Average Error: 0.0 → 0.1
Time: 11.2s
Precision: 64
\[\frac{x + 1}{1 - x}\]
↓
\[\left(\sqrt[3]{\frac{x + 1}{1 - x}} \cdot \sqrt[3]{\frac{x + 1}{1 - x}}\right) \cdot \left(\sqrt[3]{\frac{\sqrt[3]{x + 1} \cdot \sqrt[3]{x + 1}}{\sqrt[3]{1 - x} \cdot \sqrt[3]{1 - x}}} \cdot \sqrt[3]{\frac{\sqrt[3]{x + 1}}{\sqrt[3]{1 - x}}}\right)\]
\frac{x + 1}{1 - x}
↓
\left(\sqrt[3]{\frac{x + 1}{1 - x}} \cdot \sqrt[3]{\frac{x + 1}{1 - x}}\right) \cdot \left(\sqrt[3]{\frac{\sqrt[3]{x + 1} \cdot \sqrt[3]{x + 1}}{\sqrt[3]{1 - x} \cdot \sqrt[3]{1 - x}}} \cdot \sqrt[3]{\frac{\sqrt[3]{x + 1}}{\sqrt[3]{1 - x}}}\right)
double f(double x) {
        double r59196 = x;
        double r59197 = 1.0;
        double r59198 = r59196 + r59197;
        double r59199 = r59197 - r59196;
        double r59200 = r59198 / r59199;
        return r59200;
}
↓
double f(double x) {
        double r59201 = x;
        double r59202 = 1.0;
        double r59203 = r59201 + r59202;
        double r59204 = r59202 - r59201;
        double r59205 = r59203 / r59204;
        double r59206 = cbrt(r59205);
        double r59207 = r59206 * r59206;
        double r59208 = cbrt(r59203);
        double r59209 = r59208 * r59208;
        double r59210 = cbrt(r59204);
        double r59211 = r59210 * r59210;
        double r59212 = r59209 / r59211;
        double r59213 = cbrt(r59212);
        double r59214 = r59208 / r59210;
        double r59215 = cbrt(r59214);
        double r59216 = r59213 * r59215;
        double r59217 = r59207 * r59216;
        return r59217;
}

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-cube-cbrt0.2

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

  6. Applied add-cube-cbrt0.1

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

  7. Applied times-frac0.1

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

  8. Applied cbrt-prod0.1

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

  9. Final simplification0.1

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

Reproduce

herbie shell --seed 2019212 
(FPCore (x)
  :name "Prelude:atanh from fay-base-0.20.0.1"
  :precision binary64
  (/ (+ x 1) (- 1 x)))