Average Error: 0.1 → 0.1
Time: 13.5s
Precision: 64
\[x \cdot \left(1.0 - x \cdot y\right)\]
↓
\[\left(1.0 - x \cdot y\right) \cdot x\]
x \cdot \left(1.0 - x \cdot y\right)
↓
\left(1.0 - x \cdot y\right) \cdot x
double f(double x, double y) {
        double r3287184 = x;
        double r3287185 = 1.0;
        double r3287186 = y;
        double r3287187 = r3287184 * r3287186;
        double r3287188 = r3287185 - r3287187;
        double r3287189 = r3287184 * r3287188;
        return r3287189;
}
↓
double f(double x, double y) {
        double r3287190 = 1.0;
        double r3287191 = x;
        double r3287192 = y;
        double r3287193 = r3287191 * r3287192;
        double r3287194 = r3287190 - r3287193;
        double r3287195 = r3287194 * r3287191;
        return r3287195;
}

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

    \[x \cdot \left(1.0 - x \cdot y\right)\]

  2. Final simplification0.1

    \[\leadsto \left(1.0 - x \cdot y\right) \cdot x\]

Reproduce

herbie shell --seed 2019163 +o rules:numerics
(FPCore (x y)
  :name "Numeric.SpecFunctions:log1p from math-functions-0.1.5.2, A"
  (* x (- 1.0 (* x y))))