Average Error: 0.0 → 0.0
Time: 3.3s
Precision: 64
\[-\log \left(\frac{1}{x} - 1\right)\]
↓
\[-\left(\log \left(\left|\sqrt[3]{\frac{1}{x} - 1}\right| \cdot \sqrt{\sqrt[3]{\frac{1}{x} - 1}}\right) + \log \left(\sqrt{\frac{1}{x} - 1}\right)\right)\]
-\log \left(\frac{1}{x} - 1\right)
↓
-\left(\log \left(\left|\sqrt[3]{\frac{1}{x} - 1}\right| \cdot \sqrt{\sqrt[3]{\frac{1}{x} - 1}}\right) + \log \left(\sqrt{\frac{1}{x} - 1}\right)\right)
double f(double x) {
        double r29176 = 1.0;
        double r29177 = x;
        double r29178 = r29176 / r29177;
        double r29179 = r29178 - r29176;
        double r29180 = log(r29179);
        double r29181 = -r29180;
        return r29181;
}
↓
double f(double x) {
        double r29182 = 1.0;
        double r29183 = x;
        double r29184 = r29182 / r29183;
        double r29185 = r29184 - r29182;
        double r29186 = cbrt(r29185);
        double r29187 = fabs(r29186);
        double r29188 = sqrt(r29186);
        double r29189 = r29187 * r29188;
        double r29190 = log(r29189);
        double r29191 = sqrt(r29185);
        double r29192 = log(r29191);
        double r29193 = r29190 + r29192;
        double r29194 = -r29193;
        return r29194;
}

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. Applied log-prod0.0

    \[\leadsto -\color{blue}{\left(\log \left(\sqrt{\frac{1}{x} - 1}\right) + \log \left(\sqrt{\frac{1}{x} - 1}\right)\right)}\]
  5. Using strategy rm

  6. Applied add-cube-cbrt0.0

    \[\leadsto -\left(\log \left(\sqrt{\color{blue}{\left(\sqrt[3]{\frac{1}{x} - 1} \cdot \sqrt[3]{\frac{1}{x} - 1}\right) \cdot \sqrt[3]{\frac{1}{x} - 1}}}\right) + \log \left(\sqrt{\frac{1}{x} - 1}\right)\right)\]

  7. Applied sqrt-prod0.0

    \[\leadsto -\left(\log \color{blue}{\left(\sqrt{\sqrt[3]{\frac{1}{x} - 1} \cdot \sqrt[3]{\frac{1}{x} - 1}} \cdot \sqrt{\sqrt[3]{\frac{1}{x} - 1}}\right)} + \log \left(\sqrt{\frac{1}{x} - 1}\right)\right)\]

  8. Simplified0.0

    \[\leadsto -\left(\log \left(\color{blue}{\left|\sqrt[3]{\frac{1}{x} - 1}\right|} \cdot \sqrt{\sqrt[3]{\frac{1}{x} - 1}}\right) + \log \left(\sqrt{\frac{1}{x} - 1}\right)\right)\]

  9. Final simplification0.0

    \[\leadsto -\left(\log \left(\left|\sqrt[3]{\frac{1}{x} - 1}\right| \cdot \sqrt{\sqrt[3]{\frac{1}{x} - 1}}\right) + \log \left(\sqrt{\frac{1}{x} - 1}\right)\right)\]

Reproduce

herbie shell --seed 2019353 
(FPCore (x)
  :name "neg log"
  :precision binary64
  (- (log (- (/ 1 x) 1))))