Average Error: 0.0 → 0.0
Time: 5.6s
Precision: 64
\[-\log \left(\frac{1}{x} - 1\right)\]
↓
\[-\log \left(\left(\sqrt[3]{\frac{1}{x} - 1} \cdot \sqrt[3]{\frac{1}{x} - 1}\right) \cdot \sqrt[3]{\frac{1}{x} - 1}\right)\]
-\log \left(\frac{1}{x} - 1\right)
↓
-\log \left(\left(\sqrt[3]{\frac{1}{x} - 1} \cdot \sqrt[3]{\frac{1}{x} - 1}\right) \cdot \sqrt[3]{\frac{1}{x} - 1}\right)
double f(double x) {
        double r30534 = 1.0;
        double r30535 = x;
        double r30536 = r30534 / r30535;
        double r30537 = r30536 - r30534;
        double r30538 = log(r30537);
        double r30539 = -r30538;
        return r30539;
}
↓
double f(double x) {
        double r30540 = 1.0;
        double r30541 = x;
        double r30542 = r30540 / r30541;
        double r30543 = r30542 - r30540;
        double r30544 = cbrt(r30543);
        double r30545 = r30544 * r30544;
        double r30546 = r30545 * r30544;
        double r30547 = log(r30546);
        double r30548 = -r30547;
        return r30548;
}

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-cube-cbrt0.0

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

  4. Final simplification0.0

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

Reproduce

herbie shell --seed 2020045 
(FPCore (x)
  :name "neg log"
  :precision binary64
  (- (log (- (/ 1 x) 1))))