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

Average Error: 0.1 → 0.1

Time: 10.3s

Precision: 64

• Falling back on racket egraph because egg-herbie package not installed

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 r56909 = x;
        double r56910 = 1.0;
        double r56911 = y;
        double r56912 = r56909 * r56911;
        double r56913 = r56910 - r56912;
        double r56914 = r56909 * r56913;
        return r56914;
}

↓

double f(double x, double y) {
        double r56915 = x;
        double r56916 = 1.0;
        double r56917 = y;
        double r56918 = r56915 * r56917;
        double r56919 = r56916 - r56918;
        double r56920 = r56915 * r56919;
        return r56920;
}

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 2020042 +o rules:numerics
(FPCore (x y)
  :name "Numeric.SpecFunctions:log1p from math-functions-0.1.5.2, A"
  :precision binary64
  (* x (- 1 (* x y))))