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

Average Error: 0.1 → 0.1

Time: 8.2s

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 r70077 = x;
        double r70078 = 1.0;
        double r70079 = y;
        double r70080 = r70077 * r70079;
        double r70081 = r70078 - r70080;
        double r70082 = r70077 * r70081;
        return r70082;
}

↓

double f(double x, double y) {
        double r70083 = x;
        double r70084 = 1.0;
        double r70085 = y;
        double r70086 = r70083 * r70085;
        double r70087 = r70084 - r70086;
        double r70088 = r70083 * r70087;
        return r70088;
}

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 2020045 +o rules:numerics
(FPCore (x y)
  :name "Numeric.SpecFunctions:log1p from math-functions-0.1.5.2, A"
  :precision binary64
  (* x (- 1 (* x y))))