Average Error: 32.0 → 0
Time: 853.0ms
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 r35205 = re;
        double r35206 = r35205 * r35205;
        double r35207 = im;
        double r35208 = r35207 * r35207;
        double r35209 = r35206 + r35208;
        double r35210 = sqrt(r35209);
        double r35211 = log(r35210);
        return r35211;
}
↓
double f(double re, double im) {
        double r35212 = re;
        double r35213 = im;
        double r35214 = hypot(r35212, r35213);
        double r35215 = log(r35214);
        return r35215;
}

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 2020056 +o rules:numerics
(FPCore (re im)
  :name "math.log/1 on complex, real part"
  :precision binary64
  (log (sqrt (+ (* re re) (* im im)))))