Average Error: 0 → 0
Time: 851.0ms
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 r1612019 = im;
        double r1612020 = re;
        double r1612021 = atan2(r1612019, r1612020);
        return r1612021;
}
↓
double f(double re, double im) {
        double r1612022 = im;
        double r1612023 = re;
        double r1612024 = atan2(r1612022, r1612023);
        return r1612024;
}

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 2019158 +o rules:numerics
(FPCore (re im)
  :name "math.arg on complex"
  (atan2 im re))