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 r49632 = x;
        double r49633 = 1.0;
        double r49634 = y;
        double r49635 = r49632 * r49634;
        double r49636 = r49633 - r49635;
        double r49637 = r49632 * r49636;
        return r49637;
}

↓

double f(double x, double y) {
        double r49638 = x;
        double r49639 = 1.0;
        double r49640 = y;
        double r49641 = r49638 * r49640;
        double r49642 = r49639 - r49641;
        double r49643 = r49638 * r49642;
        return r49643;
}

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