Numeric.SpecFunctions:log1p from math-functions-0.1.5.2, A

Average Error: 0.1 → 0.1

Time: 15.4s

Precision: 64

Math

\[x \cdot \left(1 - x \cdot y\right)\]

↓

\[x \cdot \left(1 - x \cdot y\right)\]

C

double f(double x, double y) {
        double r5308980 = x;
        double r5308981 = 1.0;
        double r5308982 = y;
        double r5308983 = r5308980 * r5308982;
        double r5308984 = r5308981 - r5308983;
        double r5308985 = r5308980 * r5308984;
        return r5308985;
}

↓

double f(double x, double y) {
        double r5308986 = x;
        double r5308987 = 1.0;
        double r5308988 = y;
        double r5308989 = r5308986 * r5308988;
        double r5308990 = r5308987 - r5308989;
        double r5308991 = r5308986 * r5308990;
        return r5308991;
}

Error

Bits error versus x

Bits error versus y

Derivation

1. Initial program 0.1

   \[x \cdot \left(1 - x \cdot y\right)\]

2. Final simplification 0.1

   \[\leadsto x \cdot \left(1 - x \cdot y\right)\]

Reproduce

herbie shell --seed 2019174 +o rules:numerics
(FPCore (x y)
  :name "Numeric.SpecFunctions:log1p from math-functions-0.1.5.2, A"
  (* x (- 1.0 (* x y))))