Average Error: 0.0 → 0.0
Time: 19.1s
Precision: 64
\[-\log \left(\frac{1}{x} - 1\right)\]
↓
\[-\log \left(\left(\sqrt{\frac{1}{x}} + \sqrt{1}\right) \cdot \left(\sqrt{\frac{1}{x}} - \sqrt{1}\right)\right)\]
-\log \left(\frac{1}{x} - 1\right)
↓
-\log \left(\left(\sqrt{\frac{1}{x}} + \sqrt{1}\right) \cdot \left(\sqrt{\frac{1}{x}} - \sqrt{1}\right)\right)
double f(double x) {
        double r34378 = 1.0;
        double r34379 = x;
        double r34380 = r34378 / r34379;
        double r34381 = r34380 - r34378;
        double r34382 = log(r34381);
        double r34383 = -r34382;
        return r34383;
}
↓
double f(double x) {
        double r34384 = 1.0;
        double r34385 = x;
        double r34386 = r34384 / r34385;
        double r34387 = sqrt(r34386);
        double r34388 = sqrt(r34384);
        double r34389 = r34387 + r34388;
        double r34390 = r34387 - r34388;
        double r34391 = r34389 * r34390;
        double r34392 = log(r34391);
        double r34393 = -r34392;
        return r34393;
}

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

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

  4. Applied add-sqr-sqrt0.0

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

  5. Applied difference-of-squares0.0

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

  6. Final simplification0.0

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

Reproduce

herbie shell --seed 2019304 +o rules:numerics
(FPCore (x)
  :name "neg log"
  :precision binary64
  (- (log (- (/ 1 x) 1))))