neg log

Average Error: 0.1 → 0.1

Time: 3.2s

Precision: 64

Math

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

↓

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

C

double f(double x) {
        double r8048 = 1.0;
        double r8049 = x;
        double r8050 = r8048 / r8049;
        double r8051 = r8050 - r8048;
        double r8052 = log(r8051);
        double r8053 = -r8052;
        return r8053;
}

↓

double f(double x) {
        double r8054 = 1.0;
        double r8055 = x;
        double r8056 = r8054 / r8055;
        double r8057 = r8056 - r8054;
        double r8058 = log(r8057);
        double r8059 = -r8058;
        return r8059;
}

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 
(FPCore (x)
  :name "neg log"
  (- (log (- (/ 1.0 x) 1.0))))