Average Error: 31.2 → 0
Time: 1.3s
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 r29776 = re;
        double r29777 = r29776 * r29776;
        double r29778 = im;
        double r29779 = r29778 * r29778;
        double r29780 = r29777 + r29779;
        double r29781 = sqrt(r29780);
        double r29782 = log(r29781);
        return r29782;
}
↓
double f(double re, double im) {
        double r29783 = re;
        double r29784 = im;
        double r29785 = hypot(r29783, r29784);
        double r29786 = log(r29785);
        return r29786;
}

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 31.2

    \[\log \left(\sqrt{re \cdot re + im \cdot im}\right)\]
  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 2020035 +o rules:numerics
(FPCore (re im)
  :name "math.log/1 on complex, real part"
  :precision binary64
  (log (sqrt (+ (* re re) (* im im)))))