Average Error: 29.2 → 28.6
Time: 22.3s
Precision: 64
\[\left(\sqrt{x - y} - \sqrt{x}\right) - \sqrt{-y}\]
\[\left(\sqrt[3]{\frac{-y}{\sqrt{x - y} + \sqrt{x}}} \cdot \sqrt[3]{\frac{-y}{\sqrt{x - y} + \sqrt{x}}}\right) \cdot \sqrt[3]{\frac{-y}{\sqrt{x - y} + \sqrt{x}}} - \sqrt{-y}\]
\left(\sqrt{x - y} - \sqrt{x}\right) - \sqrt{-y}
\left(\sqrt[3]{\frac{-y}{\sqrt{x - y} + \sqrt{x}}} \cdot \sqrt[3]{\frac{-y}{\sqrt{x - y} + \sqrt{x}}}\right) \cdot \sqrt[3]{\frac{-y}{\sqrt{x - y} + \sqrt{x}}} - \sqrt{-y}
double f(double x, double y) {
        double r1661604 = x;
        double r1661605 = y;
        double r1661606 = r1661604 - r1661605;
        double r1661607 = sqrt(r1661606);
        double r1661608 = sqrt(r1661604);
        double r1661609 = r1661607 - r1661608;
        double r1661610 = -r1661605;
        double r1661611 = sqrt(r1661610);
        double r1661612 = r1661609 - r1661611;
        return r1661612;
}

double f(double x, double y) {
        double r1661613 = y;
        double r1661614 = -r1661613;
        double r1661615 = x;
        double r1661616 = r1661615 - r1661613;
        double r1661617 = sqrt(r1661616);
        double r1661618 = sqrt(r1661615);
        double r1661619 = r1661617 + r1661618;
        double r1661620 = r1661614 / r1661619;
        double r1661621 = cbrt(r1661620);
        double r1661622 = r1661621 * r1661621;
        double r1661623 = r1661622 * r1661621;
        double r1661624 = sqrt(r1661614);
        double r1661625 = r1661623 - r1661624;
        return r1661625;
}

Error

Bits error versus x

Bits error versus y

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 29.2

    \[\left(\sqrt{x - y} - \sqrt{x}\right) - \sqrt{-y}\]
  2. Using strategy rm
  3. Applied flip--29.2

    \[\leadsto \color{blue}{\frac{\sqrt{x - y} \cdot \sqrt{x - y} - \sqrt{x} \cdot \sqrt{x}}{\sqrt{x - y} + \sqrt{x}}} - \sqrt{-y}\]
  4. Simplified28.6

    \[\leadsto \frac{\color{blue}{\left(-y\right) + 0}}{\sqrt{x - y} + \sqrt{x}} - \sqrt{-y}\]
  5. Using strategy rm
  6. Applied add-cube-cbrt28.6

    \[\leadsto \color{blue}{\left(\sqrt[3]{\frac{\left(-y\right) + 0}{\sqrt{x - y} + \sqrt{x}}} \cdot \sqrt[3]{\frac{\left(-y\right) + 0}{\sqrt{x - y} + \sqrt{x}}}\right) \cdot \sqrt[3]{\frac{\left(-y\right) + 0}{\sqrt{x - y} + \sqrt{x}}}} - \sqrt{-y}\]
  7. Simplified28.6

    \[\leadsto \color{blue}{\left(\sqrt[3]{\frac{-y}{\sqrt{x - y} + \sqrt{x}}} \cdot \sqrt[3]{\frac{-y}{\sqrt{x - y} + \sqrt{x}}}\right)} \cdot \sqrt[3]{\frac{\left(-y\right) + 0}{\sqrt{x - y} + \sqrt{x}}} - \sqrt{-y}\]
  8. Simplified28.6

    \[\leadsto \left(\sqrt[3]{\frac{-y}{\sqrt{x - y} + \sqrt{x}}} \cdot \sqrt[3]{\frac{-y}{\sqrt{x - y} + \sqrt{x}}}\right) \cdot \color{blue}{\sqrt[3]{\frac{-y}{\sqrt{x - y} + \sqrt{x}}}} - \sqrt{-y}\]
  9. Final simplification28.6

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

Reproduce

herbie shell --seed 1 
(FPCore (x y)
  :name "sqrt(x-y)-sqrt(x)-sqrt(-y)"
  :precision binary64
  (- (- (sqrt (- x y)) (sqrt x)) (sqrt (- y))))