2cbrt (problem 3.3.4)

Average Accuracy: 53.6% → 99.3%

Time: 12.3s

Precision: binary64

Cost: 39488

Math

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

↓

\[\frac{1}{{\left(\sqrt[3]{x}\right)}^{2} + {\left(\frac{\sqrt[3]{\frac{1}{1 + x}}}{\sqrt[3]{x} + \sqrt[3]{1 + x}}\right)}^{-1}} \]

FPCore

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

↓

(FPCore (x)
 :precision binary64
 (/
  1.0
  (+
   (pow (cbrt x) 2.0)
   (pow (/ (cbrt (/ 1.0 (+ 1.0 x))) (+ (cbrt x) (cbrt (+ 1.0 x)))) -1.0))))

C

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

↓

double code(double x) {
	return 1.0 / (pow(cbrt(x), 2.0) + pow((cbrt((1.0 / (1.0 + x))) / (cbrt(x) + cbrt((1.0 + x)))), -1.0));
}

Java

public static double code(double x) {
	return Math.cbrt((x + 1.0)) - Math.cbrt(x);
}

↓

public static double code(double x) {
	return 1.0 / (Math.pow(Math.cbrt(x), 2.0) + Math.pow((Math.cbrt((1.0 / (1.0 + x))) / (Math.cbrt(x) + Math.cbrt((1.0 + x)))), -1.0));
}

Julia

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

↓

function code(x)
	return Float64(1.0 / Float64((cbrt(x) ^ 2.0) + (Float64(cbrt(Float64(1.0 / Float64(1.0 + x))) / Float64(cbrt(x) + cbrt(Float64(1.0 + x)))) ^ -1.0)))
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[(1.0 / N[(N[Power[N[Power[x, 1/3], $MachinePrecision], 2.0], $MachinePrecision] + N[Power[N[(N[Power[N[(1.0 / N[(1.0 + x), $MachinePrecision]), $MachinePrecision], 1/3], $MachinePrecision] / N[(N[Power[x, 1/3], $MachinePrecision] + N[Power[N[(1.0 + x), $MachinePrecision], 1/3], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], -1.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 53.6%

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

2. Applied egg-rr 54.5%

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

   [Start] 53.6	\[ \sqrt[3]{x + 1} - \sqrt[3]{x} \]
   flip3-- [=>] 53.7	\[ \color{blue}{\frac{{\left(\sqrt[3]{x + 1}\right)}^{3} - {\left(\sqrt[3]{x}\right)}^{3}}{\sqrt[3]{x + 1} \cdot \sqrt[3]{x + 1} + \left(\sqrt[3]{x} \cdot \sqrt[3]{x} + \sqrt[3]{x + 1} \cdot \sqrt[3]{x}\right)}} \]
   div-inv [=>] 53.7	\[ \color{blue}{\left({\left(\sqrt[3]{x + 1}\right)}^{3} - {\left(\sqrt[3]{x}\right)}^{3}\right) \cdot \frac{1}{\sqrt[3]{x + 1} \cdot \sqrt[3]{x + 1} + \left(\sqrt[3]{x} \cdot \sqrt[3]{x} + \sqrt[3]{x + 1} \cdot \sqrt[3]{x}\right)}} \]
   rem-cube-cbrt [=>] 53.5	\[ \left(\color{blue}{\left(x + 1\right)} - {\left(\sqrt[3]{x}\right)}^{3}\right) \cdot \frac{1}{\sqrt[3]{x + 1} \cdot \sqrt[3]{x + 1} + \left(\sqrt[3]{x} \cdot \sqrt[3]{x} + \sqrt[3]{x + 1} \cdot \sqrt[3]{x}\right)} \]
   rem-cube-cbrt [=>] 54.5	\[ \left(\left(x + 1\right) - \color{blue}{x}\right) \cdot \frac{1}{\sqrt[3]{x + 1} \cdot \sqrt[3]{x + 1} + \left(\sqrt[3]{x} \cdot \sqrt[3]{x} + \sqrt[3]{x + 1} \cdot \sqrt[3]{x}\right)} \]
   pow2 [=>] 54.5	\[ \left(\left(x + 1\right) - x\right) \cdot \frac{1}{\color{blue}{{\left(\sqrt[3]{x + 1}\right)}^{2}} + \left(\sqrt[3]{x} \cdot \sqrt[3]{x} + \sqrt[3]{x + 1} \cdot \sqrt[3]{x}\right)} \]
   distribute-rgt-out [=>] 54.5	\[ \left(\left(x + 1\right) - x\right) \cdot \frac{1}{{\left(\sqrt[3]{x + 1}\right)}^{2} + \color{blue}{\sqrt[3]{x} \cdot \left(\sqrt[3]{x} + \sqrt[3]{x + 1}\right)}} \]
   +-commutative [<=] 54.5	\[ \left(\left(x + 1\right) - x\right) \cdot \frac{1}{{\left(\sqrt[3]{x + 1}\right)}^{2} + \sqrt[3]{x} \cdot \color{blue}{\left(\sqrt[3]{x + 1} + \sqrt[3]{x}\right)}} \]

3. Simplified 99.2%

   \[\leadsto \color{blue}{\frac{1}{\mathsf{fma}\left(\sqrt[3]{x}, \sqrt[3]{1 + x} + \sqrt[3]{x}, {\left(\sqrt[3]{1 + x}\right)}^{2}\right)}} \]
   Proof

   [Start] 54.5	\[ \left(\left(x + 1\right) - x\right) \cdot \frac{1}{{\left(\sqrt[3]{x + 1}\right)}^{2} + \sqrt[3]{x} \cdot \left(\sqrt[3]{x + 1} + \sqrt[3]{x}\right)} \]
   associate-*r/ [=>] 54.5	\[ \color{blue}{\frac{\left(\left(x + 1\right) - x\right) \cdot 1}{{\left(\sqrt[3]{x + 1}\right)}^{2} + \sqrt[3]{x} \cdot \left(\sqrt[3]{x + 1} + \sqrt[3]{x}\right)}} \]
   *-rgt-identity [=>] 54.5	\[ \frac{\color{blue}{\left(x + 1\right) - x}}{{\left(\sqrt[3]{x + 1}\right)}^{2} + \sqrt[3]{x} \cdot \left(\sqrt[3]{x + 1} + \sqrt[3]{x}\right)} \]
   +-commutative [=>] 54.5	\[ \frac{\color{blue}{\left(1 + x\right)} - x}{{\left(\sqrt[3]{x + 1}\right)}^{2} + \sqrt[3]{x} \cdot \left(\sqrt[3]{x + 1} + \sqrt[3]{x}\right)} \]
   associate--l+ [=>] 99.2	\[ \frac{\color{blue}{1 + \left(x - x\right)}}{{\left(\sqrt[3]{x + 1}\right)}^{2} + \sqrt[3]{x} \cdot \left(\sqrt[3]{x + 1} + \sqrt[3]{x}\right)} \]
   +-inverses [=>] 99.2	\[ \frac{1 + \color{blue}{0}}{{\left(\sqrt[3]{x + 1}\right)}^{2} + \sqrt[3]{x} \cdot \left(\sqrt[3]{x + 1} + \sqrt[3]{x}\right)} \]
   metadata-eval [=>] 99.2	\[ \frac{\color{blue}{1}}{{\left(\sqrt[3]{x + 1}\right)}^{2} + \sqrt[3]{x} \cdot \left(\sqrt[3]{x + 1} + \sqrt[3]{x}\right)} \]
   +-commutative [=>] 99.2	\[ \frac{1}{\color{blue}{\sqrt[3]{x} \cdot \left(\sqrt[3]{x + 1} + \sqrt[3]{x}\right) + {\left(\sqrt[3]{x + 1}\right)}^{2}}} \]
   fma-def [=>] 99.2	\[ \frac{1}{\color{blue}{\mathsf{fma}\left(\sqrt[3]{x}, \sqrt[3]{x + 1} + \sqrt[3]{x}, {\left(\sqrt[3]{x + 1}\right)}^{2}\right)}} \]
   +-commutative [=>] 99.2	\[ \frac{1}{\mathsf{fma}\left(\sqrt[3]{x}, \sqrt[3]{\color{blue}{1 + x}} + \sqrt[3]{x}, {\left(\sqrt[3]{x + 1}\right)}^{2}\right)} \]
   +-commutative [=>] 99.2	\[ \frac{1}{\mathsf{fma}\left(\sqrt[3]{x}, \sqrt[3]{1 + x} + \sqrt[3]{x}, {\left(\sqrt[3]{\color{blue}{1 + x}}\right)}^{2}\right)} \]

4. Applied egg-rr 99.2%

   \[\leadsto \frac{1}{\color{blue}{{\left(\sqrt[3]{x}\right)}^{2} + \sqrt[3]{1 + x} \cdot \left(\sqrt[3]{1 + x} + \sqrt[3]{x}\right)}} \]
   Proof

   [Start] 99.2	\[ \frac{1}{\mathsf{fma}\left(\sqrt[3]{x}, \sqrt[3]{1 + x} + \sqrt[3]{x}, {\left(\sqrt[3]{1 + x}\right)}^{2}\right)} \]
   fma-udef [=>] 99.2	\[ \frac{1}{\color{blue}{\sqrt[3]{x} \cdot \left(\sqrt[3]{1 + x} + \sqrt[3]{x}\right) + {\left(\sqrt[3]{1 + x}\right)}^{2}}} \]
   distribute-rgt-in [=>] 99.2	\[ \frac{1}{\color{blue}{\left(\sqrt[3]{1 + x} \cdot \sqrt[3]{x} + \sqrt[3]{x} \cdot \sqrt[3]{x}\right)} + {\left(\sqrt[3]{1 + x}\right)}^{2}} \]
   +-commutative [<=] 99.2	\[ \frac{1}{\color{blue}{\left(\sqrt[3]{x} \cdot \sqrt[3]{x} + \sqrt[3]{1 + x} \cdot \sqrt[3]{x}\right)} + {\left(\sqrt[3]{1 + x}\right)}^{2}} \]
   associate-+l+ [=>] 99.2	\[ \frac{1}{\color{blue}{\sqrt[3]{x} \cdot \sqrt[3]{x} + \left(\sqrt[3]{1 + x} \cdot \sqrt[3]{x} + {\left(\sqrt[3]{1 + x}\right)}^{2}\right)}} \]
   unpow2 [=>] 99.2	\[ \frac{1}{\sqrt[3]{x} \cdot \sqrt[3]{x} + \left(\sqrt[3]{1 + x} \cdot \sqrt[3]{x} + \color{blue}{\sqrt[3]{1 + x} \cdot \sqrt[3]{1 + x}}\right)} \]
   distribute-lft-in [<=] 99.2	\[ \frac{1}{\sqrt[3]{x} \cdot \sqrt[3]{x} + \color{blue}{\sqrt[3]{1 + x} \cdot \left(\sqrt[3]{x} + \sqrt[3]{1 + x}\right)}} \]
   +-commutative [<=] 99.2	\[ \frac{1}{\sqrt[3]{x} \cdot \sqrt[3]{x} + \sqrt[3]{1 + x} \cdot \color{blue}{\left(\sqrt[3]{1 + x} + \sqrt[3]{x}\right)}} \]
   pow2 [=>] 99.2	\[ \frac{1}{\color{blue}{{\left(\sqrt[3]{x}\right)}^{2}} + \sqrt[3]{1 + x} \cdot \left(\sqrt[3]{1 + x} + \sqrt[3]{x}\right)} \]

5. Applied egg-rr 76.0%

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

   [Start] 99.2	\[ \frac{1}{{\left(\sqrt[3]{x}\right)}^{2} + \sqrt[3]{1 + x} \cdot \left(\sqrt[3]{1 + x} + \sqrt[3]{x}\right)} \]
   *-commutative [=>] 99.2	\[ \frac{1}{{\left(\sqrt[3]{x}\right)}^{2} + \color{blue}{\left(\sqrt[3]{1 + x} + \sqrt[3]{x}\right) \cdot \sqrt[3]{1 + x}}} \]
   flip-+ [=>] 75.8	\[ \frac{1}{{\left(\sqrt[3]{x}\right)}^{2} + \left(\sqrt[3]{1 + x} + \sqrt[3]{x}\right) \cdot \sqrt[3]{\color{blue}{\frac{1 \cdot 1 - x \cdot x}{1 - x}}}} \]
   cbrt-div [=>] 76.0	\[ \frac{1}{{\left(\sqrt[3]{x}\right)}^{2} + \left(\sqrt[3]{1 + x} + \sqrt[3]{x}\right) \cdot \color{blue}{\frac{\sqrt[3]{1 \cdot 1 - x \cdot x}}{\sqrt[3]{1 - x}}}} \]
   associate-*r/ [=>] 76.0	\[ \frac{1}{{\left(\sqrt[3]{x}\right)}^{2} + \color{blue}{\frac{\left(\sqrt[3]{1 + x} + \sqrt[3]{x}\right) \cdot \sqrt[3]{1 \cdot 1 - x \cdot x}}{\sqrt[3]{1 - x}}}} \]
   +-commutative [=>] 76.0	\[ \frac{1}{{\left(\sqrt[3]{x}\right)}^{2} + \frac{\color{blue}{\left(\sqrt[3]{x} + \sqrt[3]{1 + x}\right)} \cdot \sqrt[3]{1 \cdot 1 - x \cdot x}}{\sqrt[3]{1 - x}}} \]
   +-commutative [=>] 76.0	\[ \frac{1}{{\left(\sqrt[3]{x}\right)}^{2} + \frac{\left(\sqrt[3]{x} + \sqrt[3]{\color{blue}{x + 1}}\right) \cdot \sqrt[3]{1 \cdot 1 - x \cdot x}}{\sqrt[3]{1 - x}}} \]
   metadata-eval [=>] 76.0	\[ \frac{1}{{\left(\sqrt[3]{x}\right)}^{2} + \frac{\left(\sqrt[3]{x} + \sqrt[3]{x + 1}\right) \cdot \sqrt[3]{\color{blue}{1} - x \cdot x}}{\sqrt[3]{1 - x}}} \]

6. Applied egg-rr 99.3%

   \[\leadsto \frac{1}{{\left(\sqrt[3]{x}\right)}^{2} + \color{blue}{{\left(\frac{\sqrt[3]{\frac{1}{1 + x}}}{\sqrt[3]{x} + \sqrt[3]{1 + x}}\right)}^{-1}}} \]
   Proof

   [Start] 76.0	\[ \frac{1}{{\left(\sqrt[3]{x}\right)}^{2} + \frac{\left(\sqrt[3]{x} + \sqrt[3]{x + 1}\right) \cdot \sqrt[3]{1 - x \cdot x}}{\sqrt[3]{1 - x}}} \]
   clear-num [=>] 76.0	\[ \frac{1}{{\left(\sqrt[3]{x}\right)}^{2} + \color{blue}{\frac{1}{\frac{\sqrt[3]{1 - x}}{\left(\sqrt[3]{x} + \sqrt[3]{x + 1}\right) \cdot \sqrt[3]{1 - x \cdot x}}}}} \]
   inv-pow [=>] 76.0	\[ \frac{1}{{\left(\sqrt[3]{x}\right)}^{2} + \color{blue}{{\left(\frac{\sqrt[3]{1 - x}}{\left(\sqrt[3]{x} + \sqrt[3]{x + 1}\right) \cdot \sqrt[3]{1 - x \cdot x}}\right)}^{-1}}} \]

7. Final simplification 99.3%

   \[\leadsto \frac{1}{{\left(\sqrt[3]{x}\right)}^{2} + {\left(\frac{\sqrt[3]{\frac{1}{1 + x}}}{\sqrt[3]{x} + \sqrt[3]{1 + x}}\right)}^{-1}} \]

Alternatives

Alternative 1
Accuracy	61.0%
Cost	39108

\[\begin{array}{l} t_0 := \sqrt[3]{1 + x}\\ t_1 := t_0 - \sqrt[3]{x}\\ \mathbf{if}\;t_1 \leq 0:\\ \;\;\;\;\frac{1}{1 + \sqrt[3]{x} \cdot \left(\sqrt[3]{x} + t_0\right)}\\ \mathbf{else}:\\ \;\;\;\;e^{\log t_1}\\ \end{array} \]

Alternative 2
Accuracy	88.5%
Cost	33096

\[\begin{array}{l} t_0 := \sqrt[3]{1 + x}\\ t_1 := \sqrt[3]{x} + t_0\\ t_2 := \sqrt[3]{x} \cdot t_1\\ \mathbf{if}\;x \leq -1.35 \cdot 10^{+154}:\\ \;\;\;\;\frac{1}{1 + t_2}\\ \mathbf{elif}\;x \leq 1.35 \cdot 10^{+154}:\\ \;\;\;\;\frac{1}{\frac{t_0}{\frac{1}{t_1}} + \sqrt[3]{x \cdot x}}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{t_2 + e^{\mathsf{log1p}\left(x\right) \cdot 0.6666666666666666}}\\ \end{array} \]

Alternative 3
Accuracy	61.1%
Cost	33092

\[\begin{array}{l} t_0 := \sqrt[3]{1 + x}\\ t_1 := t_0 - \sqrt[3]{x}\\ \mathbf{if}\;t_1 \leq 0:\\ \;\;\;\;\frac{1}{1 + \sqrt[3]{x} \cdot \left(\sqrt[3]{x} + t_0\right)}\\ \mathbf{else}:\\ \;\;\;\;t_1\\ \end{array} \]

Alternative 4
Accuracy	88.5%
Cost	33032

\[\begin{array}{l} t_0 := \sqrt[3]{1 + x}\\ t_1 := \sqrt[3]{x} + t_0\\ \mathbf{if}\;x \leq -1.35 \cdot 10^{+154}:\\ \;\;\;\;\frac{1}{1 + \sqrt[3]{x} \cdot t_1}\\ \mathbf{elif}\;x \leq 1.35 \cdot 10^{+154}:\\ \;\;\;\;\frac{1}{\frac{t_0}{\frac{1}{t_1}} + \sqrt[3]{x \cdot x}}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\mathsf{fma}\left(\sqrt[3]{x}, t_1, {\left(1 + x\right)}^{0.6666666666666666}\right)}\\ \end{array} \]

Alternative 5
Accuracy	99.2%
Cost	33024

\[\begin{array}{l} t_0 := \sqrt[3]{1 + x}\\ \frac{1}{{\left(\sqrt[3]{x}\right)}^{2} + \frac{t_0}{\frac{1}{\sqrt[3]{x} + t_0}}} \end{array} \]

Alternative 6
Accuracy	99.3%
Cost	33024

\[\frac{1}{{\left(\sqrt[3]{x}\right)}^{2} + \frac{\sqrt[3]{x} + \sqrt[3]{1 + x}}{\sqrt[3]{\frac{1}{1 + x}}}} \]

Alternative 7
Accuracy	99.2%
Cost	32896

\[\begin{array}{l} t_0 := \sqrt[3]{1 + x}\\ \frac{1}{{\left(\sqrt[3]{x}\right)}^{2} + t_0 \cdot \left(\sqrt[3]{x} + t_0\right)} \end{array} \]

Alternative 8
Accuracy	79.2%
Cost	26960

\[\begin{array}{l} t_0 := \sqrt[3]{1 + x}\\ t_1 := \sqrt[3]{x} \cdot \left(\sqrt[3]{x} + t_0\right)\\ t_2 := \frac{1}{t_1 + \sqrt[3]{x \cdot x}}\\ t_3 := \frac{1}{1 + t_1}\\ \mathbf{if}\;x \leq -1.35 \cdot 10^{+154}:\\ \;\;\;\;t_3\\ \mathbf{elif}\;x \leq -28000000:\\ \;\;\;\;t_2\\ \mathbf{elif}\;x \leq 130000000:\\ \;\;\;\;e^{\log \left(t_0 - \sqrt[3]{x}\right)}\\ \mathbf{elif}\;x \leq 1.35 \cdot 10^{+154}:\\ \;\;\;\;t_2\\ \mathbf{else}:\\ \;\;\;\;t_3\\ \end{array} \]

Alternative 9
Accuracy	88.5%
Cost	26952

\[\begin{array}{l} t_0 := \sqrt[3]{1 + x}\\ t_1 := \sqrt[3]{x} + t_0\\ t_2 := \sqrt[3]{x} \cdot t_1\\ \mathbf{if}\;x \leq -1.35 \cdot 10^{+154}:\\ \;\;\;\;\frac{1}{1 + t_2}\\ \mathbf{elif}\;x \leq 1.35 \cdot 10^{+154}:\\ \;\;\;\;\frac{1}{\frac{t_0}{\frac{1}{t_1}} + \sqrt[3]{x \cdot x}}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{t_2 + {\left(1 + x\right)}^{0.6666666666666666}}\\ \end{array} \]

Alternative 10
Accuracy	88.5%
Cost	26824

\[\begin{array}{l} t_0 := \sqrt[3]{1 + x}\\ t_1 := \sqrt[3]{x} + t_0\\ t_2 := \sqrt[3]{x} \cdot t_1\\ \mathbf{if}\;x \leq -1.35 \cdot 10^{+154}:\\ \;\;\;\;\frac{1}{1 + t_2}\\ \mathbf{elif}\;x \leq 1.35 \cdot 10^{+154}:\\ \;\;\;\;\frac{1}{t_0 \cdot t_1 + \sqrt[3]{x \cdot x}}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{t_2 + {\left(1 + x\right)}^{0.6666666666666666}}\\ \end{array} \]

Alternative 11
Accuracy	87.4%
Cost	26760

\[\begin{array}{l} t_0 := \sqrt[3]{x} \cdot \left(\sqrt[3]{x} + \sqrt[3]{1 + x}\right)\\ \mathbf{if}\;x \leq -1.35 \cdot 10^{+154}:\\ \;\;\;\;\frac{1}{1 + t_0}\\ \mathbf{elif}\;x \leq -1:\\ \;\;\;\;\frac{1}{t_0 + \sqrt[3]{x \cdot x}}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{t_0 + {\left(1 + x\right)}^{0.6666666666666666}}\\ \end{array} \]

Alternative 12
Accuracy	56.8%
Cost	26308

\[\begin{array}{l} t_0 := \sqrt[3]{1 + x} - \sqrt[3]{x}\\ \mathbf{if}\;t_0 \leq 0:\\ \;\;\;\;\frac{1}{1 + \sqrt[3]{x \cdot x}}\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]

Alternative 13
Accuracy	60.0%
Cost	13512

\[\begin{array}{l} \mathbf{if}\;x \leq -2.1 \cdot 10^{+15}:\\ \;\;\;\;\frac{1}{1 + {\left(\sqrt[3]{x}\right)}^{2}}\\ \mathbf{elif}\;x \leq 9.5 \cdot 10^{+14}:\\ \;\;\;\;\sqrt[3]{1 + x} - \sqrt[3]{x}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{1 + e^{0.6666666666666666 \cdot \log x}}\\ \end{array} \]

Alternative 14
Accuracy	60.0%
Cost	13449

\[\begin{array}{l} \mathbf{if}\;x \leq -2.1 \cdot 10^{+15} \lor \neg \left(x \leq 9.5 \cdot 10^{+14}\right):\\ \;\;\;\;\frac{1}{1 + {\left(\sqrt[3]{x}\right)}^{2}}\\ \mathbf{else}:\\ \;\;\;\;\sqrt[3]{1 + x} - \sqrt[3]{x}\\ \end{array} \]

Alternative 15
Accuracy	52.4%
Cost	6848

\[\frac{1}{1 + \sqrt[3]{x \cdot x}} \]

Alternative 16
Accuracy	3.6%
Cost	64

\[0 \]

Alternative 17
Accuracy	49.9%
Cost	64

\[1 \]

Reproduce

herbie shell --seed 2023131 
(FPCore (x)
  :name "2cbrt (problem 3.3.4)"
  :precision binary64
  (- (cbrt (+ x 1.0)) (cbrt x)))