Average Error: 31.2 → 0.0
Time: 880.0ms
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 r29547 = re;
        double r29548 = r29547 * r29547;
        double r29549 = im;
        double r29550 = r29549 * r29549;
        double r29551 = r29548 + r29550;
        double r29552 = sqrt(r29551);
        double r29553 = log(r29552);
        return r29553;
}
↓
double f(double re, double im) {
        double r29554 = re;
        double r29555 = im;
        double r29556 = hypot(r29554, r29555);
        double r29557 = log(r29556);
        return r29557;
}

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-def0.0

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

  4. Final simplification0.0

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

Reproduce

herbie shell --seed 2019346 +o rules:numerics
(FPCore (re im)
  :name "math.log/1 on complex, real part"
  :precision binary64
  (log (sqrt (+ (* re re) (* im im)))))