neg log

Average Error: 0.0 → 0.0

Time: 1.2s

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 r1419 = 1.0;
        double r1420 = x;
        double r1421 = r1419 / r1420;
        double r1422 = r1421 - r1419;
        double r1423 = log(r1422);
        double r1424 = -r1423;
        return r1424;
}

↓

double f(double x) {
        double r1425 = 1.0;
        double r1426 = x;
        double r1427 = r1425 / r1426;
        double r1428 = r1427 - r1425;
        double r1429 = log(r1428);
        double r1430 = -r1429;
        return r1430;
}

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 
(FPCore (x)
  :name "neg log"
  :precision binary64
  (- (log (- (/ 1 x) 1))))