
	return x * exp((y * y));
}
↓
double code(double x, double y) {
	return x * (pow(sqrt(exp(y)), y) * cbrt(pow(pow(exp(y), 1.5), 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.pow(Math.sqrt(Math.exp(y)), y) * Math.cbrt(Math.pow(Math.pow(Math.exp(y), 1.5), y)));
}

function code(x, y)
	return Float64(x * exp(Float64(y * y)))
end
↓
function code(x, y)
	return Float64(x * Float64((sqrt(exp(y)) ^ y) * cbrt(((exp(y) ^ 1.5) ^ y))))
end

code[x_, y_] := N[(x * N[Exp[N[(y * y), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]
↓
code[x_, y_] := N[(x * N[(N[Power[N[Sqrt[N[Exp[y], $MachinePrecision]], $MachinePrecision], y], $MachinePrecision] * N[Power[N[Power[N[Power[N[Exp[y], $MachinePrecision], 1.5], $MachinePrecision], y], $MachinePrecision], 1/3], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

x \cdot e^{y \cdot y}
↓
x \cdot \left({\left(\sqrt{e^{y}}\right)}^{y} \cdot \sqrt[3]{{\left({\left(e^{y}\right)}^{1.5}\right)}^{y}}\right)

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

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

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

  4. Applied egg-rr0.0

    \[\leadsto x \cdot \left({\left(\sqrt{e^{y}}\right)}^{y} \cdot \color{blue}{\sqrt[3]{{\left({\left(e^{y}\right)}^{1.5}\right)}^{y}}}\right) \]

  5. Final simplification0.0

    \[\leadsto x \cdot \left({\left(\sqrt{e^{y}}\right)}^{y} \cdot \sqrt[3]{{\left({\left(e^{y}\right)}^{1.5}\right)}^{y}}\right) \]

Reproduce

herbie shell --seed 2022166 
(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))))