Average Error: 0.1 → 0.1
Time: 15.9s
Precision: 64
\[\left(x \cdot y\right) \cdot \left(1 - y\right)\]
↓
\[\left(x \cdot y\right) \cdot \left(-y\right) + \left(x \cdot y\right) \cdot 1\]
\left(x \cdot y\right) \cdot \left(1 - y\right)
↓
\left(x \cdot y\right) \cdot \left(-y\right) + \left(x \cdot y\right) \cdot 1
double f(double x, double y) {
        double r1334015 = x;
        double r1334016 = y;
        double r1334017 = r1334015 * r1334016;
        double r1334018 = 1.0;
        double r1334019 = r1334018 - r1334016;
        double r1334020 = r1334017 * r1334019;
        return r1334020;
}
↓
double f(double x, double y) {
        double r1334021 = x;
        double r1334022 = y;
        double r1334023 = r1334021 * r1334022;
        double r1334024 = -r1334022;
        double r1334025 = r1334023 * r1334024;
        double r1334026 = 1.0;
        double r1334027 = r1334023 * r1334026;
        double r1334028 = r1334025 + r1334027;
        return r1334028;
}

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 sub-neg0.1

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

  4. Applied distribute-lft-in0.1

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

  5. Final simplification0.1

    \[\leadsto \left(x \cdot y\right) \cdot \left(-y\right) + \left(x \cdot y\right) \cdot 1\]

Reproduce

herbie shell --seed 2019169 +o rules:numerics
(FPCore (x y)
  :name "Statistics.Distribution.Binomial:$cvariance from math-functions-0.1.5.2"
  (* (* x y) (- 1.0 y)))