neg log

Average Error: 0.0 → 0.0

Time: 1.1s

Precision: 64

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

Math

\[-\log \left(\frac{1}{x} - 1\right)\]

↓

\[-\log \left(\frac{1}{x} - 1\right)\]

C

double f(double x) {
        double r1423 = 1.0;
        double r1424 = x;
        double r1425 = r1423 / r1424;
        double r1426 = r1425 - r1423;
        double r1427 = log(r1426);
        double r1428 = -r1427;
        return r1428;
}

↓

double f(double x) {
        double r1429 = 1.0;
        double r1430 = x;
        double r1431 = r1429 / r1430;
        double r1432 = r1431 - r1429;
        double r1433 = log(r1432);
        double r1434 = -r1433;
        return r1434;
}

Error

Bits error versus x

Derivation

1. Initial program 0.0

   \[-\log \left(\frac{1}{x} - 1\right)\]

2. Final simplification 0.0

   \[\leadsto -\log \left(\frac{1}{x} - 1\right)\]

Reproduce

herbie shell --seed 2020047 +o rules:numerics
(FPCore (x)
  :name "neg log"
  :precision binary64
  (- (log (- (/ 1 x) 1))))