neg log

Average Error: 0.1 → 0.1

Time: 3.6s

Precision: 64

Math

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

↓

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

C

double f(double x) {
        double r8252 = 1.0;
        double r8253 = x;
        double r8254 = r8252 / r8253;
        double r8255 = r8254 - r8252;
        double r8256 = log(r8255);
        double r8257 = -r8256;
        return r8257;
}

↓

double f(double x) {
        double r8258 = 1.0;
        double r8259 = x;
        double r8260 = r8258 / r8259;
        double r8261 = r8260 - r8258;
        double r8262 = log(r8261);
        double r8263 = -r8262;
        return r8263;
}

Error

Bits error versus x

Derivation

1. Initial program 0.1

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

2. Final simplification 0.1

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

Reproduce

herbie shell --seed 2019174 +o rules:numerics
(FPCore (x)
  :name "neg log"
  (- (log (- (/ 1.0 x) 1.0))))