Average Error: 0.0 → 0.0
Time: 2.4s
Precision: 64
\[-\log \left(\frac{1}{x} - 1\right)\]
↓
\[-\log \left(\sqrt{\frac{1}{x} - 1} \cdot \sqrt{\frac{1}{x} - 1}\right)\]
-\log \left(\frac{1}{x} - 1\right)
↓
-\log \left(\sqrt{\frac{1}{x} - 1} \cdot \sqrt{\frac{1}{x} - 1}\right)
double f(double x) {
        double r9583 = 1.0;
        double r9584 = x;
        double r9585 = r9583 / r9584;
        double r9586 = r9585 - r9583;
        double r9587 = log(r9586);
        double r9588 = -r9587;
        return r9588;
}
↓
double f(double x) {
        double r9589 = 1.0;
        double r9590 = x;
        double r9591 = r9589 / r9590;
        double r9592 = r9591 - r9589;
        double r9593 = sqrt(r9592);
        double r9594 = r9593 * r9593;
        double r9595 = log(r9594);
        double r9596 = -r9595;
        return r9596;
}

Error

Bits error versus x

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.0

    \[-\log \left(\frac{1}{x} - 1\right)\]
  2. Using strategy rm

  3. Applied add-sqr-sqrt0.0

    \[\leadsto -\log \color{blue}{\left(\sqrt{\frac{1}{x} - 1} \cdot \sqrt{\frac{1}{x} - 1}\right)}\]

  4. Final simplification0.0

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

Reproduce

herbie shell --seed 2020027 +o rules:numerics
(FPCore (x)
  :name "neg log"
  :precision binary64
  (- (log (- (/ 1 x) 1))))