Numeric.Log:$clog1p from log-domain-0.10.2.1, B

Average Error: 0.2 → 0.2

Time: 4.5s

Precision: 64

Math

\[\frac{x}{1 + \sqrt{x + 1}}\]

↓

\[\frac{x}{1 + \sqrt{x + 1}}\]

C

double f(double x) {
        double r119020 = x;
        double r119021 = 1.0;
        double r119022 = r119020 + r119021;
        double r119023 = sqrt(r119022);
        double r119024 = r119021 + r119023;
        double r119025 = r119020 / r119024;
        return r119025;
}

↓

double f(double x) {
        double r119026 = x;
        double r119027 = 1.0;
        double r119028 = r119026 + r119027;
        double r119029 = sqrt(r119028);
        double r119030 = r119027 + r119029;
        double r119031 = r119026 / r119030;
        return r119031;
}

Error

Bits error versus x

Derivation

1. Initial program 0.2

   \[\frac{x}{1 + \sqrt{x + 1}}\]

2. Final simplification 0.2

   \[\leadsto \frac{x}{1 + \sqrt{x + 1}}\]

Reproduce

herbie shell --seed 2020046 +o rules:numerics
(FPCore (x)
  :name "Numeric.Log:$clog1p from log-domain-0.10.2.1, B"
  :precision binary64
  (/ x (+ 1 (sqrt (+ x 1)))))