Numeric.Integration.TanhSinh:nonNegative from integration-0.2.1

Average Error: 0.0 → 0.1

Time: 9.2s

Precision: 64

• Falling back on racket egraph because egg-herbie package not installed

Math

\[\frac{x}{1 - x}\]

↓

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

C

double f(double x) {
        double r112611 = x;
        double r112612 = 1.0;
        double r112613 = r112612 - r112611;
        double r112614 = r112611 / r112613;
        return r112614;
}

↓

double f(double x) {
        double r112615 = 1.0;
        double r112616 = 1.0;
        double r112617 = x;
        double r112618 = r112616 / r112617;
        double r112619 = -1.0;
        double r112620 = r112618 + r112619;
        double r112621 = r112615 / r112620;
        return r112621;
}

Error

Bits error versus x

Derivation

1. Initial program 0.0

   \[\frac{x}{1 - x}\]
2. Using strategy rm

3. Applied clear-num 0.1

   \[\leadsto \color{blue}{\frac{1}{\frac{1 - x}{x}}}\]

4. Simplified 0.1

   \[\leadsto \frac{1}{\color{blue}{\frac{1}{x} + -1}}\]

5. Final simplification 0.1

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

Reproduce

herbie shell --seed 2020043 +o rules:numerics
(FPCore (x)
  :name "Numeric.Integration.TanhSinh:nonNegative from integration-0.2.1"
  :precision binary64
  (/ x (- 1 x)))