# ?

Average Error: 3.9 → 3.4
Time: 10.8s
Precision: binary64
Cost: 45376

# ?

$-10 \leq x \land x \leq 10$
${x}^{\left(\frac{1}{7}\right)}$
${\left(\sqrt[3]{{x}^{0.03571428571428571}} \cdot \left(\sqrt[3]{{x}^{0.011904761904761904}} \cdot \sqrt[3]{{x}^{0.005952380952380952}}\right)\right)}^{8}$
(FPCore (x) :precision binary64 (pow x (/ 1.0 7.0)))
(FPCore (x)
:precision binary64
(pow
(*
(cbrt (pow x 0.03571428571428571))
(* (cbrt (pow x 0.011904761904761904)) (cbrt (pow x 0.005952380952380952))))
8.0))
double code(double x) {
return pow(x, (1.0 / 7.0));
}

double code(double x) {
return pow((cbrt(pow(x, 0.03571428571428571)) * (cbrt(pow(x, 0.011904761904761904)) * cbrt(pow(x, 0.005952380952380952)))), 8.0);
}

public static double code(double x) {
return Math.pow(x, (1.0 / 7.0));
}

public static double code(double x) {
return Math.pow((Math.cbrt(Math.pow(x, 0.03571428571428571)) * (Math.cbrt(Math.pow(x, 0.011904761904761904)) * Math.cbrt(Math.pow(x, 0.005952380952380952)))), 8.0);
}

function code(x)
return x ^ Float64(1.0 / 7.0)
end

function code(x)
return Float64(cbrt((x ^ 0.03571428571428571)) * Float64(cbrt((x ^ 0.011904761904761904)) * cbrt((x ^ 0.005952380952380952)))) ^ 8.0
end

code[x_] := N[Power[x, N[(1.0 / 7.0), $MachinePrecision]],$MachinePrecision]

code[x_] := N[Power[N[(N[Power[N[Power[x, 0.03571428571428571], $MachinePrecision], 1/3],$MachinePrecision] * N[(N[Power[N[Power[x, 0.011904761904761904], $MachinePrecision], 1/3],$MachinePrecision] * N[Power[N[Power[x, 0.005952380952380952], $MachinePrecision], 1/3],$MachinePrecision]), $MachinePrecision]),$MachinePrecision], 8.0], \$MachinePrecision]

{x}^{\left(\frac{1}{7}\right)}

{\left(\sqrt[3]{{x}^{0.03571428571428571}} \cdot \left(\sqrt[3]{{x}^{0.011904761904761904}} \cdot \sqrt[3]{{x}^{0.005952380952380952}}\right)\right)}^{8}


# Try it out?

Results

 In Out
Enter valid numbers for all inputs

# Derivation?

1. Initial program 3.9

${x}^{\left(\frac{1}{7}\right)}$
2. Simplified3.9

$\leadsto \color{blue}{{\left({x}^{0.017857142857142856}\right)}^{8}}$
Proof
[Start]3.9 ${x}^{\left(\frac{1}{7}\right)}$ $\color{blue}{{x}^{\left(\frac{\frac{1}{7}}{2}\right)} \cdot {x}^{\left(\frac{\frac{1}{7}}{2}\right)}}$ ${x}^{\left(\frac{\frac{1}{7}}{2}\right)} \cdot \color{blue}{\left({x}^{\left(\frac{\frac{\frac{1}{7}}{2}}{2}\right)} \cdot {x}^{\left(\frac{\frac{\frac{1}{7}}{2}}{2}\right)}\right)}$ $\color{blue}{\left({x}^{\left(\frac{\frac{1}{7}}{2}\right)} \cdot {x}^{\left(\frac{\frac{\frac{1}{7}}{2}}{2}\right)}\right) \cdot {x}^{\left(\frac{\frac{\frac{1}{7}}{2}}{2}\right)}}$ $\color{blue}{\left({x}^{\left(\frac{\frac{\frac{1}{7}}{2}}{2}\right)} \cdot {x}^{\left(\frac{\frac{1}{7}}{2}\right)}\right)} \cdot {x}^{\left(\frac{\frac{\frac{1}{7}}{2}}{2}\right)}$ $\left({x}^{\left(\frac{\frac{\frac{1}{7}}{2}}{2}\right)} \cdot {x}^{\left(\frac{\frac{1}{7}}{2}\right)}\right) \cdot \color{blue}{\left({x}^{\left(\frac{\frac{\frac{\frac{1}{7}}{2}}{2}}{2}\right)} \cdot {x}^{\left(\frac{\frac{\frac{\frac{1}{7}}{2}}{2}}{2}\right)}\right)}$ $\color{blue}{\left(\left({x}^{\left(\frac{\frac{\frac{1}{7}}{2}}{2}\right)} \cdot {x}^{\left(\frac{\frac{1}{7}}{2}\right)}\right) \cdot {x}^{\left(\frac{\frac{\frac{\frac{1}{7}}{2}}{2}}{2}\right)}\right) \cdot {x}^{\left(\frac{\frac{\frac{\frac{1}{7}}{2}}{2}}{2}\right)}}$
3. Applied egg-rr3.5

$\leadsto {\color{blue}{\left(\sqrt[3]{{x}^{0.03571428571428571}} \cdot \sqrt[3]{{x}^{0.017857142857142856}}\right)}}^{8}$
4. Applied egg-rr3.4

$\leadsto {\left(\sqrt[3]{{x}^{0.03571428571428571}} \cdot \color{blue}{\left(\sqrt[3]{{x}^{0.011904761904761904}} \cdot \sqrt[3]{{x}^{0.005952380952380952}}\right)}\right)}^{8}$
5. Final simplification3.4

$\leadsto {\left(\sqrt[3]{{x}^{0.03571428571428571}} \cdot \left(\sqrt[3]{{x}^{0.011904761904761904}} \cdot \sqrt[3]{{x}^{0.005952380952380952}}\right)\right)}^{8}$

# Alternatives

Alternative 1
Error3.5
Cost45376
$\begin{array}{l} t_0 := \sqrt[3]{{x}^{0.008928571428571428}}\\ {\left(\sqrt[3]{{x}^{0.03571428571428571}} \cdot \left(t_0 \cdot t_0\right)\right)}^{8} \end{array}$
Alternative 2
Error3.4
Cost45248
${\left(\sqrt[3]{\sqrt[3]{{\left({x}^{0.03571428571428571}\right)}^{3}}} \cdot \sqrt[3]{{x}^{0.017857142857142856}}\right)}^{8}$
Alternative 3
Error3.5
Cost38848
${\left(\sqrt[3]{{x}^{0.03571428571428571}} \cdot \sqrt[3]{e^{0.017857142857142856 \cdot \log x}}\right)}^{8}$
Alternative 4
Error3.5
Cost38784
$\sqrt{{\left(\sqrt[3]{{x}^{0.03571428571428571}} \cdot \sqrt[3]{{x}^{0.017857142857142856}}\right)}^{16}}$
Alternative 5
Error3.5
Cost32384
${\left(\sqrt[3]{{x}^{0.03571428571428571}} \cdot \sqrt[3]{{x}^{0.017857142857142856}}\right)}^{8}$
Alternative 6
Error3.6
Cost25856
${\left({\left(\sqrt[3]{{x}^{0.03571428571428571}}\right)}^{3}\right)}^{4}$
Alternative 7
Error3.6
Cost19456
$e^{4 \cdot \log \left({x}^{0.03571428571428571}\right)}$
Alternative 8
Error3.8
Cost19392
$\sqrt{e^{\log x \cdot 0.2857142857142857}}$
Alternative 9
Error3.8
Cost12992
$e^{\log x \cdot 0.14285714285714285}$
Alternative 10
Error3.9
Cost6528
${x}^{0.14285714285714285}$

# Reproduce?

herbie shell --seed 1
(FPCore (x)
:name "x^(1/7)"
:precision binary64
:pre (and (<= -10.0 x) (<= x 10.0))
(pow x (/ 1.0 7.0)))