neg log

Average Error: 0.0 → 0.0

Time: 4.4s

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 r5709 = 1.0;
        double r5710 = x;
        double r5711 = r5709 / r5710;
        double r5712 = r5711 - r5709;
        double r5713 = log(r5712);
        double r5714 = -r5713;
        return r5714;
}

↓

double f(double x) {
        double r5715 = 1.0;
        double r5716 = x;
        double r5717 = r5715 / r5716;
        double r5718 = r5717 - r5715;
        double r5719 = log(r5718);
        double r5720 = -r5719;
        return r5720;
}

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