Average Error: 0.0 → 0.0
Time: 17.5s
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 r32527 = 1.0;
        double r32528 = x;
        double r32529 = r32527 / r32528;
        double r32530 = r32529 - r32527;
        double r32531 = log(r32530);
        double r32532 = -r32531;
        return r32532;
}
↓
double f(double x) {
        double r32533 = 1.0;
        double r32534 = x;
        double r32535 = r32533 / r32534;
        double r32536 = sqrt(r32535);
        double r32537 = sqrt(r32533);
        double r32538 = r32536 + r32537;
        double r32539 = r32536 - r32537;
        double r32540 = r32538 * r32539;
        double r32541 = log(r32540);
        double r32542 = -r32541;
        return r32542;
}

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