Average Error: 0.0 → 0.1
Time: 11.2s
Precision: 64
\[\frac{x + 1}{1 - x}\]
↓
\[\left(\log \left(e^{\sqrt[3]{\frac{x + 1}{1 - x}}}\right) \cdot \sqrt[3]{\frac{x + 1}{1 - x}}\right) \cdot \sqrt[3]{\frac{x + 1}{1 - x}}\]
\frac{x + 1}{1 - x}
↓
\left(\log \left(e^{\sqrt[3]{\frac{x + 1}{1 - x}}}\right) \cdot \sqrt[3]{\frac{x + 1}{1 - x}}\right) \cdot \sqrt[3]{\frac{x + 1}{1 - x}}
double f(double x) {
        double r45224 = x;
        double r45225 = 1.0;
        double r45226 = r45224 + r45225;
        double r45227 = r45225 - r45224;
        double r45228 = r45226 / r45227;
        return r45228;
}
↓
double f(double x) {
        double r45229 = x;
        double r45230 = 1.0;
        double r45231 = r45229 + r45230;
        double r45232 = r45230 - r45229;
        double r45233 = r45231 / r45232;
        double r45234 = cbrt(r45233);
        double r45235 = exp(r45234);
        double r45236 = log(r45235);
        double r45237 = r45236 * r45234;
        double r45238 = r45237 * r45234;
        return r45238;
}

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

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

  6. Final simplification0.1

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

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)))