Average Error: 0.0 → 0.0

Time: 4.5s

Precision: binary64

Cost: 38848

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

↓

\[\begin{array}{l} t_0 := {\left(\sqrt{e^{y}}\right)}^{y}\\ x \cdot \left(t_0 \cdot t_0\right) \end{array} \]

(FPCore (x y) :precision binary64 (* x (exp (* y y))))

↓

(FPCore (x y)
 :precision binary64
 (let* ((t_0 (pow (sqrt (exp y)) y))) (* x (* t_0 t_0))))

double code(double x, double y) {
	return x * exp((y * y));
}

↓

double code(double x, double y) {
	double t_0 = pow(sqrt(exp(y)), y);
	return x * (t_0 * t_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
    real(8) :: t_0
    t_0 = sqrt(exp(y)) ** y
    code = x * (t_0 * t_0)
end function

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

↓

public static double code(double x, double y) {
	double t_0 = Math.pow(Math.sqrt(Math.exp(y)), y);
	return x * (t_0 * t_0);
}

def code(x, y):
	return x * math.exp((y * y))

↓

def code(x, y):
	t_0 = math.pow(math.sqrt(math.exp(y)), y)
	return x * (t_0 * t_0)

function code(x, y)
	return Float64(x * exp(Float64(y * y)))
end

↓

function code(x, y)
	t_0 = sqrt(exp(y)) ^ y
	return Float64(x * Float64(t_0 * t_0))
end

function tmp = code(x, y)
	tmp = x * exp((y * y));
end

↓

function tmp = code(x, y)
	t_0 = sqrt(exp(y)) ^ y;
	tmp = x * (t_0 * t_0);
end

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

↓

code[x_, y_] := Block[{t$95$0 = N[Power[N[Sqrt[N[Exp[y], $MachinePrecision]], $MachinePrecision], y], $MachinePrecision]}, N[(x * N[(t$95$0 * t$95$0), $MachinePrecision]), $MachinePrecision]]

x \cdot e^{y \cdot y}

↓

\begin{array}{l}
t_0 := {\left(\sqrt{e^{y}}\right)}^{y}\\
x \cdot \left(t_0 \cdot t_0\right)
\end{array}

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
\[x \cdot e^{y \cdot y} \]
Simplified0.0
\[\leadsto \color{blue}{x \cdot {\left(e^{y}\right)}^{y}} \]
Proof
(*.f64 x (pow.f64 (exp.f64 y) y)): 0 points increase in error, 0 points decrease in error
(*.f64 x (Rewrite<= exp-prod_binary64 (exp.f64 (*.f64 y y)))): 1 points increase in error, 0 points decrease in error
Applied egg-rr0.0
\[\leadsto x \cdot \color{blue}{\left({\left(\sqrt{e^{y}}\right)}^{y} \cdot {\left(\sqrt{e^{y}}\right)}^{y}\right)} \]
Final simplification0.0
\[\leadsto x \cdot \left({\left(\sqrt{e^{y}}\right)}^{y} \cdot {\left(\sqrt{e^{y}}\right)}^{y}\right) \]

Alternatives

Alternative 1
Error	0.0
Cost	13312

\[x \cdot {\left(e^{y \cdot 0.5}\right)}^{\left(y \cdot 2\right)} \]

Alternative 2
Error	0.0
Cost	13120

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

Alternative 3
Error	0.0
Cost	13056

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

Alternative 4
Error	0.0
Cost	6720

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

Alternative 5
Error	0.5
Cost	448

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

Alternative 6
Error	0.9
Cost	64

\[x \]

Reproduce

herbie shell --seed 2022316 
(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))))