Average Error: 0.1 → 0.1
Time: 2.3s
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 r71088 = x;
        double r71089 = 1.0;
        double r71090 = y;
        double r71091 = r71088 * r71090;
        double r71092 = r71089 - r71091;
        double r71093 = r71088 * r71092;
        return r71093;
}
↓
double f(double x, double y) {
        double r71094 = x;
        double r71095 = 1.0;
        double r71096 = r71094 * r71095;
        double r71097 = y;
        double r71098 = r71094 * r71097;
        double r71099 = -r71098;
        double r71100 = r71094 * r71099;
        double r71101 = r71096 + r71100;
        return r71101;
}

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 2020002 +o rules:numerics
(FPCore (x y)
  :name "Numeric.SpecFunctions:log1p from math-functions-0.1.5.2, A"
  :precision binary64
  (* x (- 1 (* x y))))