neg log

Average Error: 0.0 → 0.0

Time: 12.5s

Precision: 64

Math

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

↓

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

C

double f(double x) {
        double r243672 = 1.0;
        double r243673 = x;
        double r243674 = r243672 / r243673;
        double r243675 = r243674 - r243672;
        double r243676 = log(r243675);
        double r243677 = -r243676;
        return r243677;
}

↓

double f(double x) {
        double r243678 = 1.0;
        double r243679 = x;
        double r243680 = r243678 / r243679;
        double r243681 = r243680 - r243678;
        double r243682 = log(r243681);
        double r243683 = -r243682;
        return r243683;
}

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 2019162 +o rules:numerics
(FPCore (x)
  :name "neg log"
  (- (log (- (/ 1 x) 1))))