Average Error: 30.8 → 0
Time: 1.2s
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 r1135388 = re;
        double r1135389 = r1135388 * r1135388;
        double r1135390 = im;
        double r1135391 = r1135390 * r1135390;
        double r1135392 = r1135389 + r1135391;
        double r1135393 = sqrt(r1135392);
        double r1135394 = log(r1135393);
        return r1135394;
}
↓
double f(double re, double im) {
        double r1135395 = re;
        double r1135396 = im;
        double r1135397 = hypot(r1135395, r1135396);
        double r1135398 = log(r1135397);
        return r1135398;
}

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 30.8

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

  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 2019163 +o rules:numerics
(FPCore (re im)
  :name "math.log/1 on complex, real part"
  (log (sqrt (+ (* re re) (* im im)))))