Average Error: 0 → 0
Time: 886.0ms
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 r1700805 = im;
        double r1700806 = re;
        double r1700807 = atan2(r1700805, r1700806);
        return r1700807;
}
↓
double f(double re, double im) {
        double r1700808 = im;
        double r1700809 = re;
        double r1700810 = atan2(r1700808, r1700809);
        return r1700810;
}

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 2019172 +o rules:numerics
(FPCore (re im)
  :name "math.arg on complex"
  (atan2 im re))