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

Average Error: 0.1 → 0.1

Time: 9.1s

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 r92509 = x;
        double r92510 = 1.0;
        double r92511 = y;
        double r92512 = r92509 * r92511;
        double r92513 = r92510 - r92512;
        double r92514 = r92509 * r92513;
        return r92514;
}

↓

double f(double x, double y) {
        double r92515 = x;
        double r92516 = 1.0;
        double r92517 = y;
        double r92518 = r92515 * r92517;
        double r92519 = r92516 - r92518;
        double r92520 = r92515 * r92519;
        return r92520;
}

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 2020047 
(FPCore (x y)
  :name "Numeric.SpecFunctions:log1p from math-functions-0.1.5.2, A"
  :precision binary64
  (* x (- 1 (* x y))))