Average Error: 0.0 → 0.0
Time: 5.5s
Precision: 64
\[\frac{x + 1}{1 - x}\]
↓
\[\frac{x + 1}{1 - x}\]
\frac{x + 1}{1 - x}
↓
\frac{x + 1}{1 - x}
double f(double x) {
        double r44639 = x;
        double r44640 = 1.0;
        double r44641 = r44639 + r44640;
        double r44642 = r44640 - r44639;
        double r44643 = r44641 / r44642;
        return r44643;
}
↓
double f(double x) {
        double r44644 = x;
        double r44645 = 1.0;
        double r44646 = r44644 + r44645;
        double r44647 = r44645 - r44644;
        double r44648 = r44646 / r44647;
        return r44648;
}

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 *-un-lft-identity0.0

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

  4. Applied *-un-lft-identity0.0

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

  5. Applied times-frac0.0

    \[\leadsto \color{blue}{\frac{1}{1} \cdot \frac{x + 1}{1 - x}}\]

  6. Simplified0.0

    \[\leadsto \color{blue}{1} \cdot \frac{x + 1}{1 - x}\]

  7. Final simplification0.0

    \[\leadsto \frac{x + 1}{1 - x}\]

Reproduce

herbie shell --seed 2019305 +o rules:numerics
(FPCore (x)
  :name "Prelude:atanh from fay-base-0.20.0.1"
  :precision binary64
  (/ (+ x 1) (- 1 x)))