2cbrt (problem 3.3.4)

Percentage Accurate: 7.0% → 98.5%

Time: 13.4s

Alternatives: 4

Speedup: 1.0×

Specification

\[x > 1 \land x < 10^{+308}\]

Math

\[\begin{array}{l} \\ \sqrt[3]{x + 1} - \sqrt[3]{x} \end{array} \]

FPCore

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

C

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);
}

Julia

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]

Initial Program: 7.0% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ \sqrt[3]{x + 1} - \sqrt[3]{x} \end{array} \]

FPCore

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

C

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);
}

Julia

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]

Alternative 1: 98.5% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \sqrt[3]{1 + x}\\ \frac{1}{\mathsf{fma}\left(\sqrt[3]{x}, \sqrt[3]{x} + t\_0, {t\_0}^{2}\right)} \end{array} \end{array} \]

FPCore

(FPCore (x)
 :precision binary64
 (let* ((t_0 (cbrt (+ 1.0 x))))
   (/ 1.0 (fma (cbrt x) (+ (cbrt x) t_0) (pow t_0 2.0)))))

C

double code(double x) {
	double t_0 = cbrt((1.0 + x));
	return 1.0 / fma(cbrt(x), (cbrt(x) + t_0), pow(t_0, 2.0));
}

Julia

function code(x)
	t_0 = cbrt(Float64(1.0 + x))
	return Float64(1.0 / fma(cbrt(x), Float64(cbrt(x) + t_0), (t_0 ^ 2.0)))
end

Wolfram

code[x_] := Block[{t$95$0 = N[Power[N[(1.0 + x), $MachinePrecision], 1/3], $MachinePrecision]}, N[(1.0 / N[(N[Power[x, 1/3], $MachinePrecision] * N[(N[Power[x, 1/3], $MachinePrecision] + t$95$0), $MachinePrecision] + N[Power[t$95$0, 2.0], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Derivation

1. Initial program 6.5%

   \[\sqrt[3]{x + 1} - \sqrt[3]{x} \]
2. Add Preprocessing
3. Step-by-step derivation

   1. pow1/3 7.8%

      \[\leadsto \sqrt[3]{x + 1} - \color{blue}{{x}^{0.3333333333333333}} \]

4. Applied egg-rr 7.8%

   \[\leadsto \sqrt[3]{x + 1} - \color{blue}{{x}^{0.3333333333333333}} \]
5. Step-by-step derivation

   1. pow1/3 6.5%

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

   2. flip3-- 7.2%

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

   3. div-inv 7.2%

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

   4. rem-cube-cbrt 6.5%

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

   5. rem-cube-cbrt 9.3%

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

   6. pow2 9.3%

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

   7. distribute-rgt-out 9.3%

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

   8. +-commutative 9.3%

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

6. Applied egg-rr 9.3%

   \[\leadsto \color{blue}{\left(\left(x + 1\right) - x\right) \cdot \frac{1}{{\left(\sqrt[3]{x + 1}\right)}^{2} + \sqrt[3]{x} \cdot \left(\sqrt[3]{x + 1} + \sqrt[3]{x}\right)}} \]
7. Step-by-step derivation

   1. associate-*r/ 9.3%

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

   2. *-rgt-identity 9.3%

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

   3. +-commutative 9.3%

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

   4. associate--l+ 98.5%

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

   5. +-inverses 98.5%

      \[\leadsto \frac{1 + \color{blue}{0}}{{\left(\sqrt[3]{x + 1}\right)}^{2} + \sqrt[3]{x} \cdot \left(\sqrt[3]{x + 1} + \sqrt[3]{x}\right)} \]

   6. metadata-eval 98.5%

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

   7. +-commutative 98.5%

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

   8. fma-define 98.6%

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

   9. +-commutative 98.6%

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

8. Simplified 98.6%

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

9. Final simplification 98.6%

   \[\leadsto \frac{1}{\mathsf{fma}\left(\sqrt[3]{x}, \sqrt[3]{x} + \sqrt[3]{1 + x}, {\left(\sqrt[3]{1 + x}\right)}^{2}\right)} \]
10. Add Preprocessing

Alternative 2: 96.5% accurate, 1.0× speedup

Math

\[\begin{array}{l} \\ 0.3333333333333333 \cdot {\left(\sqrt[3]{x}\right)}^{-2} \end{array} \]

FPCore

(FPCore (x) :precision binary64 (* 0.3333333333333333 (pow (cbrt x) -2.0)))

C

double code(double x) {
	return 0.3333333333333333 * pow(cbrt(x), -2.0);
}

Java

public static double code(double x) {
	return 0.3333333333333333 * Math.pow(Math.cbrt(x), -2.0);
}

Julia

function code(x)
	return Float64(0.3333333333333333 * (cbrt(x) ^ -2.0))
end

Wolfram

code[x_] := N[(0.3333333333333333 * N[Power[N[Power[x, 1/3], $MachinePrecision], -2.0], $MachinePrecision]), $MachinePrecision]

Derivation

1. Initial program 6.5%

   \[\sqrt[3]{x + 1} - \sqrt[3]{x} \]
2. Add Preprocessing
3. Step-by-step derivation

   1. add-cube-cbrt 6.6%

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

   2. pow3 6.6%

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

4. Applied egg-rr 6.6%

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

5. Taylor expanded in x around inf 3.5%

   \[\leadsto \color{blue}{\left(0.1111111111111111 \cdot \left({\left({1}^{4}\right)}^{0.1111111111111111} \cdot {\left(\frac{1}{{x}^{2}}\right)}^{0.3333333333333333}\right) + \left(0.2222222222222222 \cdot {\left(\frac{1}{{x}^{2}}\right)}^{0.3333333333333333} + {x}^{0.3333333333333333}\right)\right)} - \sqrt[3]{x} \]
6. Step-by-step derivation

   1. unpow1/3 5.9%

      \[\leadsto \left(0.1111111111111111 \cdot \left({\left({1}^{4}\right)}^{0.1111111111111111} \cdot {\left(\frac{1}{{x}^{2}}\right)}^{0.3333333333333333}\right) + \left(0.2222222222222222 \cdot {\left(\frac{1}{{x}^{2}}\right)}^{0.3333333333333333} + \color{blue}{\sqrt[3]{x}}\right)\right) - \sqrt[3]{x} \]

   2. associate-+r+ 5.9%

      \[\leadsto \color{blue}{\left(\left(0.1111111111111111 \cdot \left({\left({1}^{4}\right)}^{0.1111111111111111} \cdot {\left(\frac{1}{{x}^{2}}\right)}^{0.3333333333333333}\right) + 0.2222222222222222 \cdot {\left(\frac{1}{{x}^{2}}\right)}^{0.3333333333333333}\right) + \sqrt[3]{x}\right)} - \sqrt[3]{x} \]

   3. +-commutative 5.9%

      \[\leadsto \color{blue}{\left(\sqrt[3]{x} + \left(0.1111111111111111 \cdot \left({\left({1}^{4}\right)}^{0.1111111111111111} \cdot {\left(\frac{1}{{x}^{2}}\right)}^{0.3333333333333333}\right) + 0.2222222222222222 \cdot {\left(\frac{1}{{x}^{2}}\right)}^{0.3333333333333333}\right)\right)} - \sqrt[3]{x} \]

   4. metadata-eval 5.9%

      \[\leadsto \left(\sqrt[3]{x} + \left(0.1111111111111111 \cdot \left({\color{blue}{1}}^{0.1111111111111111} \cdot {\left(\frac{1}{{x}^{2}}\right)}^{0.3333333333333333}\right) + 0.2222222222222222 \cdot {\left(\frac{1}{{x}^{2}}\right)}^{0.3333333333333333}\right)\right) - \sqrt[3]{x} \]

   5. pow-base-1 5.9%

      \[\leadsto \left(\sqrt[3]{x} + \left(0.1111111111111111 \cdot \left(\color{blue}{1} \cdot {\left(\frac{1}{{x}^{2}}\right)}^{0.3333333333333333}\right) + 0.2222222222222222 \cdot {\left(\frac{1}{{x}^{2}}\right)}^{0.3333333333333333}\right)\right) - \sqrt[3]{x} \]

   6. *-lft-identity 5.9%

      \[\leadsto \left(\sqrt[3]{x} + \left(0.1111111111111111 \cdot \color{blue}{{\left(\frac{1}{{x}^{2}}\right)}^{0.3333333333333333}} + 0.2222222222222222 \cdot {\left(\frac{1}{{x}^{2}}\right)}^{0.3333333333333333}\right)\right) - \sqrt[3]{x} \]

   7. distribute-rgt-out 5.9%

      \[\leadsto \left(\sqrt[3]{x} + \color{blue}{{\left(\frac{1}{{x}^{2}}\right)}^{0.3333333333333333} \cdot \left(0.1111111111111111 + 0.2222222222222222\right)}\right) - \sqrt[3]{x} \]

   8. unpow1/3 5.9%

      \[\leadsto \left(\sqrt[3]{x} + \color{blue}{\sqrt[3]{\frac{1}{{x}^{2}}}} \cdot \left(0.1111111111111111 + 0.2222222222222222\right)\right) - \sqrt[3]{x} \]

   9. metadata-eval 5.9%

      \[\leadsto \left(\sqrt[3]{x} + \sqrt[3]{\frac{1}{{x}^{2}}} \cdot \color{blue}{0.3333333333333333}\right) - \sqrt[3]{x} \]

7. Simplified 5.9%

   \[\leadsto \color{blue}{\left(\sqrt[3]{x} + \sqrt[3]{\frac{1}{{x}^{2}}} \cdot 0.3333333333333333\right)} - \sqrt[3]{x} \]
8. Step-by-step derivation

   1. sub-neg 5.9%

      \[\leadsto \color{blue}{\left(\sqrt[3]{x} + \sqrt[3]{\frac{1}{{x}^{2}}} \cdot 0.3333333333333333\right) + \left(-\sqrt[3]{x}\right)} \]

   2. +-commutative 5.9%

      \[\leadsto \color{blue}{\left(\sqrt[3]{\frac{1}{{x}^{2}}} \cdot 0.3333333333333333 + \sqrt[3]{x}\right)} + \left(-\sqrt[3]{x}\right) \]

   3. *-commutative 5.9%

      \[\leadsto \left(\color{blue}{0.3333333333333333 \cdot \sqrt[3]{\frac{1}{{x}^{2}}}} + \sqrt[3]{x}\right) + \left(-\sqrt[3]{x}\right) \]

   4. fma-define 5.9%

      \[\leadsto \color{blue}{\mathsf{fma}\left(0.3333333333333333, \sqrt[3]{\frac{1}{{x}^{2}}}, \sqrt[3]{x}\right)} + \left(-\sqrt[3]{x}\right) \]

   5. pow-flip 5.9%

      \[\leadsto \mathsf{fma}\left(0.3333333333333333, \sqrt[3]{\color{blue}{{x}^{\left(-2\right)}}}, \sqrt[3]{x}\right) + \left(-\sqrt[3]{x}\right) \]

   6. metadata-eval 5.9%

      \[\leadsto \mathsf{fma}\left(0.3333333333333333, \sqrt[3]{{x}^{\color{blue}{-2}}}, \sqrt[3]{x}\right) + \left(-\sqrt[3]{x}\right) \]

9. Applied egg-rr 5.9%

   \[\leadsto \color{blue}{\mathsf{fma}\left(0.3333333333333333, \sqrt[3]{{x}^{-2}}, \sqrt[3]{x}\right) + \left(-\sqrt[3]{x}\right)} \]
10. Step-by-step derivation

    1. fma-undefine 5.9%

       \[\leadsto \color{blue}{\left(0.3333333333333333 \cdot \sqrt[3]{{x}^{-2}} + \sqrt[3]{x}\right)} + \left(-\sqrt[3]{x}\right) \]

    2. associate-+l+ 55.1%

       \[\leadsto \color{blue}{0.3333333333333333 \cdot \sqrt[3]{{x}^{-2}} + \left(\sqrt[3]{x} + \left(-\sqrt[3]{x}\right)\right)} \]

    3. sub-neg 55.1%

       \[\leadsto 0.3333333333333333 \cdot \sqrt[3]{{x}^{-2}} + \color{blue}{\left(\sqrt[3]{x} - \sqrt[3]{x}\right)} \]

    4. +-inverses 55.1%

       \[\leadsto 0.3333333333333333 \cdot \sqrt[3]{{x}^{-2}} + \color{blue}{0} \]

    5. +-rgt-identity 55.1%

       \[\leadsto \color{blue}{0.3333333333333333 \cdot \sqrt[3]{{x}^{-2}}} \]

    6. unpow1/3 51.7%

       \[\leadsto 0.3333333333333333 \cdot \color{blue}{{\left({x}^{-2}\right)}^{0.3333333333333333}} \]

    7. exp-to-pow 52.0%

       \[\leadsto 0.3333333333333333 \cdot {\color{blue}{\left(e^{\log x \cdot -2}\right)}}^{0.3333333333333333} \]

    8. *-commutative 52.0%

       \[\leadsto 0.3333333333333333 \cdot {\left(e^{\color{blue}{-2 \cdot \log x}}\right)}^{0.3333333333333333} \]

    9. exp-prod 89.7%

       \[\leadsto 0.3333333333333333 \cdot \color{blue}{e^{\left(-2 \cdot \log x\right) \cdot 0.3333333333333333}} \]

    10. *-commutative 89.7%

        \[\leadsto 0.3333333333333333 \cdot e^{\color{blue}{0.3333333333333333 \cdot \left(-2 \cdot \log x\right)}} \]

    11. *-commutative 89.7%

        \[\leadsto 0.3333333333333333 \cdot e^{0.3333333333333333 \cdot \color{blue}{\left(\log x \cdot -2\right)}} \]

    12. associate-*r* 89.7%

        \[\leadsto 0.3333333333333333 \cdot e^{\color{blue}{\left(0.3333333333333333 \cdot \log x\right) \cdot -2}} \]

    13. log-pow 89.8%

        \[\leadsto 0.3333333333333333 \cdot e^{\color{blue}{\log \left({x}^{0.3333333333333333}\right)} \cdot -2} \]

    14. unpow1/3 90.6%

        \[\leadsto 0.3333333333333333 \cdot e^{\log \color{blue}{\left(\sqrt[3]{x}\right)} \cdot -2} \]

    15. exp-prod 90.6%

        \[\leadsto 0.3333333333333333 \cdot \color{blue}{{\left(e^{\log \left(\sqrt[3]{x}\right)}\right)}^{-2}} \]

    16. rem-exp-log 96.9%

        \[\leadsto 0.3333333333333333 \cdot {\color{blue}{\left(\sqrt[3]{x}\right)}}^{-2} \]

11. Simplified 96.9%

    \[\leadsto \color{blue}{0.3333333333333333 \cdot {\left(\sqrt[3]{x}\right)}^{-2}} \]

12. Final simplification 96.9%

    \[\leadsto 0.3333333333333333 \cdot {\left(\sqrt[3]{x}\right)}^{-2} \]
13. Add Preprocessing

Alternative 3: 4.1% accurate, 205.0× speedup

Math

\[\begin{array}{l} \\ 0 \end{array} \]

FPCore

(FPCore (x) :precision binary64 0.0)

C

double code(double x) {
	return 0.0;
}

Fortran

real(8) function code(x)
    real(8), intent (in) :: x
    code = 0.0d0
end function

Java

public static double code(double x) {
	return 0.0;
}

Python

def code(x):
	return 0.0

Julia

function code(x)
	return 0.0
end

MATLAB

function tmp = code(x)
	tmp = 0.0;
end

Wolfram

code[x_] := 0.0

Derivation

1. Initial program 6.5%

   \[\sqrt[3]{x + 1} - \sqrt[3]{x} \]
2. Add Preprocessing

3. Taylor expanded in x around inf 4.1%

   \[\leadsto \color{blue}{0} \]

4. Final simplification 4.1%

   \[\leadsto 0 \]
5. Add Preprocessing

Alternative 4: 6.3% accurate, 205.0× speedup

Math

\[\begin{array}{l} \\ 1 \end{array} \]

FPCore

(FPCore (x) :precision binary64 1.0)

C

double code(double x) {
	return 1.0;
}

Fortran

real(8) function code(x)
    real(8), intent (in) :: x
    code = 1.0d0
end function

Java

public static double code(double x) {
	return 1.0;
}

Python

def code(x):
	return 1.0

Julia

function code(x)
	return 1.0
end

MATLAB

function tmp = code(x)
	tmp = 1.0;
end

Wolfram

code[x_] := 1.0

Derivation

1. Initial program 6.5%

   \[\sqrt[3]{x + 1} - \sqrt[3]{x} \]
2. Add Preprocessing

3. Taylor expanded in x around 0 6.4%

   \[\leadsto \color{blue}{1} \]

4. Final simplification 6.4%

   \[\leadsto 1 \]
5. Add Preprocessing

Developer target: 98.5% accurate, 0.3× speedup

Math

\[\begin{array}{l} \\ \begin{array}{l} t_0 := \sqrt[3]{x + 1}\\ \frac{1}{\left(t\_0 \cdot t\_0 + \sqrt[3]{x} \cdot t\_0\right) + \sqrt[3]{x} \cdot \sqrt[3]{x}} \end{array} \end{array} \]

FPCore

(FPCore (x)
 :precision binary64
 (let* ((t_0 (cbrt (+ x 1.0))))
   (/ 1.0 (+ (+ (* t_0 t_0) (* (cbrt x) t_0)) (* (cbrt x) (cbrt x))))))

C

double code(double x) {
	double t_0 = cbrt((x + 1.0));
	return 1.0 / (((t_0 * t_0) + (cbrt(x) * t_0)) + (cbrt(x) * cbrt(x)));
}

Java

public static double code(double x) {
	double t_0 = Math.cbrt((x + 1.0));
	return 1.0 / (((t_0 * t_0) + (Math.cbrt(x) * t_0)) + (Math.cbrt(x) * Math.cbrt(x)));
}

Julia

function code(x)
	t_0 = cbrt(Float64(x + 1.0))
	return Float64(1.0 / Float64(Float64(Float64(t_0 * t_0) + Float64(cbrt(x) * t_0)) + Float64(cbrt(x) * cbrt(x))))
end

Wolfram

code[x_] := Block[{t$95$0 = N[Power[N[(x + 1.0), $MachinePrecision], 1/3], $MachinePrecision]}, N[(1.0 / N[(N[(N[(t$95$0 * t$95$0), $MachinePrecision] + N[(N[Power[x, 1/3], $MachinePrecision] * t$95$0), $MachinePrecision]), $MachinePrecision] + N[(N[Power[x, 1/3], $MachinePrecision] * N[Power[x, 1/3], $MachinePrecision]), $MachinePrecision]), $MachinePrecision]), $MachinePrecision]]

Reproduce

herbie shell --seed 2024036 
(FPCore (x)
  :name "2cbrt (problem 3.3.4)"
  :precision binary64
  :pre (and (> x 1.0) (< x 1e+308))

  :herbie-target
  (/ 1.0 (+ (+ (* (cbrt (+ x 1.0)) (cbrt (+ x 1.0))) (* (cbrt x) (cbrt (+ x 1.0)))) (* (cbrt x) (cbrt x))))

  (- (cbrt (+ x 1.0)) (cbrt x)))