Average Error: 29.4 → 0.4
Time: 10.0s
Precision: binary64
Cost: 33160
\[\sqrt[3]{x + 1} - \sqrt[3]{x} \]
↓
\[\begin{array}{l} \mathbf{if}\;x \leq -7.17214385910263 \cdot 10^{+18}:\\ \;\;\;\;\frac{\sqrt[3]{x} \cdot 0.3333333333333333}{x}\\ \mathbf{elif}\;x \leq 39443295874996.02:\\ \;\;\;\;\frac{1}{\sqrt[3]{x} \cdot \left(\sqrt[3]{1 + x} + \sqrt[3]{x}\right) + \sqrt[3]{{\left(1 + x\right)}^{2}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{\sqrt[3]{x}}{\frac{x}{0.3333333333333333}}\\ \end{array} \]
(FPCore (x) :precision binary64 (- (cbrt (+ x 1.0)) (cbrt x)))
↓
(FPCore (x)
 :precision binary64
 (if (<= x -7.17214385910263e+18)
   (/ (* (cbrt x) 0.3333333333333333) x)
   (if (<= x 39443295874996.02)
     (/
      1.0
      (+
       (* (cbrt x) (+ (cbrt (+ 1.0 x)) (cbrt x)))
       (cbrt (pow (+ 1.0 x) 2.0))))
     (/ (cbrt x) (/ x 0.3333333333333333)))))
double code(double x) {
	return cbrt((x + 1.0)) - cbrt(x);
}
↓
double code(double x) {
	double tmp;
	if (x <= -7.17214385910263e+18) {
		tmp = (cbrt(x) * 0.3333333333333333) / x;
	} else if (x <= 39443295874996.02) {
		tmp = 1.0 / ((cbrt(x) * (cbrt((1.0 + x)) + cbrt(x))) + cbrt(pow((1.0 + x), 2.0)));
	} else {
		tmp = cbrt(x) / (x / 0.3333333333333333);
	}
	return tmp;
}

public static double code(double x) {
	return Math.cbrt((x + 1.0)) - Math.cbrt(x);
}
↓
public static double code(double x) {
	double tmp;
	if (x <= -7.17214385910263e+18) {
		tmp = (Math.cbrt(x) * 0.3333333333333333) / x;
	} else if (x <= 39443295874996.02) {
		tmp = 1.0 / ((Math.cbrt(x) * (Math.cbrt((1.0 + x)) + Math.cbrt(x))) + Math.cbrt(Math.pow((1.0 + x), 2.0)));
	} else {
		tmp = Math.cbrt(x) / (x / 0.3333333333333333);
	}
	return tmp;
}

function code(x)
	return Float64(cbrt(Float64(x + 1.0)) - cbrt(x))
end
↓
function code(x)
	tmp = 0.0
	if (x <= -7.17214385910263e+18)
		tmp = Float64(Float64(cbrt(x) * 0.3333333333333333) / x);
	elseif (x <= 39443295874996.02)
		tmp = Float64(1.0 / Float64(Float64(cbrt(x) * Float64(cbrt(Float64(1.0 + x)) + cbrt(x))) + cbrt((Float64(1.0 + x) ^ 2.0))));
	else
		tmp = Float64(cbrt(x) / Float64(x / 0.3333333333333333));
	end
	return tmp
end

code[x_] := N[(N[Power[N[(x + 1.0), $MachinePrecision], 1/3], $MachinePrecision] - N[Power[x, 1/3], $MachinePrecision]), $MachinePrecision]
↓
code[x_] := If[LessEqual[x, -7.17214385910263e+18], N[(N[(N[Power[x, 1/3], $MachinePrecision] * 0.3333333333333333), $MachinePrecision] / x), $MachinePrecision], If[LessEqual[x, 39443295874996.02], N[(1.0 / N[(N[(N[Power[x, 1/3], $MachinePrecision] * N[(N[Power[N[(1.0 + x), $MachinePrecision], 1/3], $MachinePrecision] + N[Power[x, 1/3], $MachinePrecision]), $MachinePrecision]), $MachinePrecision] + N[Power[N[Power[N[(1.0 + x), $MachinePrecision], 2.0], $MachinePrecision], 1/3], $MachinePrecision]), $MachinePrecision]), $MachinePrecision], N[(N[Power[x, 1/3], $MachinePrecision] / N[(x / 0.3333333333333333), $MachinePrecision]), $MachinePrecision]]]

\sqrt[3]{x + 1} - \sqrt[3]{x}
↓
\begin{array}{l}
\mathbf{if}\;x \leq -7.17214385910263 \cdot 10^{+18}:\\
\;\;\;\;\frac{\sqrt[3]{x} \cdot 0.3333333333333333}{x}\\

\mathbf{elif}\;x \leq 39443295874996.02:\\
\;\;\;\;\frac{1}{\sqrt[3]{x} \cdot \left(\sqrt[3]{1 + x} + \sqrt[3]{x}\right) + \sqrt[3]{{\left(1 + x\right)}^{2}}}\\

\mathbf{else}:\\
\;\;\;\;\frac{\sqrt[3]{x}}{\frac{x}{0.3333333333333333}}\\


\end{array}

Error

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Split input into 3 regimes

  2. if x < -7172143859102629900

    1. Initial program 61.3

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

    2. Applied egg-rr64.0

      \[\leadsto \color{blue}{\left({\left(x + 1\right)}^{0.16666666666666666} + {x}^{0.16666666666666666}\right) \cdot \left({\left(x + 1\right)}^{0.16666666666666666} - {x}^{0.16666666666666666}\right)} \]

    3. Taylor expanded in x around -inf 64.0

      \[\leadsto \color{blue}{0.3333333333333333 \cdot \frac{{\left(e^{0.16666666666666666 \cdot \left(-1 \cdot \log \left(\frac{-1}{x}\right) + \log -1\right)}\right)}^{2}}{x}} \]

    4. Simplified64.0

      \[\leadsto \color{blue}{\frac{0.3333333333333333}{x} \cdot \sqrt[3]{e^{\log x}}} \]
      Proof
      (*.f64 (/.f64 1/3 x) (cbrt.f64 (exp.f64 (log.f64 x)))): 0 points increase in error, 0 points decrease in error
      (*.f64 (/.f64 1/3 x) (cbrt.f64 (exp.f64 (Rewrite<= remove-double-neg_binary64 (neg.f64 (neg.f64 (log.f64 x))))))): 0 points increase in error, 0 points decrease in error
      (*.f64 (/.f64 1/3 x) (cbrt.f64 (exp.f64 (Rewrite=> neg-sub0_binary64 (-.f64 0 (neg.f64 (log.f64 x))))))): 0 points increase in error, 0 points decrease in error
      (*.f64 (/.f64 1/3 x) (cbrt.f64 (exp.f64 (-.f64 (Rewrite<= +-inverses_binary64 (-.f64 (log.f64 -1) (log.f64 -1))) (neg.f64 (log.f64 x)))))): 137 points increase in error, 0 points decrease in error
      (*.f64 (/.f64 1/3 x) (cbrt.f64 (exp.f64 (Rewrite<= associate--r+_binary64 (-.f64 (log.f64 -1) (+.f64 (log.f64 -1) (neg.f64 (log.f64 x)))))))): 0 points increase in error, 0 points decrease in error
      (*.f64 (/.f64 1/3 x) (cbrt.f64 (exp.f64 (-.f64 (log.f64 -1) (Rewrite<= sub-neg_binary64 (-.f64 (log.f64 -1) (log.f64 x))))))): 0 points increase in error, 0 points decrease in error
      (*.f64 (/.f64 1/3 x) (cbrt.f64 (exp.f64 (-.f64 (log.f64 -1) (Rewrite<= log-div_binary64 (log.f64 (/.f64 -1 x))))))): 0 points increase in error, 0 points decrease in error
      (*.f64 (/.f64 1/3 x) (cbrt.f64 (exp.f64 (Rewrite<= unsub-neg_binary64 (+.f64 (log.f64 -1) (neg.f64 (log.f64 (/.f64 -1 x)))))))): 0 points increase in error, 0 points decrease in error
      (*.f64 (/.f64 1/3 x) (cbrt.f64 (exp.f64 (+.f64 (log.f64 -1) (Rewrite<= mul-1-neg_binary64 (*.f64 -1 (log.f64 (/.f64 -1 x)))))))): 0 points increase in error, 0 points decrease in error
      (*.f64 (/.f64 1/3 x) (cbrt.f64 (exp.f64 (Rewrite<= +-commutative_binary64 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))))): 0 points increase in error, 0 points decrease in error
      (*.f64 (/.f64 1/3 x) (Rewrite<= unpow1/3_binary64 (pow.f64 (exp.f64 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1))) 1/3))): 0 points increase in error, 0 points decrease in error
      (*.f64 (/.f64 1/3 x) (Rewrite<= exp-prod_binary64 (exp.f64 (*.f64 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)) 1/3)))): 0 points increase in error, 0 points decrease in error
      (*.f64 (/.f64 1/3 x) (exp.f64 (*.f64 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)) (Rewrite<= metadata-eval (+.f64 1/6 1/6))))): 0 points increase in error, 0 points decrease in error
      (*.f64 (/.f64 1/3 x) (exp.f64 (Rewrite<= distribute-rgt-out_binary64 (+.f64 (*.f64 1/6 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1))) (*.f64 1/6 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1))))))): 0 points increase in error, 0 points decrease in error
      (*.f64 (/.f64 1/3 x) (Rewrite<= prod-exp_binary64 (*.f64 (exp.f64 (*.f64 1/6 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (exp.f64 (*.f64 1/6 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1))))))): 0 points increase in error, 0 points decrease in error
      (*.f64 (/.f64 1/3 x) (Rewrite<= unpow2_binary64 (pow.f64 (exp.f64 (*.f64 1/6 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 2))): 0 points increase in error, 0 points decrease in error
      (Rewrite<= associate-/r/_binary64 (/.f64 1/3 (/.f64 x (pow.f64 (exp.f64 (*.f64 1/6 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 2)))): 0 points increase in error, 0 points decrease in error
      (Rewrite<= associate-/l*_binary64 (/.f64 (*.f64 1/3 (pow.f64 (exp.f64 (*.f64 1/6 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 2)) x)): 0 points increase in error, 0 points decrease in error
      (Rewrite<= associate-*r/_binary64 (*.f64 1/3 (/.f64 (pow.f64 (exp.f64 (*.f64 1/6 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 2) x))): 0 points increase in error, 0 points decrease in error

    5. Applied egg-rr0.6

      \[\leadsto \color{blue}{\frac{0.3333333333333333 \cdot \sqrt[3]{x}}{x}} \]

    if -7172143859102629900 < x < 39443295874996.0234

    1. Initial program 1.6

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

    2. Applied egg-rr0.4

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

    3. Taylor expanded in x around 0 0.1

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

    4. Applied egg-rr0.1

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

    if 39443295874996.0234 < x

    1. Initial program 61.2

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

    2. Applied egg-rr61.2

      \[\leadsto \color{blue}{\left({\left(x + 1\right)}^{0.16666666666666666} + {x}^{0.16666666666666666}\right) \cdot \left({\left(x + 1\right)}^{0.16666666666666666} - {x}^{0.16666666666666666}\right)} \]

    3. Taylor expanded in x around -inf 64.0

      \[\leadsto \color{blue}{0.3333333333333333 \cdot \frac{{\left(e^{0.16666666666666666 \cdot \left(-1 \cdot \log \left(\frac{-1}{x}\right) + \log -1\right)}\right)}^{2}}{x}} \]

    4. Simplified4.4

      \[\leadsto \color{blue}{\frac{0.3333333333333333}{x} \cdot \sqrt[3]{e^{\log x}}} \]
      Proof
      (*.f64 (/.f64 1/3 x) (cbrt.f64 (exp.f64 (log.f64 x)))): 0 points increase in error, 0 points decrease in error
      (*.f64 (/.f64 1/3 x) (cbrt.f64 (exp.f64 (Rewrite<= remove-double-neg_binary64 (neg.f64 (neg.f64 (log.f64 x))))))): 0 points increase in error, 0 points decrease in error
      (*.f64 (/.f64 1/3 x) (cbrt.f64 (exp.f64 (Rewrite=> neg-sub0_binary64 (-.f64 0 (neg.f64 (log.f64 x))))))): 0 points increase in error, 0 points decrease in error
      (*.f64 (/.f64 1/3 x) (cbrt.f64 (exp.f64 (-.f64 (Rewrite<= +-inverses_binary64 (-.f64 (log.f64 -1) (log.f64 -1))) (neg.f64 (log.f64 x)))))): 137 points increase in error, 0 points decrease in error
      (*.f64 (/.f64 1/3 x) (cbrt.f64 (exp.f64 (Rewrite<= associate--r+_binary64 (-.f64 (log.f64 -1) (+.f64 (log.f64 -1) (neg.f64 (log.f64 x)))))))): 0 points increase in error, 0 points decrease in error
      (*.f64 (/.f64 1/3 x) (cbrt.f64 (exp.f64 (-.f64 (log.f64 -1) (Rewrite<= sub-neg_binary64 (-.f64 (log.f64 -1) (log.f64 x))))))): 0 points increase in error, 0 points decrease in error
      (*.f64 (/.f64 1/3 x) (cbrt.f64 (exp.f64 (-.f64 (log.f64 -1) (Rewrite<= log-div_binary64 (log.f64 (/.f64 -1 x))))))): 0 points increase in error, 0 points decrease in error
      (*.f64 (/.f64 1/3 x) (cbrt.f64 (exp.f64 (Rewrite<= unsub-neg_binary64 (+.f64 (log.f64 -1) (neg.f64 (log.f64 (/.f64 -1 x)))))))): 0 points increase in error, 0 points decrease in error
      (*.f64 (/.f64 1/3 x) (cbrt.f64 (exp.f64 (+.f64 (log.f64 -1) (Rewrite<= mul-1-neg_binary64 (*.f64 -1 (log.f64 (/.f64 -1 x)))))))): 0 points increase in error, 0 points decrease in error
      (*.f64 (/.f64 1/3 x) (cbrt.f64 (exp.f64 (Rewrite<= +-commutative_binary64 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))))): 0 points increase in error, 0 points decrease in error
      (*.f64 (/.f64 1/3 x) (Rewrite<= unpow1/3_binary64 (pow.f64 (exp.f64 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1))) 1/3))): 0 points increase in error, 0 points decrease in error
      (*.f64 (/.f64 1/3 x) (Rewrite<= exp-prod_binary64 (exp.f64 (*.f64 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)) 1/3)))): 0 points increase in error, 0 points decrease in error
      (*.f64 (/.f64 1/3 x) (exp.f64 (*.f64 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)) (Rewrite<= metadata-eval (+.f64 1/6 1/6))))): 0 points increase in error, 0 points decrease in error
      (*.f64 (/.f64 1/3 x) (exp.f64 (Rewrite<= distribute-rgt-out_binary64 (+.f64 (*.f64 1/6 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1))) (*.f64 1/6 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1))))))): 0 points increase in error, 0 points decrease in error
      (*.f64 (/.f64 1/3 x) (Rewrite<= prod-exp_binary64 (*.f64 (exp.f64 (*.f64 1/6 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) (exp.f64 (*.f64 1/6 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1))))))): 0 points increase in error, 0 points decrease in error
      (*.f64 (/.f64 1/3 x) (Rewrite<= unpow2_binary64 (pow.f64 (exp.f64 (*.f64 1/6 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 2))): 0 points increase in error, 0 points decrease in error
      (Rewrite<= associate-/r/_binary64 (/.f64 1/3 (/.f64 x (pow.f64 (exp.f64 (*.f64 1/6 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 2)))): 0 points increase in error, 0 points decrease in error
      (Rewrite<= associate-/l*_binary64 (/.f64 (*.f64 1/3 (pow.f64 (exp.f64 (*.f64 1/6 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 2)) x)): 0 points increase in error, 0 points decrease in error
      (Rewrite<= associate-*r/_binary64 (*.f64 1/3 (/.f64 (pow.f64 (exp.f64 (*.f64 1/6 (+.f64 (*.f64 -1 (log.f64 (/.f64 -1 x))) (log.f64 -1)))) 2) x))): 0 points increase in error, 0 points decrease in error

    5. Applied egg-rr0.8

      \[\leadsto \color{blue}{\frac{\sqrt[3]{x}}{\frac{x}{0.3333333333333333}}} \]
  3. Recombined 3 regimes into one program.

  4. Final simplification0.4

    \[\leadsto \begin{array}{l} \mathbf{if}\;x \leq -7.17214385910263 \cdot 10^{+18}:\\ \;\;\;\;\frac{\sqrt[3]{x} \cdot 0.3333333333333333}{x}\\ \mathbf{elif}\;x \leq 39443295874996.02:\\ \;\;\;\;\frac{1}{\sqrt[3]{x} \cdot \left(\sqrt[3]{1 + x} + \sqrt[3]{x}\right) + \sqrt[3]{{\left(1 + x\right)}^{2}}}\\ \mathbf{else}:\\ \;\;\;\;\frac{\sqrt[3]{x}}{\frac{x}{0.3333333333333333}}\\ \end{array} \]

Alternatives

Alternative 1
Error0.9
Cost46020
\[\begin{array}{l} t_0 := \sqrt[3]{1 + x}\\ \mathbf{if}\;t_0 - \sqrt[3]{x} \leq 10^{-6}:\\ \;\;\;\;\frac{\sqrt[3]{x} \cdot 0.3333333333333333}{x}\\ \mathbf{else}:\\ \;\;\;\;\frac{1}{\sqrt[3]{x} \cdot \left(t_0 + \sqrt[3]{x}\right) + e^{0.6666666666666666 \cdot \mathsf{log1p}\left(x\right)}}\\ \end{array} \]
Alternative 2
Error0.5
Cost32896
\[\begin{array}{l} t_0 := \sqrt[3]{1 + x}\\ \frac{1}{{t_0}^{2} + \sqrt[3]{x} \cdot \left(t_0 + \sqrt[3]{x}\right)} \end{array} \]
Alternative 3
Error1.0
Cost26440
\[\begin{array}{l} \mathbf{if}\;x \leq -216712653.40025404:\\ \;\;\;\;\frac{\sqrt[3]{x} \cdot 0.3333333333333333}{x}\\ \mathbf{elif}\;x \leq 68715.65870822774:\\ \;\;\;\;\sqrt[3]{1 + x} - \mathsf{expm1}\left(\mathsf{log1p}\left(\sqrt[3]{x}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;{\left(\sqrt[3]{x}\right)}^{-5} \cdot -0.1111111111111111 + 0.3333333333333333 \cdot {\left(\sqrt[3]{x}\right)}^{-2}\\ \end{array} \]
Alternative 4
Error1.0
Cost26184
\[\begin{array}{l} \mathbf{if}\;x \leq -216712653.40025404:\\ \;\;\;\;\frac{\sqrt[3]{x} \cdot 0.3333333333333333}{x}\\ \mathbf{elif}\;x \leq 747582.6933135068:\\ \;\;\;\;\sqrt[3]{1 + x} - \mathsf{expm1}\left(\mathsf{log1p}\left(\sqrt[3]{x}\right)\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\sqrt[3]{x}}{\frac{x}{0.3333333333333333}}\\ \end{array} \]
Alternative 5
Error0.7
Cost13384
\[\begin{array}{l} \mathbf{if}\;x \leq -216712653.40025404:\\ \;\;\;\;\frac{\sqrt[3]{x} \cdot 0.3333333333333333}{x}\\ \mathbf{elif}\;x \leq 747582.6933135068:\\ \;\;\;\;\sqrt[3]{1 + x} - \sqrt[3]{x}\\ \mathbf{else}:\\ \;\;\;\;\frac{\sqrt[3]{x}}{\frac{x}{0.3333333333333333}}\\ \end{array} \]
Alternative 6
Error1.6
Cost7112
\[\begin{array}{l} \mathbf{if}\;x \leq -216712653.40025404:\\ \;\;\;\;\frac{\sqrt[3]{x} \cdot 0.3333333333333333}{x}\\ \mathbf{elif}\;x \leq 7.357464671497419 \cdot 10^{-7}:\\ \;\;\;\;\left(1 + x \cdot 0.3333333333333333\right) - \sqrt[3]{x}\\ \mathbf{else}:\\ \;\;\;\;\frac{\sqrt[3]{x}}{\frac{x}{0.3333333333333333}}\\ \end{array} \]
Alternative 7
Error1.6
Cost7112
\[\begin{array}{l} \mathbf{if}\;x \leq -216712653.40025404:\\ \;\;\;\;\frac{\sqrt[3]{x} \cdot 0.3333333333333333}{x}\\ \mathbf{elif}\;x \leq 7.357464671497419 \cdot 10^{-7}:\\ \;\;\;\;1 + \left(x \cdot 0.3333333333333333 - \sqrt[3]{x}\right)\\ \mathbf{else}:\\ \;\;\;\;\frac{\sqrt[3]{x}}{\frac{x}{0.3333333333333333}}\\ \end{array} \]
Alternative 8
Error1.8
Cost6984
\[\begin{array}{l} t_0 := \frac{\sqrt[3]{x} \cdot 0.3333333333333333}{x}\\ \mathbf{if}\;x \leq -216712653.40025404:\\ \;\;\;\;t_0\\ \mathbf{elif}\;x \leq 7.357464671497419 \cdot 10^{-7}:\\ \;\;\;\;1 - \sqrt[3]{x}\\ \mathbf{else}:\\ \;\;\;\;t_0\\ \end{array} \]
Alternative 9
Error1.8
Cost6984
\[\begin{array}{l} \mathbf{if}\;x \leq -216712653.40025404:\\ \;\;\;\;\frac{\sqrt[3]{x} \cdot 0.3333333333333333}{x}\\ \mathbf{elif}\;x \leq 7.357464671497419 \cdot 10^{-7}:\\ \;\;\;\;1 - \sqrt[3]{x}\\ \mathbf{else}:\\ \;\;\;\;\sqrt[3]{x} \cdot \frac{0.3333333333333333}{x}\\ \end{array} \]
Alternative 10
Error1.8
Cost6984
\[\begin{array}{l} \mathbf{if}\;x \leq -216712653.40025404:\\ \;\;\;\;\frac{\sqrt[3]{x} \cdot 0.3333333333333333}{x}\\ \mathbf{elif}\;x \leq 7.357464671497419 \cdot 10^{-7}:\\ \;\;\;\;1 - \sqrt[3]{x}\\ \mathbf{else}:\\ \;\;\;\;\frac{\sqrt[3]{x}}{\frac{x}{0.3333333333333333}}\\ \end{array} \]
Alternative 11
Error17.3
Cost6788
\[\begin{array}{l} \mathbf{if}\;x \leq 7.357464671497419 \cdot 10^{-7}:\\ \;\;\;\;1 - \sqrt[3]{x}\\ \mathbf{else}:\\ \;\;\;\;0.3333333333333333 \cdot {x}^{-0.6666666666666666}\\ \end{array} \]
Alternative 12
Error31.1
Cost6592
\[1 - \sqrt[3]{x} \]
Alternative 13
Error31.6
Cost64
\[1 \]

Error

Reproduce

herbie shell --seed 2022300 
(FPCore (x)
  :name "2cbrt (problem 3.3.4)"
  :precision binary64
  (- (cbrt (+ x 1.0)) (cbrt x)))