neg log

Average Error: 0.0 → 0.0

Time: 4.1s

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 r5286 = 1.0;
        double r5287 = x;
        double r5288 = r5286 / r5287;
        double r5289 = r5288 - r5286;
        double r5290 = log(r5289);
        double r5291 = -r5290;
        return r5291;
}

↓

double f(double x) {
        double r5292 = 1.0;
        double r5293 = x;
        double r5294 = r5292 / r5293;
        double r5295 = r5294 - r5292;
        double r5296 = log(r5295);
        double r5297 = -r5296;
        return r5297;
}

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 2020046 +o rules:numerics
(FPCore (x)
  :name "neg log"
  :precision binary64
  (- (log (- (/ 1 x) 1))))