Average Error: 0.0 → 0.0
Time: 5.1s
Precision: 64
\[\frac{x + 1}{1 - x}\]
↓
\[\frac{1 + x}{1 - x}\]
\frac{x + 1}{1 - x}
↓
\frac{1 + x}{1 - x}
double f(double x) {
        double r1219380 = x;
        double r1219381 = 1.0;
        double r1219382 = r1219380 + r1219381;
        double r1219383 = r1219381 - r1219380;
        double r1219384 = r1219382 / r1219383;
        return r1219384;
}
↓
double f(double x) {
        double r1219385 = 1.0;
        double r1219386 = x;
        double r1219387 = r1219385 + r1219386;
        double r1219388 = r1219385 - r1219386;
        double r1219389 = r1219387 / r1219388;
        return r1219389;
}

Error

Bits error versus x

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Results

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Derivation

  1. Initial program 0.0

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

  2. Final simplification0.0

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

Reproduce

herbie shell --seed 2019171 
(FPCore (x)
  :name "Prelude:atanh from fay-base-0.20.0.1"
  (/ (+ x 1.0) (- 1.0 x)))