Average Error: 0.0 → 0.1
Time: 12.2s
Precision: 64
\[\frac{x + 1}{1 - x}\]
↓
\[\left(\sqrt[3]{\frac{x + 1}{1 - x}} \cdot \log \left(e^{\sqrt[3]{\frac{x + 1}{1 - x}}}\right)\right) \cdot \sqrt[3]{\frac{x + 1}{1 - x}}\]
\frac{x + 1}{1 - x}
↓
\left(\sqrt[3]{\frac{x + 1}{1 - x}} \cdot \log \left(e^{\sqrt[3]{\frac{x + 1}{1 - x}}}\right)\right) \cdot \sqrt[3]{\frac{x + 1}{1 - x}}
double f(double x) {
        double r46940 = x;
        double r46941 = 1.0;
        double r46942 = r46940 + r46941;
        double r46943 = r46941 - r46940;
        double r46944 = r46942 / r46943;
        return r46944;
}
↓
double f(double x) {
        double r46945 = x;
        double r46946 = 1.0;
        double r46947 = r46945 + r46946;
        double r46948 = r46946 - r46945;
        double r46949 = r46947 / r46948;
        double r46950 = cbrt(r46949);
        double r46951 = exp(r46950);
        double r46952 = log(r46951);
        double r46953 = r46950 * r46952;
        double r46954 = r46953 * r46950;
        return r46954;
}

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

    \[\frac{x + 1}{1 - x}\]
  2. Using strategy rm

  3. Applied add-cube-cbrt0.1

    \[\leadsto \color{blue}{\left(\sqrt[3]{\frac{x + 1}{1 - x}} \cdot \sqrt[3]{\frac{x + 1}{1 - x}}\right) \cdot \sqrt[3]{\frac{x + 1}{1 - x}}}\]
  4. Using strategy rm

  5. Applied add-log-exp0.1

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

  6. Final simplification0.1

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

Reproduce

herbie shell --seed 2020042 +o rules:numerics
(FPCore (x)
  :name "Prelude:atanh from fay-base-0.20.0.1"
  :precision binary64
  (/ (+ x 1) (- 1 x)))