Average Error: 0.1 → 0.1
Time: 2.5s
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 r44389 = x;
        double r44390 = 1.0;
        double r44391 = y;
        double r44392 = r44389 * r44391;
        double r44393 = r44390 - r44392;
        double r44394 = r44389 * r44393;
        return r44394;
}
↓
double f(double x, double y) {
        double r44395 = x;
        double r44396 = 1.0;
        double r44397 = r44395 * r44396;
        double r44398 = y;
        double r44399 = r44395 * r44398;
        double r44400 = -r44399;
        double r44401 = r44395 * r44400;
        double r44402 = r44397 + r44401;
        return r44402;
}

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 2019347 +o rules:numerics
(FPCore (x y)
  :name "Numeric.SpecFunctions:log1p from math-functions-0.1.5.2, A"
  :precision binary64
  (* x (- 1 (* x y))))