Average Error: 31.2 → 0
Time: 1.0s
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 r87041 = re;
        double r87042 = r87041 * r87041;
        double r87043 = im;
        double r87044 = r87043 * r87043;
        double r87045 = r87042 + r87044;
        double r87046 = sqrt(r87045);
        double r87047 = log(r87046);
        return r87047;
}
↓
double f(double re, double im) {
        double r87048 = re;
        double r87049 = im;
        double r87050 = hypot(r87048, r87049);
        double r87051 = log(r87050);
        return r87051;
}

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 31.2

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

  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 2019209 +o rules:numerics
(FPCore (re im)
  :name "math.log/1 on complex, real part"
  :precision binary64
  (log (sqrt (+ (* re re) (* im im)))))