Average Error: 0 → 0
Time: 655.0ms
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 r30932 = im;
        double r30933 = re;
        double r30934 = atan2(r30932, r30933);
        return r30934;
}
↓
double f(double re, double im) {
        double r30935 = im;
        double r30936 = re;
        double r30937 = atan2(r30935, r30936);
        return r30937;
}

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 2019212 +o rules:numerics
(FPCore (re im)
  :name "math.log/1 on complex, imaginary part"
  :precision binary64
  (atan2 im re))