Average Error: 0 → 0
Time: 427.0ms
Precision: 64
\[\tan^{-1}_* \frac{im}{re}\]
↓
\[\tan^{-1}_* \frac{im}{re}\]
\tan^{-1}_* \frac{im}{re}
↓
\tan^{-1}_* \frac{im}{re}
double f(double re, double im) {
        double r45906 = im;
        double r45907 = re;
        double r45908 = atan2(r45906, r45907);
        return r45908;
}
↓
double f(double re, double im) {
        double r45909 = im;
        double r45910 = re;
        double r45911 = atan2(r45909, r45910);
        return r45911;
}

Error

Bits error versus re

Bits error versus im

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 0

    \[\tan^{-1}_* \frac{im}{re}\]

  2. Final simplification0

    \[\leadsto \tan^{-1}_* \frac{im}{re}\]

Reproduce

herbie shell --seed 2020036 +o rules:numerics
(FPCore (re im)
  :name "math.arg on complex"
  :precision binary64
  (atan2 im re))