?

Average Error: 0.05% → 0.06%
Time: 3.7s
Precision: binary64
Cost: 19584

?

\[x \cdot e^{y \cdot y} \]
↓
\[x \cdot \sqrt{{\left(e^{y}\right)}^{\left(y \cdot 2\right)}} \]
(FPCore (x y) :precision binary64 (* x (exp (* y y))))
↓
(FPCore (x y) :precision binary64 (* x (sqrt (pow (exp y) (* y 2.0)))))
double code(double x, double y) {
	return x * exp((y * y));
}
↓
double code(double x, double y) {
	return x * sqrt(pow(exp(y), (y * 2.0)));
}

real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = x * exp((y * y))
end function
↓
real(8) function code(x, y)
    real(8), intent (in) :: x
    real(8), intent (in) :: y
    code = x * sqrt((exp(y) ** (y * 2.0d0)))
end function

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.sqrt(Math.pow(Math.exp(y), (y * 2.0)));
}

def code(x, y):
	return x * math.exp((y * y))
↓
def code(x, y):
	return x * math.sqrt(math.pow(math.exp(y), (y * 2.0)))

function code(x, y)
	return Float64(x * exp(Float64(y * y)))
end
↓
function code(x, y)
	return Float64(x * sqrt((exp(y) ^ Float64(y * 2.0))))
end

function tmp = code(x, y)
	tmp = x * exp((y * y));
end
↓
function tmp = code(x, y)
	tmp = x * sqrt((exp(y) ^ (y * 2.0)));
end

code[x_, y_] := N[(x * N[Exp[N[(y * y), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]
↓
code[x_, y_] := N[(x * N[Sqrt[N[Power[N[Exp[y], $MachinePrecision], N[(y * 2.0), $MachinePrecision]], $MachinePrecision]], $MachinePrecision]), $MachinePrecision]

x \cdot e^{y \cdot y}
↓
x \cdot \sqrt{{\left(e^{y}\right)}^{\left(y \cdot 2\right)}}

Error?

Try it out?

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original0.05%
Target0.04%
Herbie0.06%
\[x \cdot {\left(e^{y}\right)}^{y} \]

Derivation?

  1. Initial program 0.05

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

  2. Simplified0.04

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

    [Start]0.05

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

    exp-prod [=>]0.04

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

  3. Applied egg-rr0.06

    \[\leadsto x \cdot \color{blue}{\sqrt{{\left(e^{y}\right)}^{\left(2 \cdot y\right)}}} \]

  4. Final simplification0.06

    \[\leadsto x \cdot \sqrt{{\left(e^{y}\right)}^{\left(y \cdot 2\right)}} \]

Alternatives

Alternative 1
Error0.05%
Cost6720
\[x \cdot e^{y \cdot y} \]
Alternative 2
Error0.73%
Cost960
\[x + x \cdot \left(\left(y \cdot y\right) \cdot \left(\left(y \cdot y\right) \cdot 0.5 + 1\right)\right) \]
Alternative 3
Error0.93%
Cost448
\[x \cdot \left(y \cdot y + 1\right) \]
Alternative 4
Error0.93%
Cost448
\[x + x \cdot \left(y \cdot y\right) \]
Alternative 5
Error1.46%
Cost64
\[x \]

Error

Reproduce?

herbie shell --seed 2023103 
(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))))