neg log

Average Error: 0.0 → 0.0

Time: 5.2s

Precision: 64

Math

\[-\log \left(\frac{1}{x} - 1\right)\]

↓

\[-\log \left(\frac{1}{x} - 1\right)\]

C

double f(double x) {
        double r36787 = 1.0;
        double r36788 = x;
        double r36789 = r36787 / r36788;
        double r36790 = r36789 - r36787;
        double r36791 = log(r36790);
        double r36792 = -r36791;
        return r36792;
}

↓

double f(double x) {
        double r36793 = 1.0;
        double r36794 = x;
        double r36795 = r36793 / r36794;
        double r36796 = r36795 - r36793;
        double r36797 = log(r36796);
        double r36798 = -r36797;
        return r36798;
}

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 2019128 +o rules:numerics
(FPCore (x)
  :name "neg log"
  (- (log (- (/ 1 x) 1))))