Average Error: 0.1 → 0.1
Time: 3.0s
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 r77473 = x;
        double r77474 = 1.0;
        double r77475 = y;
        double r77476 = r77473 * r77475;
        double r77477 = r77474 - r77476;
        double r77478 = r77473 * r77477;
        return r77478;
}
↓
double f(double x, double y) {
        double r77479 = x;
        double r77480 = 1.0;
        double r77481 = r77479 * r77480;
        double r77482 = y;
        double r77483 = r77479 * r77482;
        double r77484 = -r77483;
        double r77485 = r77479 * r77484;
        double r77486 = r77481 + r77485;
        return r77486;
}

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 2020047 
(FPCore (x y)
  :name "Numeric.SpecFunctions:log1p from math-functions-0.1.5.2, A"
  :precision binary64
  (* x (- 1 (* x y))))