Average Error: 0.0 → 0.0
Time: 7.2s
Precision: 64
\[\frac{x + 1.0}{1.0 - x}\]
↓
\[\sqrt[3]{\frac{1.0 + x}{1.0 - x} \cdot \left(\frac{1.0 + x}{1.0 - x} \cdot \frac{1.0 + x}{1.0 - x}\right)}\]
\frac{x + 1.0}{1.0 - x}
↓
\sqrt[3]{\frac{1.0 + x}{1.0 - x} \cdot \left(\frac{1.0 + x}{1.0 - x} \cdot \frac{1.0 + x}{1.0 - x}\right)}
double f(double x) {
        double r836963 = x;
        double r836964 = 1.0;
        double r836965 = r836963 + r836964;
        double r836966 = r836964 - r836963;
        double r836967 = r836965 / r836966;
        return r836967;
}
↓
double f(double x) {
        double r836968 = 1.0;
        double r836969 = x;
        double r836970 = r836968 + r836969;
        double r836971 = r836968 - r836969;
        double r836972 = r836970 / r836971;
        double r836973 = r836972 * r836972;
        double r836974 = r836972 * r836973;
        double r836975 = cbrt(r836974);
        return r836975;
}

Error

Bits error versus x

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Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0.0

    \[\frac{x + 1.0}{1.0 - x}\]
  2. Using strategy rm

  3. Applied add-cbrt-cube0.0

    \[\leadsto \color{blue}{\sqrt[3]{\left(\frac{x + 1.0}{1.0 - x} \cdot \frac{x + 1.0}{1.0 - x}\right) \cdot \frac{x + 1.0}{1.0 - x}}}\]

  4. Final simplification0.0

    \[\leadsto \sqrt[3]{\frac{1.0 + x}{1.0 - x} \cdot \left(\frac{1.0 + x}{1.0 - x} \cdot \frac{1.0 + x}{1.0 - x}\right)}\]

Reproduce

herbie shell --seed 2019156 
(FPCore (x)
  :name "Prelude:atanh from fay-base-0.20.0.1"
  (/ (+ x 1.0) (- 1.0 x)))