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

Average Error: 0.1 → 0.1

Time: 9.5s

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 r82056 = x;
        double r82057 = 1.0;
        double r82058 = y;
        double r82059 = r82056 * r82058;
        double r82060 = r82057 - r82059;
        double r82061 = r82056 * r82060;
        return r82061;
}

↓

double f(double x, double y) {
        double r82062 = x;
        double r82063 = 1.0;
        double r82064 = y;
        double r82065 = r82062 * r82064;
        double r82066 = r82063 - r82065;
        double r82067 = r82062 * r82066;
        return r82067;
}

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 2019350 
(FPCore (x y)
  :name "Numeric.SpecFunctions:log1p from math-functions-0.1.5.2, A"
  :precision binary64
  (* x (- 1 (* x y))))