neg log

Average Error: 0.0 → 0.0

Time: 4.3s

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 r7250 = 1.0;
        double r7251 = x;
        double r7252 = r7250 / r7251;
        double r7253 = r7252 - r7250;
        double r7254 = log(r7253);
        double r7255 = -r7254;
        return r7255;
}

↓

double f(double x) {
        double r7256 = 1.0;
        double r7257 = x;
        double r7258 = r7256 / r7257;
        double r7259 = r7258 - r7256;
        double r7260 = log(r7259);
        double r7261 = -r7260;
        return r7261;
}

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 2019351 
(FPCore (x)
  :name "neg log"
  :precision binary64
  (- (log (- (/ 1 x) 1))))