Average Error: 31.5 → 0.0
Time: 3.5s
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 r24240 = re;
        double r24241 = r24240 * r24240;
        double r24242 = im;
        double r24243 = r24242 * r24242;
        double r24244 = r24241 + r24243;
        double r24245 = sqrt(r24244);
        double r24246 = log(r24245);
        return r24246;
}
↓
double f(double re, double im) {
        double r24247 = re;
        double r24248 = im;
        double r24249 = hypot(r24247, r24248);
        double r24250 = log(r24249);
        return r24250;
}

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. Simplified0.0

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

  3. Final simplification0.0

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

Reproduce

herbie shell --seed 2019326 +o rules:numerics
(FPCore (re im)
  :name "math.log/1 on complex, real part"
  :precision binary64
  (log (sqrt (+ (* re re) (* im im)))))