neg log

Average Error: 0.0 → 0.0

Time: 6.0s

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 r6533 = 1.0;
        double r6534 = x;
        double r6535 = r6533 / r6534;
        double r6536 = r6535 - r6533;
        double r6537 = log(r6536);
        double r6538 = -r6537;
        return r6538;
}

↓

double f(double x) {
        double r6539 = 1.0;
        double r6540 = x;
        double r6541 = r6539 / r6540;
        double r6542 = r6541 - r6539;
        double r6543 = log(r6542);
        double r6544 = -r6543;
        return r6544;
}

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 2019350 
(FPCore (x)
  :name "neg log"
  :precision binary64
  (- (log (- (/ 1 x) 1))))