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

Average Error: 0.1 → 0.1

Time: 11.5s

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 r96306 = x;
        double r96307 = 1.0;
        double r96308 = y;
        double r96309 = r96306 * r96308;
        double r96310 = r96307 - r96309;
        double r96311 = r96306 * r96310;
        return r96311;
}

↓

double f(double x, double y) {
        double r96312 = x;
        double r96313 = 1.0;
        double r96314 = y;
        double r96315 = r96312 * r96314;
        double r96316 = r96313 - r96315;
        double r96317 = r96312 * r96316;
        return r96317;
}

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