?

Average Error: 0.0 → 0.0
Time: 5.0s
Precision: binary64
Cost: 19648

?

\[x \cdot e^{y \cdot y} \]
↓
\[x \cdot {\left({\left(e^{y \cdot y}\right)}^{3}\right)}^{0.3333333333333333} \]
(FPCore (x y) :precision binary64 (* x (exp (* y y))))
↓
(FPCore (x y)
 :precision binary64
 (* x (pow (pow (exp (* y y)) 3.0) 0.3333333333333333)))
double code(double x, double y) {
	return x * exp((y * y));
}
↓
double code(double x, double y) {
	return x * pow(pow(exp((y * y)), 3.0), 0.3333333333333333);
}

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 * ((exp((y * y)) ** 3.0d0) ** 0.3333333333333333d0)
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.pow(Math.pow(Math.exp((y * y)), 3.0), 0.3333333333333333);
}

def code(x, y):
	return x * math.exp((y * y))
↓
def code(x, y):
	return x * math.pow(math.pow(math.exp((y * y)), 3.0), 0.3333333333333333)

function code(x, y)
	return Float64(x * exp(Float64(y * y)))
end
↓
function code(x, y)
	return Float64(x * ((exp(Float64(y * y)) ^ 3.0) ^ 0.3333333333333333))
end

function tmp = code(x, y)
	tmp = x * exp((y * y));
end
↓
function tmp = code(x, y)
	tmp = x * ((exp((y * y)) ^ 3.0) ^ 0.3333333333333333);
end

code[x_, y_] := N[(x * N[Exp[N[(y * y), $MachinePrecision]], $MachinePrecision]), $MachinePrecision]
↓
code[x_, y_] := N[(x * N[Power[N[Power[N[Exp[N[(y * y), $MachinePrecision]], $MachinePrecision], 3.0], $MachinePrecision], 0.3333333333333333], $MachinePrecision]), $MachinePrecision]

x \cdot e^{y \cdot y}
↓
x \cdot {\left({\left(e^{y \cdot y}\right)}^{3}\right)}^{0.3333333333333333}

Error?

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. Applied egg-rr0.0

    \[\leadsto x \cdot \color{blue}{{\left({\left(e^{y \cdot y}\right)}^{3}\right)}^{0.3333333333333333}} \]

  3. Final simplification0.0

    \[\leadsto x \cdot {\left({\left(e^{y \cdot y}\right)}^{3}\right)}^{0.3333333333333333} \]

Alternatives

Alternative 1
Error0.0
Cost13120
\[x \cdot {e}^{\left(y \cdot y\right)} \]
Alternative 2
Error0.0
Cost13056
\[x \cdot {\left(e^{y}\right)}^{y} \]
Alternative 3
Error0.0
Cost6720
\[x \cdot e^{y \cdot y} \]
Alternative 4
Error0.5
Cost448
\[x \cdot \left(y \cdot y + 1\right) \]
Alternative 5
Error0.5
Cost448
\[x + x \cdot \left(y \cdot y\right) \]
Alternative 6
Error0.9
Cost64
\[x \]

Error

Reproduce?

herbie shell --seed 2023187 
(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))))