Average Error: 0.1 → 0.4
Time: 19.9s
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 r1058571 = x;
        double r1058572 = y;
        double r1058573 = r1058571 * r1058572;
        double r1058574 = 1.0;
        double r1058575 = r1058574 - r1058572;
        double r1058576 = r1058573 * r1058575;
        return r1058576;
}
↓
double f(double x, double y) {
        double r1058577 = y;
        double r1058578 = x;
        double r1058579 = r1058577 * r1058578;
        double r1058580 = 1.0;
        double r1058581 = r1058579 * r1058580;
        double r1058582 = cbrt(r1058577);
        double r1058583 = r1058582 * r1058582;
        double r1058584 = r1058579 * r1058582;
        double r1058585 = -r1058584;
        double r1058586 = r1058583 * r1058585;
        double r1058587 = r1058581 + r1058586;
        return r1058587;
}

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 +o rules:numerics
(FPCore (x y)
  :name "Statistics.Distribution.Binomial:$cvariance from math-functions-0.1.5.2"
  (* (* x y) (- 1.0 y)))