Average Error: 30.6 → 0
Time: 1.5s
Precision: 64
\[\log \left(\sqrt{re \cdot re + im \cdot im}\right)\]
↓
\[\log \left(\mathsf{hypot}\left(re, im\right)\right)\]
\log \left(\sqrt{re \cdot re + im \cdot im}\right)
↓
\log \left(\mathsf{hypot}\left(re, im\right)\right)
double f(double re, double im) {
        double r487995 = re;
        double r487996 = r487995 * r487995;
        double r487997 = im;
        double r487998 = r487997 * r487997;
        double r487999 = r487996 + r487998;
        double r488000 = sqrt(r487999);
        double r488001 = log(r488000);
        return r488001;
}
↓
double f(double re, double im) {
        double r488002 = re;
        double r488003 = im;
        double r488004 = hypot(r488002, r488003);
        double r488005 = log(r488004);
        return r488005;
}

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 30.6

    \[\log \left(\sqrt{re \cdot re + im \cdot im}\right)\]

  2. Simplified0

    \[\leadsto \color{blue}{\log \left(\mathsf{hypot}\left(re, im\right)\right)}\]

  3. Final simplification0

    \[\leadsto \log \left(\mathsf{hypot}\left(re, im\right)\right)\]

Reproduce

herbie shell --seed 2019139 +o rules:numerics
(FPCore (re im)
  :name "math.log/1 on complex, real part"
  (log (sqrt (+ (* re re) (* im im)))))