Average Error: 32.0 → 0
Time: 724.0ms
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 r30828 = re;
        double r30829 = r30828 * r30828;
        double r30830 = im;
        double r30831 = r30830 * r30830;
        double r30832 = r30829 + r30831;
        double r30833 = sqrt(r30832);
        double r30834 = log(r30833);
        return r30834;
}
↓
double f(double re, double im) {
        double r30835 = re;
        double r30836 = im;
        double r30837 = hypot(r30835, r30836);
        double r30838 = log(r30837);
        return r30838;
}

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 2020036 +o rules:numerics
(FPCore (re im)
  :name "math.log/1 on complex, real part"
  :precision binary64
  (log (sqrt (+ (* re re) (* im im)))))