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 r88816 = x;
        double r88817 = 1.0;
        double r88818 = y;
        double r88819 = r88816 * r88818;
        double r88820 = r88817 - r88819;
        double r88821 = r88816 * r88820;
        return r88821;
}
↓
double f(double x, double y) {
        double r88822 = x;
        double r88823 = 1.0;
        double r88824 = r88822 * r88823;
        double r88825 = y;
        double r88826 = r88822 * r88825;
        double r88827 = -r88826;
        double r88828 = r88822 * r88827;
        double r88829 = r88824 + r88828;
        return r88829;
}

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 2020025 
(FPCore (x y)
  :name "Numeric.SpecFunctions:log1p from math-functions-0.1.5.2, A"
  :precision binary64
  (* x (- 1 (* x y))))