Average Error: 31.9 → 0
Time: 3.2s
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 r45017 = re;
        double r45018 = r45017 * r45017;
        double r45019 = im;
        double r45020 = r45019 * r45019;
        double r45021 = r45018 + r45020;
        double r45022 = sqrt(r45021);
        double r45023 = log(r45022);
        return r45023;
}
↓
double f(double re, double im) {
        double r45024 = re;
        double r45025 = im;
        double r45026 = hypot(r45024, r45025);
        double r45027 = log(r45026);
        return r45027;
}

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 31.9

    \[\log \left(\sqrt{re \cdot re + im \cdot im}\right)\]

  2. Simplified0

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

  3. Final simplification0

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

Reproduce

herbie shell --seed 2020043 +o rules:numerics
(FPCore (re im)
  :name "math.log/1 on complex, real part"
  :precision binary64
  (log (sqrt (+ (* re re) (* im im)))))