Average Error: 31.7 → 0
Time: 693.0ms
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 r91234 = re;
        double r91235 = r91234 * r91234;
        double r91236 = im;
        double r91237 = r91236 * r91236;
        double r91238 = r91235 + r91237;
        double r91239 = sqrt(r91238);
        double r91240 = log(r91239);
        return r91240;
}
↓
double f(double re, double im) {
        double r91241 = re;
        double r91242 = im;
        double r91243 = hypot(r91241, r91242);
        double r91244 = log(r91243);
        return r91244;
}

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 31.7

    \[\log \left(\sqrt{re \cdot re + im \cdot im}\right)\]
  2. Using strategy rm

  3. Applied hypot-def0

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

  4. Final simplification0

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

Reproduce

herbie shell --seed 2019362 +o rules:numerics
(FPCore (re im)
  :name "math.log/1 on complex, real part"
  :precision binary64
  (log (sqrt (+ (* re re) (* im im)))))