# ?

Average Error: 0.3 → 0.0
Time: 6.6s
Precision: binary64
Cost: 13248

# ?

$\left(\left(0 \leq x \land x \leq 10\right) \land \left(0 \leq a \land a \leq 1\right)\right) \land \left(0 \leq y \land y \leq 10\right)$
${x}^{a} \cdot {y}^{\left(1 - a\right)}$
${x}^{a} \cdot \frac{y}{{y}^{a}}$
(FPCore (x a y) :precision binary64 (* (pow x a) (pow y (- 1.0 a))))
(FPCore (x a y) :precision binary64 (* (pow x a) (/ y (pow y a))))
double code(double x, double a, double y) {
return pow(x, a) * pow(y, (1.0 - a));
}

double code(double x, double a, double y) {
return pow(x, a) * (y / pow(y, a));
}

real(8) function code(x, a, y)
real(8), intent (in) :: x
real(8), intent (in) :: a
real(8), intent (in) :: y
code = (x ** a) * (y ** (1.0d0 - a))
end function

real(8) function code(x, a, y)
real(8), intent (in) :: x
real(8), intent (in) :: a
real(8), intent (in) :: y
code = (x ** a) * (y / (y ** a))
end function

public static double code(double x, double a, double y) {
return Math.pow(x, a) * Math.pow(y, (1.0 - a));
}

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

def code(x, a, y):
return math.pow(x, a) * math.pow(y, (1.0 - a))

def code(x, a, y):
return math.pow(x, a) * (y / math.pow(y, a))

function code(x, a, y)
return Float64((x ^ a) * (y ^ Float64(1.0 - a)))
end

function code(x, a, y)
return Float64((x ^ a) * Float64(y / (y ^ a)))
end

function tmp = code(x, a, y)
tmp = (x ^ a) * (y ^ (1.0 - a));
end

function tmp = code(x, a, y)
tmp = (x ^ a) * (y / (y ^ a));
end

code[x_, a_, y_] := N[(N[Power[x, a], $MachinePrecision] * N[Power[y, N[(1.0 - a),$MachinePrecision]], $MachinePrecision]),$MachinePrecision]

code[x_, a_, y_] := N[(N[Power[x, a], $MachinePrecision] * N[(y / N[Power[y, a],$MachinePrecision]), $MachinePrecision]),$MachinePrecision]

{x}^{a} \cdot {y}^{\left(1 - a\right)}

{x}^{a} \cdot \frac{y}{{y}^{a}}


# Try it out?

Results

 In Out
Enter valid numbers for all inputs

# Derivation?

1. Initial program 0.3

${x}^{a} \cdot {y}^{\left(1 - a\right)}$
2. Applied egg-rr58.4

$\leadsto {x}^{a} \cdot \color{blue}{\left(e^{\mathsf{log1p}\left(\frac{y}{{y}^{a}}\right)} - 1\right)}$
3. Simplified0.0

$\leadsto {x}^{a} \cdot \color{blue}{\frac{y}{{y}^{a}}}$
Proof
[Start]58.4 ${x}^{a} \cdot \left(e^{\mathsf{log1p}\left(\frac{y}{{y}^{a}}\right)} - 1\right)$ ${x}^{a} \cdot \color{blue}{\mathsf{expm1}\left(\mathsf{log1p}\left(\frac{y}{{y}^{a}}\right)\right)}$ ${x}^{a} \cdot \color{blue}{\frac{y}{{y}^{a}}}$
4. Final simplification0.0

$\leadsto {x}^{a} \cdot \frac{y}{{y}^{a}}$

# Alternatives

Alternative 1
Error1.6
Cost64
$y$

# Reproduce?

herbie shell --seed 1
(FPCore (x a y)
:name "x ^(a) * y ^ (1-a)"
:precision binary64
:pre (and (and (and (<= 0.0 x) (<= x 10.0)) (and (<= 0.0 a) (<= a 1.0))) (and (<= 0.0 y) (<= y 10.0)))
(* (pow x a) (pow y (- 1.0 a))))