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 r54997 = x;
        double r54998 = 1.0;
        double r54999 = y;
        double r55000 = r54997 * r54999;
        double r55001 = r54998 - r55000;
        double r55002 = r54997 * r55001;
        return r55002;
}
↓
double f(double x, double y) {
        double r55003 = x;
        double r55004 = 1.0;
        double r55005 = r55003 * r55004;
        double r55006 = y;
        double r55007 = r55003 * r55006;
        double r55008 = -r55007;
        double r55009 = r55003 * r55008;
        double r55010 = r55005 + r55009;
        return r55010;
}

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 2020049 
(FPCore (x y)
  :name "Numeric.SpecFunctions:log1p from math-functions-0.1.5.2, A"
  :precision binary64
  (* x (- 1 (* x y))))