Average Error: 32.0 → 0
Time: 837.0ms
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 r37305 = re;
        double r37306 = r37305 * r37305;
        double r37307 = im;
        double r37308 = r37307 * r37307;
        double r37309 = r37306 + r37308;
        double r37310 = sqrt(r37309);
        double r37311 = log(r37310);
        return r37311;
}
↓
double f(double re, double im) {
        double r37312 = re;
        double r37313 = im;
        double r37314 = hypot(r37312, r37313);
        double r37315 = log(r37314);
        return r37315;
}

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 32.0

    \[\log \left(\sqrt{re \cdot re + im \cdot im}\right)\]
  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 2020083 +o rules:numerics
(FPCore (re im)
  :name "math.log/1 on complex, real part"
  :precision binary64
  (log (sqrt (+ (* re re) (* im im)))))