Average Error: 31.5 → 0
Time: 3.2s
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 r25044 = re;
        double r25045 = r25044 * r25044;
        double r25046 = im;
        double r25047 = r25046 * r25046;
        double r25048 = r25045 + r25047;
        double r25049 = sqrt(r25048);
        double r25050 = log(r25049);
        return r25050;
}
↓
double f(double re, double im) {
        double r25051 = re;
        double r25052 = im;
        double r25053 = hypot(r25051, r25052);
        double r25054 = log(r25053);
        return r25054;
}

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 31.5

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

  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 2019325 +o rules:numerics
(FPCore (re im)
  :name "math.log/1 on complex, real part"
  :precision binary64
  (log (sqrt (+ (* re re) (* im im)))))