Average Error: 0.1 → 0.1
Time: 12.9s
Precision: 64
\[\frac{x + y}{x - y} - 3 \cdot x\]
\[\sqrt[3]{{\left(\frac{x + y}{x - y}\right)}^{3}} - 3 \cdot x\]
\frac{x + y}{x - y} - 3 \cdot x
\sqrt[3]{{\left(\frac{x + y}{x - y}\right)}^{3}} - 3 \cdot x
double f(double x, double y) {
        double r3476647 = x;
        double r3476648 = y;
        double r3476649 = r3476647 + r3476648;
        double r3476650 = r3476647 - r3476648;
        double r3476651 = r3476649 / r3476650;
        double r3476652 = 3.0;
        double r3476653 = r3476652 * r3476647;
        double r3476654 = r3476651 - r3476653;
        return r3476654;
}

double f(double x, double y) {
        double r3476655 = x;
        double r3476656 = y;
        double r3476657 = r3476655 + r3476656;
        double r3476658 = r3476655 - r3476656;
        double r3476659 = r3476657 / r3476658;
        double r3476660 = 3.0;
        double r3476661 = pow(r3476659, r3476660);
        double r3476662 = cbrt(r3476661);
        double r3476663 = 3.0;
        double r3476664 = r3476663 * r3476655;
        double r3476665 = r3476662 - r3476664;
        return r3476665;
}

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 0.1

    \[\frac{x + y}{x - y} - 3 \cdot x\]
  2. Using strategy rm
  3. Applied add-cbrt-cube17.4

    \[\leadsto \frac{x + y}{\color{blue}{\sqrt[3]{\left(\left(x - y\right) \cdot \left(x - y\right)\right) \cdot \left(x - y\right)}}} - 3 \cdot x\]
  4. Applied add-cbrt-cube42.4

    \[\leadsto \frac{\color{blue}{\sqrt[3]{\left(\left(x + y\right) \cdot \left(x + y\right)\right) \cdot \left(x + y\right)}}}{\sqrt[3]{\left(\left(x - y\right) \cdot \left(x - y\right)\right) \cdot \left(x - y\right)}} - 3 \cdot x\]
  5. Applied cbrt-undiv42.4

    \[\leadsto \color{blue}{\sqrt[3]{\frac{\left(\left(x + y\right) \cdot \left(x + y\right)\right) \cdot \left(x + y\right)}{\left(\left(x - y\right) \cdot \left(x - y\right)\right) \cdot \left(x - y\right)}}} - 3 \cdot x\]
  6. Simplified0.1

    \[\leadsto \sqrt[3]{\color{blue}{{\left(\frac{x + y}{x - y}\right)}^{3}}} - 3 \cdot x\]
  7. Final simplification0.1

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

Reproduce

herbie shell --seed 1 
(FPCore (x y)
  :name "(x+y)/(x-y) - 3*x"
  :precision binary64
  (- (/ (+ x y) (- x y)) (* 3 x)))