neg log

Average Error: 0.0 → 0.0

Time: 7.5s

Precision: 64

Math

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

↓

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

C

double f(double x) {
        double r17205 = 1.0;
        double r17206 = x;
        double r17207 = r17205 / r17206;
        double r17208 = r17207 - r17205;
        double r17209 = log(r17208);
        double r17210 = -r17209;
        return r17210;
}

↓

double f(double x) {
        double r17211 = 1.0;
        double r17212 = x;
        double r17213 = r17211 / r17212;
        double r17214 = r17213 - r17211;
        double r17215 = log(r17214);
        double r17216 = -r17215;
        return r17216;
}

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 2019291 
(FPCore (x)
  :name "neg log"
  :precision binary64
  (- (log (- (/ 1 x) 1))))