2cbrt (problem 3.3.4)

Average Error: 30.4 → 30.5

Time: 9.6s

Precision: binary64

Cost: 19904

Math

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

↓

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

FPCore

(FPCore (x) :precision binary64 (- (cbrt (+ x 1.0)) (cbrt x)))

↓

(FPCore (x)
 :precision binary64
 (- (cbrt (+ x 1.0)) (+ (* (cbrt x) 4.0) (* (cbrt x) -3.0))))

C

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(x) * -3.0));
}

Java

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(x) * -3.0));
}

Julia

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(x) * 4.0) + Float64(cbrt(x) * -3.0)))
end

Wolfram

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[x, 1/3], $MachinePrecision] * 4.0), $MachinePrecision] + N[(N[Power[x, 1/3], $MachinePrecision] * -3.0), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 30.4

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

2. Applied egg-rr 30.5

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

3. Final simplification 30.5

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

Alternatives

Alternative 1
Error	30.4
Cost	13120

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

Alternative 2
Error	61.7
Cost	64

\[0 \]

Alternative 3
Error	32.6
Cost	64

\[1 \]

Reproduce

herbie shell --seed 2023097 
(FPCore (x)
  :name "2cbrt (problem 3.3.4)"
  :precision binary64
  (- (cbrt (+ x 1.0)) (cbrt x)))