Average Error: 30.7 → 0.0
Time: 1.6s
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 r613042 = re;
        double r613043 = r613042 * r613042;
        double r613044 = im;
        double r613045 = r613044 * r613044;
        double r613046 = r613043 + r613045;
        double r613047 = sqrt(r613046);
        double r613048 = log(r613047);
        return r613048;
}
↓
double f(double re, double im) {
        double r613049 = re;
        double r613050 = im;
        double r613051 = hypot(r613049, r613050);
        double r613052 = log(r613051);
        return r613052;
}

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 30.7

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

  2. Simplified0.0

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

  3. Final simplification0.0

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

Reproduce

herbie shell --seed 2019121 +o rules:numerics
(FPCore (re im)
  :name "math.log/1 on complex, real part"
  (log (sqrt (+ (* re re) (* im im)))))