Average Error: 0.0 → 0.1
Time: 10.0s
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 r63345 = x;
        double r63346 = 1.0;
        double r63347 = r63345 + r63346;
        double r63348 = r63346 - r63345;
        double r63349 = r63347 / r63348;
        return r63349;
}
↓
double f(double x) {
        double r63350 = x;
        double r63351 = 1.0;
        double r63352 = r63350 + r63351;
        double r63353 = r63351 - r63350;
        double r63354 = r63352 / r63353;
        double r63355 = cbrt(r63354);
        double r63356 = r63355 * r63355;
        double r63357 = cbrt(r63352);
        double r63358 = r63357 * r63357;
        double r63359 = cbrt(r63353);
        double r63360 = r63359 * r63359;
        double r63361 = r63358 / r63360;
        double r63362 = cbrt(r63361);
        double r63363 = r63357 / r63359;
        double r63364 = cbrt(r63363);
        double r63365 = r63362 * r63364;
        double r63366 = r63356 * r63365;
        return r63366;
}

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