Average Error: 0.0 → 0.1
Time: 5.2s
Precision: 64
\[2 \cdot \left(x \cdot x - x \cdot y\right)\]
↓
\[x \cdot \left(\left(x - y\right) \cdot 2\right)\]
2 \cdot \left(x \cdot x - x \cdot y\right)
↓
x \cdot \left(\left(x - y\right) \cdot 2\right)
double f(double x, double y) {
        double r534420 = 2.0;
        double r534421 = x;
        double r534422 = r534421 * r534421;
        double r534423 = y;
        double r534424 = r534421 * r534423;
        double r534425 = r534422 - r534424;
        double r534426 = r534420 * r534425;
        return r534426;
}
↓
double f(double x, double y) {
        double r534427 = x;
        double r534428 = y;
        double r534429 = r534427 - r534428;
        double r534430 = 2.0;
        double r534431 = r534429 * r534430;
        double r534432 = r534427 * r534431;
        return r534432;
}

Error

Bits error versus x

Bits error versus y

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Target

Original0.0
Target0.0
Herbie0.1
\[\left(x \cdot 2\right) \cdot \left(x - y\right)\]

Derivation

  1. Initial program 0.0

    \[2 \cdot \left(x \cdot x - x \cdot y\right)\]

  2. Simplified0.0

    \[\leadsto \color{blue}{\left(x \cdot \left(x - y\right)\right) \cdot 2}\]

  3. Taylor expanded around 0 0.0

    \[\leadsto \color{blue}{2 \cdot {x}^{2} - 2 \cdot \left(x \cdot y\right)}\]

  4. Simplified0.1

    \[\leadsto \color{blue}{x \cdot \left(\left(x - y\right) \cdot 2\right)}\]

  5. Final simplification0.1

    \[\leadsto x \cdot \left(\left(x - y\right) \cdot 2\right)\]

Reproduce

herbie shell --seed 2020045 +o rules:numerics
(FPCore (x y)
  :name "Linear.Matrix:fromQuaternion from linear-1.19.1.3, A"
  :precision binary64

  :herbie-target
  (* (* x 2) (- x y))

  (* 2 (- (* x x) (* x y))))