Average Error: 0.1 → 0.1
Time: 2.6s
Precision: 64
\[x \cdot \left(1 - x \cdot y\right)\]
↓
\[x \cdot 1 + x \cdot \left(-x \cdot y\right)\]
x \cdot \left(1 - x \cdot y\right)
↓
x \cdot 1 + x \cdot \left(-x \cdot y\right)
double f(double x, double y) {
        double r54406 = x;
        double r54407 = 1.0;
        double r54408 = y;
        double r54409 = r54406 * r54408;
        double r54410 = r54407 - r54409;
        double r54411 = r54406 * r54410;
        return r54411;
}
↓
double f(double x, double y) {
        double r54412 = x;
        double r54413 = 1.0;
        double r54414 = r54412 * r54413;
        double r54415 = y;
        double r54416 = r54412 * r54415;
        double r54417 = -r54416;
        double r54418 = r54412 * r54417;
        double r54419 = r54414 + r54418;
        return r54419;
}

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

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

  3. Applied sub-neg0.1

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

  4. Applied distribute-lft-in0.1

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

  5. Final simplification0.1

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

Reproduce

herbie shell --seed 2020062 +o rules:numerics
(FPCore (x y)
  :name "Numeric.SpecFunctions:log1p from math-functions-0.1.5.2, A"
  :precision binary64
  (* x (- 1 (* x y))))