Average Error: 0.1 → 0.4
Time: 17.1s
Precision: 64
\[\left(x \cdot y\right) \cdot \left(1 - y\right)\]
↓
\[\left(y \cdot x\right) \cdot 1 + \left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right) \cdot \left(-\left(y \cdot x\right) \cdot \sqrt[3]{y}\right)\]
\left(x \cdot y\right) \cdot \left(1 - y\right)
↓
\left(y \cdot x\right) \cdot 1 + \left(\sqrt[3]{y} \cdot \sqrt[3]{y}\right) \cdot \left(-\left(y \cdot x\right) \cdot \sqrt[3]{y}\right)
double f(double x, double y) {
        double r1832620 = x;
        double r1832621 = y;
        double r1832622 = r1832620 * r1832621;
        double r1832623 = 1.0;
        double r1832624 = r1832623 - r1832621;
        double r1832625 = r1832622 * r1832624;
        return r1832625;
}
↓
double f(double x, double y) {
        double r1832626 = y;
        double r1832627 = x;
        double r1832628 = r1832626 * r1832627;
        double r1832629 = 1.0;
        double r1832630 = r1832628 * r1832629;
        double r1832631 = cbrt(r1832626);
        double r1832632 = r1832631 * r1832631;
        double r1832633 = r1832628 * r1832631;
        double r1832634 = -r1832633;
        double r1832635 = r1832632 * r1832634;
        double r1832636 = r1832630 + r1832635;
        return r1832636;
}

Error

Bits error versus x

Bits error versus y

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Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.1

    \[\left(x \cdot y\right) \cdot \left(1 - y\right)\]
  2. Using strategy rm

  3. Applied sub-neg0.1

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

  4. Applied distribute-rgt-in0.1

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

  6. Applied add-cube-cbrt0.4

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

  7. Applied distribute-rgt-neg-in0.4

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

  8. Applied associate-*l*0.4

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

  9. Final simplification0.4

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

Reproduce

herbie shell --seed 2019172 
(FPCore (x y)
  :name "Statistics.Distribution.Binomial:$cvariance from math-functions-0.1.5.2"
  (* (* x y) (- 1.0 y)))