Average Error: 32.2 → 0
Time: 980.0ms
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 r91639 = re;
        double r91640 = r91639 * r91639;
        double r91641 = im;
        double r91642 = r91641 * r91641;
        double r91643 = r91640 + r91642;
        double r91644 = sqrt(r91643);
        double r91645 = log(r91644);
        return r91645;
}
↓
double f(double re, double im) {
        double r91646 = re;
        double r91647 = im;
        double r91648 = hypot(r91646, r91647);
        double r91649 = log(r91648);
        return r91649;
}

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 32.2

    \[\log \left(\sqrt{re \cdot re + im \cdot im}\right)\]
  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 2020033 +o rules:numerics
(FPCore (re im)
  :name "math.log/1 on complex, real part"
  :precision binary64
  (log (sqrt (+ (* re re) (* im im)))))