?

Average Error: 30.1 → 30.2
Time: 15.3s
Precision: binary64
Cost: 26304

?

\[\sqrt[3]{x + 1} - \sqrt[3]{x} \]
↓
\[\sqrt[3]{x + 1} - \left(\sqrt[3]{x \cdot 4} \cdot \sqrt[3]{2}\right) \cdot \sqrt[3]{0.125} \]
(FPCore (x) :precision binary64 (- (cbrt (+ x 1.0)) (cbrt x)))
↓
(FPCore (x)
 :precision binary64
 (- (cbrt (+ x 1.0)) (* (* (cbrt (* x 4.0)) (cbrt 2.0)) (cbrt 0.125))))
double code(double x) {
	return cbrt((x + 1.0)) - cbrt(x);
}
↓
double code(double x) {
	return cbrt((x + 1.0)) - ((cbrt((x * 4.0)) * cbrt(2.0)) * cbrt(0.125));
}

public static double code(double x) {
	return Math.cbrt((x + 1.0)) - Math.cbrt(x);
}
↓
public static double code(double x) {
	return Math.cbrt((x + 1.0)) - ((Math.cbrt((x * 4.0)) * Math.cbrt(2.0)) * Math.cbrt(0.125));
}

function code(x)
	return Float64(cbrt(Float64(x + 1.0)) - cbrt(x))
end
↓
function code(x)
	return Float64(cbrt(Float64(x + 1.0)) - Float64(Float64(cbrt(Float64(x * 4.0)) * cbrt(2.0)) * cbrt(0.125)))
end

code[x_] := N[(N[Power[N[(x + 1.0), $MachinePrecision], 1/3], $MachinePrecision] - N[Power[x, 1/3], $MachinePrecision]), $MachinePrecision]
↓
code[x_] := N[(N[Power[N[(x + 1.0), $MachinePrecision], 1/3], $MachinePrecision] - N[(N[(N[Power[N[(x * 4.0), $MachinePrecision], 1/3], $MachinePrecision] * N[Power[2.0, 1/3], $MachinePrecision]), $MachinePrecision] * N[Power[0.125, 1/3], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

\sqrt[3]{x + 1} - \sqrt[3]{x}
↓
\sqrt[3]{x + 1} - \left(\sqrt[3]{x \cdot 4} \cdot \sqrt[3]{2}\right) \cdot \sqrt[3]{0.125}

Error?

Try it out?

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation?

  1. Initial program 30.1

    \[\sqrt[3]{x + 1} - \sqrt[3]{x} \]

  2. Applied egg-rr30.3

    \[\leadsto \sqrt[3]{x + 1} - \color{blue}{\sqrt[3]{x \cdot 8} \cdot \sqrt[3]{0.125}} \]

  3. Applied egg-rr30.2

    \[\leadsto \sqrt[3]{x + 1} - \color{blue}{\left(\sqrt[3]{x \cdot 4} \cdot \sqrt[3]{2}\right)} \cdot \sqrt[3]{0.125} \]

  4. Final simplification30.2

    \[\leadsto \sqrt[3]{x + 1} - \left(\sqrt[3]{x \cdot 4} \cdot \sqrt[3]{2}\right) \cdot \sqrt[3]{0.125} \]

Alternatives

Alternative 1
Error30.1
Cost13120
\[\sqrt[3]{x + 1} - \sqrt[3]{x} \]
Alternative 2
Error31.8
Cost6848
\[\left(1 - \sqrt[3]{x}\right) + 0.3333333333333333 \cdot x \]
Alternative 3
Error61.7
Cost64
\[0 \]
Alternative 4
Error32.4
Cost64
\[1 \]

Error

Reproduce?

herbie shell --seed 2023075 
(FPCore (x)
  :name "2cbrt (problem 3.3.4)"
  :precision binary64
  (- (cbrt (+ x 1.0)) (cbrt x)))