2cbrt (problem 3.3.4)

Average Error: 29.6 → 29.6

Time: 1.4s

Precision: binary64

Cost: 13120

Math

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

↓

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

FPCore

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

↓

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

C

double code(double x) {
	return cbrt((x + 1.0)) - cbrt(x);
}

↓

double code(double x) {
	return cbrt((x + 1.0)) - cbrt(x);
}

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);
}

Julia

function code(x)
	return Float64(cbrt(Float64(x + 1.0)) - cbrt(x))
end

↓

function code(x)
	return Float64(cbrt(Float64(x + 1.0)) - cbrt(x))
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[Power[x, 1/3], $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 29.6

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

2. Final simplification 29.6

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

Alternatives

Alternative 1
Error	31.3
Cost	6848

\[\left(1 - \sqrt[3]{x}\right) + 0.3333333333333333 \cdot x \]

Alternative 2
Error	31.3
Cost	6848

\[\left(0.3333333333333333 \cdot x - \sqrt[3]{x}\right) + 1 \]

Alternative 3
Error	31.5
Cost	6592

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

Alternative 4
Error	61.7
Cost	64

\[0 \]

Alternative 5
Error	32.0
Cost	64

\[1 \]

Reproduce

herbie shell --seed 2023053 
(FPCore (x)
  :name "2cbrt (problem 3.3.4)"
  :precision binary64
  (- (cbrt (+ x 1.0)) (cbrt x)))