Average Error: 0.0 → 0.0
Time: 7.6s
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 r32118 = 1.0;
        double r32119 = x;
        double r32120 = r32118 / r32119;
        double r32121 = r32120 - r32118;
        double r32122 = log(r32121);
        double r32123 = -r32122;
        return r32123;
}
↓
double f(double x) {
        double r32124 = 1.0;
        double r32125 = x;
        double r32126 = r32124 / r32125;
        double r32127 = r32126 - r32124;
        double r32128 = cbrt(r32127);
        double r32129 = r32128 * r32128;
        double r32130 = r32129 * r32128;
        double r32131 = log(r32130);
        double r32132 = -r32131;
        return r32132;
}

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