Average Error: 29.5 → 0.6
Time: 40.7s
Precision: 64
\[\sqrt[3]{x + 1} - \sqrt[3]{x}\]
↓
\[\frac{1}{\sqrt[3]{x + 1} \cdot \sqrt[3]{x + 1} + \left(\sqrt[3]{x + 1} \cdot \sqrt[3]{x} + \sqrt[3]{\sqrt[3]{x} \cdot \sqrt[3]{x}} \cdot \left(\sqrt[3]{\sqrt[3]{x} \cdot \sqrt[3]{x}} \cdot \sqrt[3]{\sqrt[3]{x} \cdot \sqrt[3]{x}}\right)\right)}\]
\sqrt[3]{x + 1} - \sqrt[3]{x}
↓
\frac{1}{\sqrt[3]{x + 1} \cdot \sqrt[3]{x + 1} + \left(\sqrt[3]{x + 1} \cdot \sqrt[3]{x} + \sqrt[3]{\sqrt[3]{x} \cdot \sqrt[3]{x}} \cdot \left(\sqrt[3]{\sqrt[3]{x} \cdot \sqrt[3]{x}} \cdot \sqrt[3]{\sqrt[3]{x} \cdot \sqrt[3]{x}}\right)\right)}
double f(double x) {
        double r3251633 = x;
        double r3251634 = 1.0;
        double r3251635 = r3251633 + r3251634;
        double r3251636 = cbrt(r3251635);
        double r3251637 = cbrt(r3251633);
        double r3251638 = r3251636 - r3251637;
        return r3251638;
}
↓
double f(double x) {
        double r3251639 = 1.0;
        double r3251640 = x;
        double r3251641 = r3251640 + r3251639;
        double r3251642 = cbrt(r3251641);
        double r3251643 = r3251642 * r3251642;
        double r3251644 = cbrt(r3251640);
        double r3251645 = r3251642 * r3251644;
        double r3251646 = r3251644 * r3251644;
        double r3251647 = cbrt(r3251646);
        double r3251648 = r3251647 * r3251647;
        double r3251649 = r3251647 * r3251648;
        double r3251650 = r3251645 + r3251649;
        double r3251651 = r3251643 + r3251650;
        double r3251652 = r3251639 / r3251651;
        return r3251652;
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 29.5

    \[\sqrt[3]{x + 1} - \sqrt[3]{x}\]
  2. Using strategy rm

  3. Applied flip3--29.5

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

  4. Taylor expanded around -inf 0.5

    \[\leadsto \frac{\color{blue}{1}}{\sqrt[3]{x + 1} \cdot \sqrt[3]{x + 1} + \left(\sqrt[3]{x} \cdot \sqrt[3]{x} + \sqrt[3]{x + 1} \cdot \sqrt[3]{x}\right)}\]
  5. Using strategy rm

  6. Applied add-cube-cbrt0.6

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

  7. Final simplification0.6

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

Reproduce

herbie shell --seed 2019112 
(FPCore (x)
  :name "2cbrt (problem 3.3.4)"
  (- (cbrt (+ x 1)) (cbrt x)))