Average Error: 0.1 → 0.1
Time: 11.3s
Precision: 64
\[\left(x \cdot y\right) \cdot \left(1 - y\right)\]
↓
\[y \cdot \left(x \cdot \left({\left(\sqrt[3]{1}\right)}^{3} - y\right)\right) + \left(\left(y - y\right) \cdot x\right) \cdot y\]
\left(x \cdot y\right) \cdot \left(1 - y\right)
↓
y \cdot \left(x \cdot \left({\left(\sqrt[3]{1}\right)}^{3} - y\right)\right) + \left(\left(y - y\right) \cdot x\right) \cdot y
double f(double x, double y) {
        double r17582 = x;
        double r17583 = y;
        double r17584 = r17582 * r17583;
        double r17585 = 1.0;
        double r17586 = r17585 - r17583;
        double r17587 = r17584 * r17586;
        return r17587;
}
↓
double f(double x, double y) {
        double r17588 = y;
        double r17589 = x;
        double r17590 = 1.0;
        double r17591 = cbrt(r17590);
        double r17592 = 3.0;
        double r17593 = pow(r17591, r17592);
        double r17594 = r17593 - r17588;
        double r17595 = r17589 * r17594;
        double r17596 = r17588 * r17595;
        double r17597 = r17588 - r17588;
        double r17598 = r17597 * r17589;
        double r17599 = r17598 * r17588;
        double r17600 = r17596 + r17599;
        return r17600;
}

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

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

  3. Applied add-cube-cbrt0.4

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

  4. Applied add-cube-cbrt0.4

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

  5. Applied prod-diff0.4

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

  6. Applied distribute-lft-in0.4

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

  7. Simplified0.1

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

  8. Simplified0.1

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

  9. Final simplification0.1

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

Reproduce

herbie shell --seed 2020043 +o rules:numerics
(FPCore (x y)
  :name "Statistics.Distribution.Binomial:$cvariance from math-functions-0.1.5.2"
  :precision binary64
  (* (* x y) (- 1 y)))